├── .gitignore ├── .vscode ├── ltex.dictionary.en-US.txt └── settings.json ├── LICENSE ├── README.md ├── ap_first_semester ├── advanced_astrophysics.pdf ├── advanced_astrophysics │ ├── 01oct.tex │ ├── 02dec.tex │ ├── 03dec.tex │ ├── 04nov.tex │ ├── 06nov.tex │ ├── 07oct.tex │ ├── 08oct.tex │ ├── 09dec.tex │ ├── 10dec.tex │ ├── 11nov.tex │ ├── 12nov.tex │ ├── 14oct.tex │ ├── 15oct.tex │ ├── 16dec.tex │ ├── 17dec.tex │ ├── 18nov.tex │ ├── 19nov.tex │ ├── 21oct.tex │ ├── 22oct.tex │ ├── 25nov.tex │ ├── 26nov.tex │ ├── 28oct.tex │ ├── 29oct.tex │ ├── 30sep.tex │ ├── figures │ │ ├── RR_Lyr_frequency_differences.pdf │ │ ├── atmosphere_critical_radius.pdf │ │ ├── burning_stages.py │ │ ├── critical_radius_position.pdf │ │ ├── estimates.py │ │ ├── flux_1_MeV.png │ │ ├── gamma_nu_luminosities.pdf │ │ ├── line_acceleration_profile.pdf │ │ ├── line_acceleration_profile.py │ │ ├── velocity_density_isothermal.pdf │ │ └── velocity_profile.py │ ├── main.pdf │ └── main.tex ├── astrophysics_cosmology │ ├── 03oct.tex │ ├── 04oct.tex │ ├── 05dec.tex │ ├── 06dec.tex │ ├── 07nov.tex │ ├── 08jan.tex │ ├── 08nov.tex │ ├── 09jan.tex │ ├── 10oct.tex │ ├── 11oct.tex │ ├── 12dec.tex │ ├── 13dec.tex │ ├── 14nov-1.cpt │ ├── 14nov-2.cpt │ ├── 14nov.tex │ ├── 15nov.tex │ ├── 17oct.tex │ ├── 18oct.tex │ ├── 19dec.tex │ ├── 20dec.tex │ ├── 21nov.tex │ ├── 22nov.tex │ ├── 25oct.tex │ ├── 28nov.tex │ ├── 29nov.tex │ ├── 31oct-1.cpt │ ├── 31oct.tex │ ├── cosmo.bib │ ├── figures │ │ ├── Dark_matter.pdf │ │ ├── Schechter.pdf │ │ ├── __pycache__ │ │ │ ├── basic_units.cpython-37.pyc │ │ │ └── basic_units.cpython-38.pyc │ │ ├── basic_units.py │ │ ├── beta_core_pressure.py │ │ ├── beta_star_core_pressure.pdf │ │ ├── beta_star_core_pressure.png │ │ ├── chandrasekhar.py │ │ ├── chandrasekhar_limit.pdf │ │ ├── cosine_positive_curvature.py │ │ ├── current_time_curved_model.py │ │ ├── curved_universe_age.pdf │ │ ├── dark_matter.py │ │ ├── degenerate_relativistic.ipynb │ │ ├── global_energy_contributions.pdf │ │ ├── global_energy_contributions.py │ │ ├── hubble_original.png │ │ ├── hyperbolic.py │ │ ├── ionization.pdf │ │ ├── ionization_nophotons.pdf │ │ ├── positive_curvature_a.pdf │ │ ├── positive_curvature_a_vs_t.pdf │ │ ├── recombination.ipynb │ │ ├── relativisticity_degeneracy.pdf │ │ └── sin_vs_sinh.pdf │ ├── format.fmt │ ├── header.tex │ ├── main-1.cpt │ ├── main-2.cpt │ ├── main-3.cpt │ ├── main-4.cpt │ ├── main-5.cpt │ ├── main-6.cpt │ ├── main.pdf │ └── main.tex ├── astrophysics_cosmology_with_notes.pdf ├── astrophysics_lab.pdf ├── astrophysics_lab │ ├── 01oct.tex │ ├── 02oct.tex │ ├── 03dec.tex │ ├── 04dec.tex │ ├── 05nov.tex │ ├── 06nov.tex │ ├── 08oct.tex │ ├── 09oct.tex │ ├── 10dec.tex │ ├── 11dec.tex │ ├── 12nov.tex │ ├── 13nov.tex │ ├── 15oct.tex │ ├── 16oct.tex │ ├── 17dec.tex │ ├── 18dec.tex │ ├── 19nov.tex │ ├── 22oct.tex │ ├── 23oct.tex │ ├── 26nov.tex │ ├── 27nov.tex │ ├── 29oct.tex │ ├── 30oct.tex │ ├── 30sep.tex │ ├── main.pdf │ └── main.tex ├── file_creator.py ├── general_relativity.pdf ├── general_relativity │ ├── 03oct.tex │ ├── 04oct.tex │ ├── 05dec.tex │ ├── 06dec.tex │ ├── 07nov.tex │ ├── 08nov.tex │ ├── 09jan.tex │ ├── 10jan.tex │ ├── 10oct.tex │ ├── 11oct.tex │ ├── 12dec.tex │ ├── 13dec.tex │ ├── 14nov.tex │ ├── 15nov.tex │ ├── 17oct.tex │ ├── 18oct.tex │ ├── 19dec.tex │ ├── 20dec.tex │ ├── 21nov.tex │ ├── 22nov.tex │ ├── 24oct.tex │ ├── 25oct.tex │ ├── 28nov.tex │ ├── 29nov.tex │ ├── figures │ │ ├── fixed_L_orbits.pdf │ │ ├── kruskal.py │ │ ├── kruskal_constant_V.pdf │ │ └── rindlerU2-V2.pdf │ ├── main.pdf │ └── main.tex ├── gr_exercises.pdf ├── gr_exercises │ ├── figures │ │ ├── Visualization of accelerational time dilation.ggb │ │ ├── Visualization_of_accelerational_time_dilation-eps-converted-to.pdf │ │ ├── Visualization_of_accelerational_time_dilation.eps │ │ ├── allowed_velocities.pdf │ │ ├── critical_psi.pdf │ │ ├── gauss.pdf │ │ ├── limiting_angle_a_0_6838.pdf │ │ ├── limiting_angle_a_0_9000.pdf │ │ ├── limiting_angle_a_0_9684.pdf │ │ ├── limiting_angle_a_0_9900.pdf │ │ ├── limiting_angle_a_0_9968.pdf │ │ ├── photon_effective_potential.pdf │ │ ├── potential_barrier.pdf │ │ ├── refined_limiting_angle_a_0_6838.pdf │ │ ├── refined_limiting_angle_a_0_9000.pdf │ │ ├── refined_limiting_angle_a_0_9684.pdf │ │ ├── refined_limiting_angle_a_0_9900.pdf │ │ ├── refined_limiting_angle_a_0_9968.pdf │ │ └── velocity.pdf │ ├── main.pdf │ ├── main.tex │ ├── python │ │ ├── .ipynb_checkpoints │ │ │ ├── GR_homeworks-checkpoint.ipynb │ │ │ └── sheet_10-checkpoint.ipynb │ │ ├── GR_homeworks.ipynb │ │ ├── GR_homeworks.py │ │ ├── allowed_angular_velocities_Kerr.py │ │ ├── sheet2.py │ │ ├── sheet7_1.py │ │ ├── sheet7_2.py │ │ ├── sheet7_3.py │ │ ├── sheet9_1.py │ │ └── sheet_10.ipynb │ ├── sheet1.tex │ ├── sheet10.tex │ ├── sheet11.tex │ ├── sheet12.tex │ ├── sheet2.tex │ ├── sheet3.tex │ ├── sheet4.tex │ ├── sheet5.tex │ ├── sheet6.tex │ ├── sheet7.tex │ ├── sheet8.tex │ └── sheet9.tex ├── header.tex ├── numerical_methods.pdf ├── numerical_methods │ ├── 05dec.tex │ ├── 06dec.tex │ ├── 07nov.tex │ ├── 08nov.tex │ ├── 12dec.tex │ ├── 13dec.tex │ ├── 14nov.tex │ ├── 15nov.tex │ ├── 19dec.tex │ ├── 20dec.tex │ ├── 21nov.tex │ ├── 22nov.tex │ ├── 28nov.tex │ ├── 29nov.tex │ ├── main.pdf │ └── main.tex └── subeq_align.py ├── ap_second_semester ├── astroparticle_physics.pdf ├── astroparticle_physics │ ├── apr01.tex │ ├── apr07.tex │ ├── apr08.tex │ ├── apr15.tex │ ├── apr21.tex │ ├── apr22.tex │ ├── apr28.tex │ ├── apr29.tex │ ├── astroparticle_physics.bib │ ├── jun03.tex │ ├── main.tex │ ├── mar10.tex │ ├── mar11.tex │ ├── mar17.tex │ ├── mar18.tex │ ├── mar24.tex │ ├── mar25.tex │ ├── mar31.tex │ ├── may05.tex │ ├── may06.tex │ ├── may12.tex │ ├── may13.tex │ ├── may19.tex │ ├── may20.tex │ ├── may26.tex │ └── may27.tex ├── file_creator.py ├── gravitational_physics.pdf ├── gravitational_physics │ ├── apr03.tex │ ├── apr06.tex │ ├── apr10.tex │ ├── apr17.tex │ ├── apr20.tex │ ├── apr24.tex │ ├── apr27.tex │ ├── figures │ │ ├── .ipynb_checkpoints │ │ │ └── Binary GW angular spectrum-checkpoint.ipynb │ │ ├── Binary GW angular spectrum.ipynb │ │ ├── amplitude_estimation.py │ │ ├── binary_angular_GW_spectrum.py │ │ ├── binary_averaged_angular_spectrum.pdf │ │ └── binary_averaged_angular_spectrum_no_sin.pdf │ ├── gravitational_physics.bib │ ├── jun01.tex │ ├── jun05.tex │ ├── main.tex │ ├── mar09.tex │ ├── mar13.tex │ ├── mar16.tex │ ├── mar20.tex │ ├── mar23.tex │ ├── mar27.tex │ ├── mar30.tex │ ├── may01.tex │ ├── may04.tex │ ├── may08.tex │ ├── may11.tex │ ├── may15.tex │ ├── may18.tex │ ├── may22.tex │ └── may29.tex ├── gravitational_wave_astrophysics.pdf ├── gravitational_wave_astrophysics │ ├── apr01.tex │ ├── apr03.tex │ ├── figures │ │ └── Eddington_alpha_dependence.pdf │ ├── gravitational_wave_astrophysics.bib │ ├── main.tex │ ├── mar23.tex │ ├── mar24.tex │ ├── mar25.tex │ ├── mar27.tex │ ├── mar30.tex │ └── mar31.tex ├── header.tex ├── multimessenger_astrophysics.pdf ├── path_integral.pdf ├── path_integral │ ├── applications.tex │ ├── intro.tex │ ├── main.tex │ ├── path_integral.tex │ └── statistical_methods.tex ├── radiative_processes.pdf ├── radiative_processes │ ├── apr01.tex │ ├── apr02.tex │ ├── apr08.tex │ ├── apr09.tex │ ├── apr15.tex │ ├── apr16.tex │ ├── apr22.tex │ ├── apr23.tex │ ├── apr29.tex │ ├── apr30.tex │ ├── figures │ │ ├── compton-sigma.pdf │ │ └── compton-sigma.png │ ├── jun03.tex │ ├── jun04.tex │ ├── main.tex │ ├── mar11.tex │ ├── mar12.tex │ ├── mar18.tex │ ├── mar19.tex │ ├── mar25.tex │ ├── mar26.tex │ ├── may06.tex │ ├── may07.tex │ ├── may13.tex │ ├── may14.tex │ ├── may20.tex │ ├── may21.tex │ ├── may27.tex │ ├── may28.tex │ └── radiative_processes.bib ├── subeq_align.py ├── theoretical_cosmology.pdf ├── theoretical_cosmology │ ├── apr02.tex │ ├── apr03.tex │ ├── apr09.tex │ ├── apr10.tex │ ├── apr16.tex │ ├── apr17.tex │ ├── apr23.tex │ ├── apr24.tex │ ├── apr30.tex │ ├── jun04.tex │ ├── main.tex │ ├── mar12.tex │ ├── mar13.tex │ ├── mar19.tex │ ├── mar20.tex │ ├── mar26.tex │ ├── mar27.tex │ ├── may07.tex │ ├── may08.tex │ ├── may14.tex │ ├── may15.tex │ ├── may20-extra.tex │ ├── may21.tex │ ├── may22.tex │ ├── may28.tex │ ├── may29.tex │ └── theoretical_cosmology.bib ├── theoretical_physics.pdf └── theoretical_physics │ ├── apr06.tex │ ├── apr07.tex │ ├── apr20.tex │ ├── apr21.tex │ ├── apr27.tex │ ├── apr28.tex │ ├── exercises7.tex │ ├── figures │ ├── angular_distribution.pdf │ ├── angular_distribution.png │ ├── angular_distribution.py │ ├── primed_momentum_potential.pdf │ └── primed_momentum_potential.py │ ├── main.tex │ ├── mar09.tex │ ├── mar10.tex │ ├── mar16.tex │ ├── mar17.tex │ ├── mar23.tex │ ├── mar24.tex │ ├── mar30.tex │ ├── mar31.tex │ ├── may04.tex │ ├── may05.tex │ ├── may11.tex │ ├── may12.tex │ ├── sheet11b.tex │ ├── sheet14.tex │ ├── sheet15.tex │ ├── sheet16.tex │ ├── sheet17.tex │ └── theoretical_physics.bib ├── ap_third_semester ├── astrostat_homework.pdf ├── astrostat_homework │ ├── .ipynb_checkpoints │ │ ├── exercises_123-checkpoint.ipynb │ │ └── sheet_1-checkpoint.ipynb │ ├── __pycache__ │ │ ├── MCMC.cpython-37.pyc │ │ ├── MCMC.cpython-38.pyc │ │ ├── MVN.cpython-37.pyc │ │ ├── MVN.cpython-38.pyc │ │ └── multiple_chains.cpython-38.pyc │ ├── amplitude_marginalization.ipynb │ ├── circular_marginalization.ipynb │ ├── exercise_10.ipynb │ ├── exercise_10.tex │ ├── exercise_7 │ │ ├── .ipynb_checkpoints │ │ │ └── exercise_7-checkpoint.ipynb │ │ ├── MCMC.py │ │ ├── MVN.py │ │ ├── exercise_7.ipynb │ │ ├── mh_minimal.ipynb │ │ └── multiple_chains.py │ ├── exercises_123.ipynb │ ├── exercises_456.tex │ ├── exercises_89.tex │ ├── figures │ │ ├── chisquare_omega.pdf │ │ ├── large_pulsation.pdf │ │ ├── large_pulsation.py │ │ ├── marginalization.pdf │ │ └── signal.pdf │ └── main.tex ├── astrostatistics_cosmology.pdf ├── astrostatistics_cosmology │ ├── AstroStatistics_and_Cosmology.bib │ ├── dec01.tex │ ├── dec14.tex │ ├── dec15.tex │ ├── dec21.tex │ ├── dec22.tex │ ├── figures │ │ └── markov.ipynb │ ├── main.tex │ ├── nov02.tex │ ├── nov03.tex │ ├── nov09.tex │ ├── nov10.tex │ ├── nov16.tex │ ├── nov17.tex │ ├── nov23.tex │ ├── nov24.tex │ ├── nov30.tex │ ├── oct05.tex │ ├── oct06.tex │ ├── oct12.tex │ ├── oct13.tex │ ├── oct19.tex │ ├── oct20.tex │ ├── oct26.tex │ ├── oct27.tex │ ├── sep28.tex │ └── sep29.tex ├── compact_objects.pdf ├── compact_objects │ ├── Compact_Objects.bib │ ├── calculations │ │ ├── beginners.cnb │ │ ├── metrics.ipynb │ │ ├── quick_calculations.py │ │ ├── roche.cnb │ │ ├── roche.cnb~ │ │ ├── schwarzschild.cnb │ │ ├── schwarzschild.cnb~ │ │ ├── test.tex │ │ └── transsonic.ipynb │ ├── dec01.tex │ ├── dec02.tex │ ├── dec09.tex │ ├── dec15.tex │ ├── dec16.tex │ ├── dec22.tex │ ├── dec23.tex │ ├── figures │ │ ├── NS-interior.png │ │ ├── NS-temperature.pdf │ │ ├── NS-temperature.py │ │ ├── Rcirc_vs_R1.py │ │ ├── alfven-accretion.png │ │ ├── dipole-field.png │ │ ├── neutron-proton-ratio-density.pdf │ │ ├── neutron-proton-ratio.pdf │ │ ├── neutron-proton-ratio.py │ │ ├── p-pdot-diagram.png │ │ ├── relativisticity_degeneracy.pdf │ │ ├── roche-equipotential.png │ │ ├── roche-lobe-radius.pdf │ │ ├── roche-lobe-radius.py │ │ ├── roche-lobe-relative-corrections.pdf │ │ ├── roche-vs-circularization.pdf │ │ ├── roche.ipynb │ │ ├── schwarzschild_orbit_inversions.pdf │ │ ├── schwarzschild_orbits.ipynb │ │ ├── timescales.png │ │ ├── turbulent-eddies-accretion.png │ │ ├── urca-murca.pdf │ │ └── urca-murca.py │ ├── main.tex │ ├── nov03.tex │ ├── nov04.tex │ ├── nov10.tex │ ├── nov11.tex │ ├── nov17.tex │ ├── nov18.tex │ ├── nov24.tex │ ├── nov25.tex │ ├── oct06.tex │ ├── oct07.tex │ ├── oct13.tex │ ├── oct14.tex │ ├── oct20.tex │ ├── oct21.tex │ ├── oct27.tex │ ├── oct28.tex │ ├── sep29.tex │ └── sep30.tex ├── early_universe.pdf ├── early_universe │ ├── Early_Universe.bib │ ├── dec02.tex │ ├── dec09.tex │ ├── dec14.tex │ ├── dec16.tex │ ├── dec21.tex │ ├── dec22.tex │ ├── dec23.tex │ ├── figures │ │ ├── finite_temperature_SSB.ipynb │ │ └── hybrid_dual_field.ipynb │ ├── jan11.tex │ ├── jan13.tex │ ├── main.tex │ ├── nov02.tex │ ├── nov04.tex │ ├── nov09.tex │ ├── nov11.tex │ ├── nov16.tex │ ├── nov18.tex │ ├── nov23.tex │ ├── nov25.tex │ ├── nov30.tex │ ├── oct05.tex │ ├── oct07.tex │ ├── oct12.tex │ ├── oct14.tex │ ├── oct19.tex │ ├── oct21.tex │ ├── oct26.tex │ ├── oct28.tex │ ├── sep28.tex │ └── sep30.tex ├── file_creator.py ├── header.tex └── subeq_align.py ├── astronomy ├── Interdisciplinary_Astronomy.bib ├── apr07.tex ├── apr08.tex ├── apr09.tex ├── apr15.tex ├── apr16.tex ├── header.tex ├── main.pdf ├── main.tex ├── may05.tex ├── may06.tex ├── may12.tex ├── project.pdf └── project │ ├── content.tex │ ├── data │ ├── farnese.csv │ └── farnese.ipynb │ ├── figures │ ├── Ursa.pdf │ ├── aries_on_colure_184_BC.png │ ├── ecliptic_grid_athens_now.png │ ├── equatorial_grid_125BC_athens.png │ ├── ursa_maior_today.png │ └── ursa_names.png │ ├── main.tex │ └── ursa │ └── ursa.ipynb ├── circledsteps.sty ├── info_Q ├── header.tex ├── montangero │ ├── 12-6-19.tex │ ├── main.pdf │ ├── main_montangero.tex │ ├── montangero1.tex │ └── montangero2.tex └── zanardi │ ├── main.pdf │ ├── main_zanardi.tex │ ├── zanardi1.tex │ ├── zanardi2.tex │ ├── zanardi3.tex │ └── zanardi4.tex ├── phd_courses ├── High Energy Astrophysics.bib ├── experimental_gravitation_cosmology.pdf ├── experimental_gravitation_cosmology │ ├── GW.bib │ ├── dec03.tex │ ├── dec06.tex │ ├── dec20.tex │ ├── dec21.tex │ ├── dec22.tex │ ├── feb02.tex │ ├── feb03.tex │ ├── figures │ │ ├── __pycache__ │ │ │ └── make_all_figures.cpython-38.pyc │ │ ├── husini.pdf │ │ ├── make_all_figures.py │ │ ├── polarization.pdf │ │ ├── polarization.py │ │ └── squeezing.py │ ├── jan10.tex │ ├── jan11.tex │ ├── jan13.tex │ ├── jan14.tex │ ├── jan17.tex │ ├── jan21.tex │ ├── jan25.tex │ ├── main.tex │ ├── nov17.tex │ ├── nov22.tex │ └── nov23.tex ├── experimental_high_energy_astroparticle.pdf ├── experimental_high_energy_astroparticle │ ├── dec02.tex │ ├── dec16.tex │ ├── dec20.tex │ ├── dec21.tex │ ├── figures │ │ ├── angular_distribution_shift.pdf │ │ ├── angular_distribution_shift.py │ │ ├── bethe_bloch.py │ │ ├── cosmic_ray_diffusion.pdf │ │ ├── cosmic_rays_energies.pdf │ │ ├── cosmic_rays_energies.py │ │ ├── make_all_figures.py │ │ ├── rapidity.pdf │ │ └── rapidity.py │ ├── jan13.tex │ ├── jan17.tex │ ├── jan18.tex │ ├── jan19.tex │ ├── jan20.tex │ ├── jan21.tex │ ├── main.tex │ ├── nov08.tex │ ├── nov09.tex │ ├── nov11.tex │ ├── nov16.tex │ ├── nov18.tex │ └── nov23.tex ├── experimental_low_energy_astroparticle.pdf ├── experimental_low_energy_astroparticle │ ├── Dark Matter.bib │ ├── calculations │ │ └── neutron_dipole.py │ ├── dec01.tex │ ├── dec01a.tex │ ├── dec07.tex │ ├── dec09.tex │ ├── dec13.tex │ ├── dec15.tex │ ├── figures │ │ ├── __pycache__ │ │ │ └── make_all_figures.cpython-38.pyc │ │ ├── juno_flux.pdf │ │ ├── low_background_statistics.py │ │ ├── make_all_figures.py │ │ ├── oscillations.pdf │ │ ├── oscillations.py │ │ └── poisson.pdf │ ├── main.tex │ ├── nov09.tex │ ├── nov11.tex │ ├── nov15.tex │ ├── nov16.tex │ ├── nov18.tex │ ├── nov19.tex │ ├── nov25.tex │ ├── nov29.tex │ └── nov30.tex ├── file_creator.py ├── general_relativity_exercises │ ├── BH.bib │ ├── figures │ │ ├── __pycache__ │ │ │ └── make_all_figures.cpython-39.pyc │ │ ├── conformal_rindler.py │ │ ├── conformal_trajectory.pdf │ │ ├── ef_geodesics.py │ │ ├── ef_infall.pdf │ │ ├── effective_potential.pdf │ │ ├── kerr_infall.pdf │ │ ├── kerr_infall.py │ │ ├── kerr_killing.pdf │ │ ├── kerr_killing.py │ │ ├── kerr_trajectory.pdf │ │ ├── killing_kruskal.pdf │ │ ├── kruskal.py │ │ ├── make_all_figures.py │ │ ├── negative_mass_geodesics.pdf │ │ ├── negative_mass_geodesics.py │ │ ├── photon_orbits.py │ │ ├── potential_barrier.pdf │ │ ├── rho_radius.py │ │ └── spacetime_ef.pdf │ ├── main.tex │ ├── sheet1.tex │ └── sheet2.tex ├── gravitational_waves.pdf ├── gravitational_waves │ ├── GW.bib │ ├── apr12.tex │ ├── apr19.tex │ ├── apr26.tex │ ├── figures │ │ └── Screenshot from 2021-06-29 14-16-02.png │ ├── jul01.tex │ ├── jul05.tex │ ├── jul12.tex │ ├── jul14.tex │ ├── jul26.tex │ ├── jun07.tex │ ├── jun14.tex │ ├── jun21.tex │ ├── jun28.tex │ ├── main.tex │ ├── may03.tex │ ├── may10.tex │ ├── may17.tex │ ├── may24.tex │ └── may31.tex ├── gravitational_waves_exercises.pdf ├── gravitational_waves_exercises │ ├── cadabra │ │ ├── output_proj.tex │ │ ├── proj.cnb │ │ ├── proj.cnb~ │ │ ├── projector_properties.cnb │ │ ├── projector_properties.cnb~ │ │ ├── projector_properties.tex │ │ ├── schwarzschild.cnb │ │ ├── schwarzschild.cnb~ │ │ ├── schwarzschild.html │ │ └── schwarzschild.tex │ ├── calculations │ │ ├── amplitude_estimation.py │ │ └── tidal_deformation.py │ ├── main.tex │ ├── sheet1.tex │ ├── sheet2.tex │ ├── sheet3.tex │ ├── tutorial1.tex │ ├── tutorial2.tex │ ├── tutorial3.tex │ └── tutorial4.tex ├── header.tex ├── numerical_relativity.pdf ├── numerical_relativity │ ├── apr13.tex │ ├── apr20.tex │ ├── apr27.tex │ ├── jul06.tex │ ├── jul13.tex │ ├── jul27.tex │ ├── jun01.tex │ ├── jun08.tex │ ├── jun15.tex │ ├── jun22.tex │ ├── jun29.tex │ ├── main.tex │ ├── may04.tex │ ├── may11.tex │ ├── may18.tex │ └── may25.tex ├── numerical_relativity_exercises │ ├── main.tex │ ├── sheet1.tex │ ├── tutorial2.tex │ ├── tutorial3.tex │ └── tutorial4.tex ├── subeq_align.py ├── theoretical_gravitation_cosmology.pdf ├── theoretical_gravitation_cosmology │ ├── dec01.tex │ ├── dec17.tex │ ├── exercises.tex │ ├── exercises │ │ └── einstein_carousel.cdb │ ├── feb01.tex │ ├── feb02.tex │ ├── figures │ │ ├── __pycache__ │ │ │ └── make_all_figures.cpython-39.pyc │ │ ├── hubble_rate.pdf │ │ ├── make_all_figures.py │ │ ├── universe_composition.pdf │ │ └── universe_composition.py │ ├── jan24.tex │ ├── jan25.tex │ ├── jan26.tex │ ├── jan27.tex │ ├── jan28.tex │ ├── jan31.tex │ ├── main.tex │ ├── nov10.tex │ ├── nov15.tex │ ├── nov17.tex │ ├── nov22.tex │ ├── nov24.tex │ └── nov29.tex ├── theoretical_high_energy_astroparticle.pdf ├── theoretical_high_energy_astroparticle │ ├── dec14.tex │ ├── dec22.tex │ ├── exercise.tex │ ├── figures │ │ ├── __pycache__ │ │ │ ├── make_all_figures.cpython-37.pyc │ │ │ └── make_all_figures.cpython-39.pyc │ │ ├── cosmic_ray_diffusion.py │ │ ├── cosmic_ray_reacceleration_far.pdf │ │ ├── cosmic_ray_reacceleration_near.pdf │ │ ├── diffusion_over_time.pdf │ │ ├── diffusion_over_time_nice.pdf │ │ ├── final_point_variation.pdf │ │ ├── make_all_figures.py │ │ ├── shock_acceleration_distribution.pdf │ │ ├── shock_acceleration_distribution.py │ │ ├── show_high_alpha_spectrum.pdf │ │ ├── show_low_alpha_spectrum.pdf │ │ └── show_two_alpha_spectrums.pdf │ ├── jan10.tex │ ├── jan11.tex │ ├── jan14.tex │ ├── jan18.tex │ ├── jan19.tex │ ├── jan20.tex │ ├── jan24.tex │ ├── main.dvi │ ├── main.tex │ ├── nov08.tex │ ├── nov10.tex │ ├── nov18.tex │ ├── nov24.tex │ ├── nov25.tex │ └── nov30.tex ├── theoretical_low_energy_astroparticle.pdf └── theoretical_low_energy_astroparticle │ ├── dec06.tex │ ├── dec07.tex │ ├── dec09.tex │ ├── dec10.tex │ ├── dec13.tex │ ├── dec14.tex │ ├── dec15.tex │ ├── dec16.tex │ ├── feb01.tex │ ├── feb02.tex │ ├── feb03.tex │ ├── figures │ ├── __pycache__ │ │ └── make_all_figures.cpython-39.pyc │ ├── make_all_figures.py │ ├── mass_plot_io.pdf │ ├── mass_plot_no.pdf │ └── neutrino_mass_plots.py │ ├── jan25.tex │ ├── jan26.tex │ ├── jan27.tex │ ├── jan28.tex │ ├── jan31.tex │ └── main.tex ├── quantum_optics ├── 08jan.tex ├── 10jan.tex ├── 13jan.tex ├── 17jan.tex ├── apr03.tex ├── apr10.tex ├── figures │ └── statistics_comparison.py ├── header.tex ├── main.pdf ├── main.tex ├── mar16.tex ├── mar20.tex ├── mar27.tex ├── may12.tex └── quantum_optics.bib └── quick_files ├── coulomb ├── Coulomb-term-correction.tex ├── figures │ ├── odd_A_fit.pdf │ └── odd_A_residuals.pdf └── quadrupole_fission.tex ├── header.tex ├── latex_testing ├── main.pdf └── main.tex ├── old_header.tex ├── qft ├── breit-wigner.png ├── delta_meson.png ├── eta.png └── subnuclear_question.tex ├── scout ├── azimuth.pdf ├── azimuth.tex └── figures │ ├── 128027241-compass-face-with-wind-rose-and-dial.jpg │ └── CompassRoseSimple.png ├── seminars ├── SIGRAV_GW_sources.tex ├── SIGRAV_compact_object.tex ├── asteroid_bombardment.tex ├── gravitational_waves.tex ├── ice_cube.tex ├── main.pdf ├── main.tex ├── results_from_alpha_spectrometer.tex └── svelare_l_universo.tex ├── summer_STEM ├── 800px-Electromagnetic_waves.png ├── Electromagnetic-Spectrum.png ├── STEM_Indivisibility.bib ├── Speed_of_light_calculation_using_Foucault's_rotating_mirror.png ├── Speed_of_light_calculation_using_Foucault's_rotating_mirror.xcf ├── alumni-logo.png ├── alumni-logored.png ├── alumni-logowhite.png ├── alumnistem.sty ├── indivisibility.pdf ├── indivisibility.tex ├── introduzione.tex ├── main.pdf ├── morgagni.png ├── solutions.tex ├── spdc.tex ├── stem-logo.png └── wave.ipynb └── throwaway ├── main.tex ├── mar22.tex └── test.tex /.vscode/ltex.dictionary.en-US.txt: -------------------------------------------------------------------------------- 1 | hypersurfaces 2 | helixes 3 | collisionless 4 | inhomogeneities 5 | Multimessenger 6 | -------------------------------------------------------------------------------- /.vscode/settings.json: -------------------------------------------------------------------------------- 1 | { 2 | "files.exclude": { 3 | "**/*fls": true, 4 | "**/*fdb_latexmk": true, 5 | "**/*pdf": true, 6 | "**/*log": true, 7 | "**/*out": true, 8 | "**/*aux": true, 9 | "**/*synctex*": true, 10 | "**/*main.pdf": false 11 | }, 12 | "python.linting.enabled": false, 13 | "python.pythonPath": "/usr/bin/python3", 14 | "cSpell.enableFiletypes": [ 15 | "!python", 16 | "latex" 17 | ], 18 | "ltex.ignoreRuleInSentence": [ 19 | { 20 | "rule": "KIND_OF_A", 21 | "sentence": "^\\QThe type of a tensor in this space is then said to be \\EDummy[0-9]+\\Q, and its rank is \\EDummy[0-9]+\\Q.\\E$" 22 | }, 23 | { 24 | "rule": "MASS_AGREEMENT", 25 | "sentence": "^\\QThis better be so: otherwise we would have proven that the first derivatives of the metric are zero in a neighborhood of a generic point \\EDummy[0-9]+\\Q, so the metric is constant in the whole neighborhood, which is nonphysical.\\E$" 26 | } 27 | ], 28 | "ltex.workspaceFolderDictionary": { 29 | "en-US": [ 30 | "anisotropies", 31 | "attractor", 32 | "ergodicity", 33 | "FLRW", 34 | "Frequentist", 35 | "frequentist", 36 | "functionals", 37 | "inhomogeneities", 38 | "prefactor" 39 | ] 40 | }, 41 | "jupyter.jupyterServerType": "local", 42 | "python.testing.promptToConfigure": false, 43 | "python.testing.pytestEnabled": false, 44 | "python.testing.unittestEnabled": false, 45 | "python.testing.nosetestsEnabled": false 46 | } -------------------------------------------------------------------------------- /ap_first_semester/advanced_astrophysics.pdf: -------------------------------------------------------------------------------- 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12 | mu = .62 13 | T= 1e7*u.K 14 | 15 | a = np.sqrt(R * T / mu) 16 | 17 | fs = np.logspace(-5, 0, num=1000) * ac.GM_sun / ac.R_sun**2 18 | 19 | def r(f): 20 | numerator = np.sqrt(1 + f * ac.GM_sun / a ** 4) - 1 21 | denominator = f / a ** 2 22 | return (numerator / denominator) 23 | 24 | plt.plot(fs[1:] / ac.GM_sun * ac.R_sun ** 2, r(fs[1:]) / ac.R_sun) 25 | plt.xlabel("Normalized force: $f / (GM_\\odot / R_\\odot^2)$") 26 | plt.ylabel("Normalized critical radius: $r_c / R_\\odot$") 27 | plt.show(block=False) 28 | -------------------------------------------------------------------------------- /ap_first_semester/advanced_astrophysics/figures/flux_1_MeV.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/advanced_astrophysics/figures/flux_1_MeV.png -------------------------------------------------------------------------------- /ap_first_semester/advanced_astrophysics/figures/gamma_nu_luminosities.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/advanced_astrophysics/figures/gamma_nu_luminosities.pdf -------------------------------------------------------------------------------- /ap_first_semester/advanced_astrophysics/figures/line_acceleration_profile.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/advanced_astrophysics/figures/line_acceleration_profile.pdf -------------------------------------------------------------------------------- /ap_first_semester/advanced_astrophysics/figures/line_acceleration_profile.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | plt.style.use(astropy_mpl_style) 5 | 6 | rs = np.linspace(1, 3, num=400) 7 | 8 | a = .6 9 | b = .7 10 | 11 | gs = rs ** (-2) * (1 - 1 / rs)**(a * (2 * b - 1)) 12 | 13 | plt.plot(rs, gs) 14 | plt.xlabel("Normalized radius $r / R_*$") 15 | plt.ylabel("Acceleration due to the line (arbitrary units) $g_L$") 16 | plt.show(block=False) -------------------------------------------------------------------------------- /ap_first_semester/advanced_astrophysics/figures/velocity_density_isothermal.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/advanced_astrophysics/figures/velocity_density_isothermal.pdf -------------------------------------------------------------------------------- /ap_first_semester/advanced_astrophysics/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/advanced_astrophysics/main.pdf -------------------------------------------------------------------------------- /ap_first_semester/advanced_astrophysics/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \title{Advanced astrophysics notes} 5 | 6 | \usepackage{subfiles} 7 | 8 | \begin{document} 9 | 10 | \maketitle 11 | \tableofcontents 12 | 13 | \chapter{Stellar oscillations} 14 | 15 | \subfile{30sep} 16 | \subfile{01oct} 17 | 18 | \subfile{07oct} 19 | \subfile{08oct} 20 | 21 | \subfile{14oct} 22 | \subfile{15oct} 23 | 24 | \subfile{21oct} 25 | \subfile{22oct} 26 | 27 | \chapter{Stellar winds} 28 | 29 | \subfile{28oct} 30 | \subfile{29oct} 31 | 32 | \subfile{04nov} 33 | \subfile{06nov} 34 | 35 | \subfile{11nov} 36 | \subfile{12nov} 37 | 38 | \subfile{18nov} 39 | \subfile{19nov} 40 | 41 | \subfile{25nov} 42 | \subfile{26nov} 43 | 44 | \subfile{02dec} 45 | \subfile{03dec} 46 | 47 | \chapter{Massive and very massive stars} 48 | 49 | \subfile{09dec} 50 | \subfile{10dec} 51 | 52 | 53 | \subfile{16dec} 54 | \subfile{17dec} 55 | 56 | 57 | \end{document} 58 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/14nov-1.cpt: -------------------------------------------------------------------------------- 1 | The result comes about from the following code: \begin{lstlisting}[language=Python] 2 | from astropy.cosmology import Planck15 as cosmo 3 | import numpy as np 4 | import astropy.units as u 5 | from astropy.constants import codata2018 as ac 6 | H0 = u.littleh *100 * u.km/u.s / u.Mpc 7 | rhoC = 3 * H0**2 / (8 * np.pi * ac.G) 8 | (rhoC * cosmo.Ob0 / ac.m_p).to(u.cm**-3 * u.littleh**2) 9 | \end{lstlisting}^^E^^L 10 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/14nov-2.cpt: -------------------------------------------------------------------------------- 1 | The result comes about from the following code: \begin{lstlisting}[language=Python] 2 | from astropy.cosmology import Planck15 as cosmo 3 | import numpy as np 4 | import astropy.units as u 5 | from astropy.constants import codata2018 as ac 6 | z3 = np.sum([n**-3 for n in range(1, 1000000)]) 7 | (2 * z3 / np.pi**2 * cosmo.Tcmb0**3 * (ac.k_B / ac.hbar / ac.c)**3).cgs 8 | \end{lstlisting}^^E^^L 9 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/31oct-1.cpt: -------------------------------------------------------------------------------- 1 | All the calculations were made automatically using the \texttt{astropy} package, using a flat \(\Lambda \)CDM model with parameters obtained from the Planck mission \cite[]{adePlanck2015Results2016}. 2 | \begin{lstlisting}[language=Python] 3 | from astropy.cosmology import Planck15 as cosmo 4 | import numpy as np 5 | import astropy.units as u 6 | z_LS = 1089 7 | dx = (cosmo.comoving_distance(np.inf) - cosmo.comoving_distance(z_LS)) * cosmo.scale_factor(z_LS) 8 | dA = cosmo.angular_diameter_distance(z_LS) 9 | (dx / dA).to(u.degree, equivalencies=u.dimensionless_angles()) 10 | \end{lstlisting}^^E^^L 11 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/Dark_matter.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/figures/Dark_matter.pdf -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/Schechter.pdf: 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https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/figures/__pycache__/basic_units.cpython-38.pyc -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/beta_core_pressure.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from matplotlib import rc 4 | rc('font',**{'family':'serif','serif':['Palatino']}) 5 | rc('text', usetex=True) 6 | rc('text.latex', preamble=r'''\usepackage{amsmath} 7 | \usepackage{physics} 8 | \usepackage{siunitx} 9 | ''') 10 | from matplotlib import ticker 11 | from tqdm import tqdm 12 | 13 | import scipy.constants as sc 14 | from astropy.constants import codata2018 as ac 15 | from astropy.constants import iau2015 as aa 16 | import astropy.units as u 17 | from astropy.cosmology import Planck15 as cosmo 18 | 19 | from astropy.visualization import quantity_support 20 | 21 | # a = np.pi ** 2 * ac.k_B**2 / 15 / ac.hbar**3 / ac.c**3 22 | a = ac.sigma_sb * 4 /ac.c 23 | 24 | beta = np.linspace(0, 1, num=200) 25 | mbar = .62 * ac.m_p 26 | 27 | M = np.sqrt(ac.G ** (-3 ) * (np.pi / 36)**(-1) * (3/a * (1-beta) / beta**4) * (ac.k_B / mbar)**(4)) 28 | 29 | with quantity_support(): 30 | plt.semilogx(M.to(u.M_sun), beta) 31 | plt.xlabel('Mass [$M_{\\odot}$]') 32 | plt.ylabel('Nonrelativistic pressure fraction $\\beta$') 33 | plt.savefig('beta_star_core_pressure.pdf') 34 | 35 | # the units don't work! 36 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/beta_star_core_pressure.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/figures/beta_star_core_pressure.pdf 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import scipy.constants as sc 14 | from astropy.constants import codata2018 as ac 15 | from astropy.constants import iau2015 as aa 16 | import astropy.units as u 17 | from astropy.cosmology import Planck15 as cosmo 18 | 19 | from astropy.visualization import quantity_support 20 | 21 | x = np.linspace(0,10, num=200) 22 | 23 | I = 3 / 2 / x ** 4 * (x * (1 + x ** 2)**(1 / 2)* (2 * x ** 2 / 3 - 1) + np.log(x + (1 + x ** 2)**(1 / 2))) 24 | 25 | plt.plot(I ** (3 / 2), x) 26 | plt.ylabel('$x_F$') 27 | plt.xlabel('$M / M _{\\text{Ch}} = I(x_F)^{3/2}$') 28 | plt.savefig('chandrasekhar_limit.pdf') 29 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/chandrasekhar_limit.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/figures/chandrasekhar_limit.pdf -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/cosine_positive_curvature.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | plt.style.use(astropy_mpl_style) 5 | from matplotlib import rc 6 | rc('font',**{'family':'serif','serif':['Palatino']}) 7 | rc('text', usetex=True) 8 | rc('text.latex', preamble=r'''\usepackage{amsmath} 9 | \usepackage{physics} 10 | \usepackage{siunitx} 11 | ''') 12 | 13 | from basic_units import cos,sin, radians 14 | 15 | theta_r = np.linspace(0, 2 * np.pi, num=1000) 16 | theta = np.array([x * radians for x in theta_r]) 17 | 18 | a = (1 - cos(theta)) / 2 19 | t = (theta_r - sin(theta)) / 2 20 | 21 | plt.plot(theta, a, label='Scale factor $a$') 22 | plt.plot(theta, t, label='Time $t$') 23 | plt.xlabel('Angle parameter $\\theta$') 24 | plt.ylabel('Normalized scale factor $a / \\widetilde{a}_0$ or time $t / \\widetilde{t}_0$') 25 | plt.legend() 26 | plt.savefig('positive_curvature_a.pdf', format = 'pdf') 27 | # plt.show() 28 | plt.close() 29 | 30 | plt.plot(t, a) 31 | plt.xlabel("Time $t / \\widetilde{t}_0$") 32 | plt.ylabel("Scale factor $a / \\widetilde{a}_0$") 33 | plt.savefig('positive_curvature_a_vs_t.pdf', format = 'pdf') -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/current_time_curved_model.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | plt.style.use(astropy_mpl_style) 5 | from matplotlib import rc 6 | rc('font',**{'family':'serif','serif':['Palatino']}) 7 | rc('text', usetex=True) 8 | rc('text.latex', preamble=r'''\usepackage{amsmath} 9 | \usepackage{physics} 10 | \usepackage{siunitx} 11 | ''') 12 | 13 | Omega0 = np.linspace(1.00001, 2) 14 | Omega0_less = np.linspace(.01, .99999) 15 | 16 | t = 1 / 2 * Omega0 / (Omega0 - 1)**(3 / 2)\ 17 | * (np.arccos(2 / Omega0 - 1) - 2 / Omega0 * np.sqrt(Omega0 - 1)) 18 | t_less = - 1 / 2 * Omega0_less / (1- Omega0_less)**(3 / 2)\ 19 | * (np.arccosh(2 / Omega0_less - 1) - 2 / Omega0_less * np.sqrt(1 - Omega0_less )) 20 | 21 | plt.plot(Omega0, t, label='Curved model, $k=1$') 22 | plt.plot(Omega0_less, t_less, label='Curved model, $k=-1$') 23 | plt.axhline(2/3, ls='dashed', lw=1, label='Flat model ') 24 | plt.xlabel('Current ratio of density to critical density $\\Omega_0$') 25 | plt.ylabel('Universe age $t_0$ in units of $H_0^{-1}$') 26 | plt.legend() 27 | plt.savefig('curved_universe_age.pdf', format = 'pdf') 28 | # plt.show() -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/curved_universe_age.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/figures/curved_universe_age.pdf -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/dark_matter.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | plt.style.use(astropy_mpl_style) 5 | plt.xkcd(randomness=1) 6 | 7 | R1 = np.linspace(0, 1) 8 | R2 = np.linspace(1, 6) 9 | 10 | v_ob1 = R1 11 | v_ob2 = np.ones_like(R2) 12 | v_th2 = R2 ** (-1 / 2) 13 | 14 | plt.plot(R1, v_ob1, c='black') 15 | plt.plot(R2, v_ob2, c='black', ls = '-', label='Observed') 16 | plt.plot(R2, v_th2, c='black', ls='--', label='Predicted') 17 | 18 | plt.legend() 19 | # plt.axis('off') 20 | plt.ylabel('$v(R)$') 21 | plt.xlabel('$R$') 22 | 23 | plt.show() -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/global_energy_contributions.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/figures/global_energy_contributions.pdf -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/global_energy_contributions.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | plt.style.use(astropy_mpl_style) 5 | import scipy.constants as sc 6 | from astropy.constants import codata2018 as ac 7 | from astropy.constants import iau2015 as aa 8 | import astropy.units as u 9 | from astropy.cosmology import Planck15 as cosmo 10 | import astropy.uncertainty as aun 11 | 12 | a = np.linspace(.01, 3, num=1000) 13 | # a=1 now 14 | 15 | Om0 = cosmo.Om0 16 | Olambda0 = 1 - cosmo.Om0 - cosmo.Ob0 17 | Orad0 = (2.5e-5 * u.littleh**-2).to(u.dimensionless_unscaled, equivalencies=u.with_H0()) 18 | 19 | def get_rho(a, w, O0): 20 | return(O0 * a**(-3*(1+w))) 21 | 22 | plt.plot(a, get_rho(a, -1, Olambda0), label='Cosmological constant') 23 | plt.plot(a, get_rho(a, 1/3, Orad0), label='Radiation') 24 | plt.plot(a, get_rho(a, 0, Om0), label='Matter') 25 | plt.xlabel('Scale factor: $a / a_0$') 26 | plt.ylabel('Energy density: $\\rho / \\rho_{0c}$') 27 | plt.axvline(x=1, label='Now', c='black') 28 | plt.ylim(0,2) 29 | plt.legend() 30 | plt.savefig('global_energy_contributions.pdf', format = 'pdf') -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/hubble_original.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/figures/hubble_original.png -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/hyperbolic.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | import matplotlib.pyplot as plt 4 | from astropy.visualization import astropy_mpl_style 5 | plt.style.use(astropy_mpl_style) 6 | from mpl_toolkits import mplot3d 7 | 8 | x = np.linspace(-2, 2, num=20) 9 | y = np.linspace(-2, 2, num=20) 10 | X, Y = np.meshgrid(x, y) 11 | 12 | def hyper(x, y): 13 | # return(np.sqrt(5 + x ** 2 - y ** 2)) 14 | return(x ** 2 - y ** 2) 15 | 16 | """ 17 | Metric is: 18 | g_μν = 19 | [[1 + 4x**2, -4xy], 20 | [-4xy, 1+4y**2]] 21 | 22 | """ 23 | 24 | Z = hyper(X, Y) 25 | 26 | def plot_line(x0, y0, x1, y1): 27 | x_line = np.linspace(x0, x1) 28 | y_line = np.linspace(y0, y1) 29 | ax.plot(x_line, y_line, hyper(x_line, y_line), c='b') 30 | 31 | 32 | fig = plt.figure() 33 | ax = plt.axes(projection='3d') 34 | 35 | ax.plot_surface(X, Y, Z, cmap='viridis', edgecolor='black', linewidth=.5, alpha=.6) 36 | plot_line(-1.5, -1.5, 0.5, 0) 37 | plt.show() -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/ionization.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/figures/ionization.pdf -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/figures/ionization_nophotons.pdf: 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-------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/format.fmt: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/format.fmt -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/main-1.cpt: -------------------------------------------------------------------------------- 1 | All the calculations were made automatically using the \texttt{astropy} package, using a flat \(\Lambda \)CDM model with parameters obtained from the Planck mission \cite[]{adePlanck2015Results2016}. 2 | \begin{lstlisting}[language=Python] 3 | from astropy.cosmology import Planck15 as cosmo 4 | import numpy as np 5 | import astropy.units as u 6 | z_LS = 1089 7 | dx = (cosmo.comoving_distance(np.inf) - cosmo.comoving_distance(z_LS)) * cosmo.scale_factor(z_LS) 8 | dA = cosmo.angular_diameter_distance(z_LS) 9 | (dx / dA).to(u.degree, equivalencies=u.dimensionless_angles()) 10 | \end{lstlisting}^^E^^L 11 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/main-2.cpt: -------------------------------------------------------------------------------- 1 | The result comes about from the following code: \begin{lstlisting}[language=Python] 2 | from astropy.cosmology import Planck15 as cosmo 3 | import numpy as np 4 | import astropy.units as u 5 | from astropy.constants import codata2018 as ac 6 | H0 = u.littleh *100 * u.km/u.s / u.Mpc 7 | rhoC = 3 * H0**2 / (8 * np.pi * ac.G) 8 | (rhoC * cosmo.Ob0 / ac.m_p).to(u.cm**-3 * u.littleh**2) 9 | \end{lstlisting}^^E^^L 10 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/main-3.cpt: -------------------------------------------------------------------------------- 1 | The result comes about from the following code: \begin{lstlisting}[language=Python] 2 | from astropy.cosmology import Planck15 as cosmo 3 | import numpy as np 4 | import astropy.units as u 5 | from astropy.constants import codata2018 as ac 6 | z3 = np.sum([n**-3 for n in range(1, 1000000)]) 7 | (2 * z3 / np.pi**2 * cosmo.Tcmb0**3 * (ac.k_B / ac.hbar / ac.c)**3).cgs 8 | \end{lstlisting}^^E^^L 9 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/main-4.cpt: -------------------------------------------------------------------------------- 1 | All the calculations were made automatically using the \texttt{astropy} package, using a flat \(\Lambda \)CDM model with parameters obtained from the Planck mission \cite[]{adePlanck2015Results2016}. 2 | \begin{lstlisting}[language=Python] 3 | from astropy.cosmology import Planck15 as cosmo 4 | import numpy as np 5 | import astropy.units as u 6 | z_LS = 1089 7 | dx = (cosmo.comoving_distance(np.inf) - cosmo.comoving_distance(z_LS)) * cosmo.scale_factor(z_LS) 8 | dA = cosmo.angular_diameter_distance(z_LS) 9 | (dx / dA).to(u.degree, equivalencies=u.dimensionless_angles()) 10 | \end{lstlisting}^^E^^L 11 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/main-5.cpt: -------------------------------------------------------------------------------- 1 | The result comes about from the following code: \begin{lstlisting}[language=Python] 2 | from astropy.cosmology import Planck15 as cosmo 3 | import numpy as np 4 | import astropy.units as u 5 | from astropy.constants import codata2018 as ac 6 | H0 = u.littleh *100 * u.km/u.s / u.Mpc 7 | rhoC = 3 * H0**2 / (8 * np.pi * ac.G) 8 | (rhoC * cosmo.Ob0 / ac.m_p).to(u.cm**-3 * u.littleh**2) 9 | \end{lstlisting}^^E^^L 10 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/main-6.cpt: -------------------------------------------------------------------------------- 1 | The result comes about from the following code: \begin{lstlisting}[language=Python] 2 | from astropy.cosmology import Planck15 as cosmo 3 | import numpy as np 4 | import astropy.units as u 5 | from astropy.constants import codata2018 as ac 6 | z3 = np.sum([n**-3 for n in range(1, 1000000)]) 7 | (2 * z3 / np.pi**2 * cosmo.Tcmb0**3 * (ac.k_B / ac.hbar / ac.c)**3).cgs 8 | \end{lstlisting}^^E^^L 9 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology/main.pdf -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{header.tex} 4 | 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601, 10 | backref=true 11 | ]{biblatex} 12 | 13 | \addbibresource{cosmo.bib} 14 | 15 | \title{Astrophysics and cosmology notes} 16 | \author{Jacopo Tissino, Giorgio Mentasti, Eleonora Vanzan} 17 | 18 | \usepackage{subfiles} 19 | 20 | \begin{document} 21 | 22 | \maketitle 23 | 24 | \tableofcontents 25 | 26 | \subfile{03oct} 27 | \subfile{04oct} 28 | 29 | \subfile{10oct} 30 | \subfile{11oct} 31 | 32 | \subfile{17oct} 33 | \subfile{18oct} 34 | 35 | \subfile{25oct} 36 | 37 | \subfile{31oct} 38 | 39 | \subfile{07nov} 40 | \subfile{08nov} 41 | \subfile{14nov} 42 | \subfile{15nov} 43 | 44 | \subfile{21nov} 45 | \subfile{22nov} 46 | 47 | \subfile{28nov} 48 | \subfile{29nov} 49 | 50 | \subfile{05dec} 51 | \subfile{06dec} 52 | 53 | \subfile{12dec} 54 | \subfile{13dec} 55 | 56 | \subfile{19dec} 57 | \subfile{20dec} 58 | 59 | % Neglecting the last two lectures, since they were off-topic from the main course - might recover them later! 60 | % \subfile{08jan} 61 | % \subfile{09jan} 62 | 63 | \printbibliography[title=Bibliography] 64 | 65 | \end{document} 66 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_cosmology_with_notes.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_cosmology_with_notes.pdf -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_lab.pdf -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/01oct.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{1 October} 5 | 6 | \url{http://people.na.infn.it/~barbarin/MaterialeDidattico/0-corso%20Fisica%20astroparticellare/0-libro-longair.pdf} 7 | 8 | Slides are found at: 9 | \url{http://www.thebotta.com/students/students.htm} 10 | 11 | Username: \texttt{stud}, Password: \texttt{stud\_pd}. 12 | 13 | Bisogna fare una presentazione sui dati che ci faranno analizzare e discuterla poi. Analisi dati al pc molto su dati di alte energie e raggi X, gamma in generale. 14 | 15 | Parla dell'importanza degli interferometri LIGO e VIRGO; dei neutrini (Kamiokande, IceCube etc.); raggi cosmici, si incazza coi fisici che usano l'eV per misurare tutto lol. Insomma, le alte energie sono tutto nella vita per un ricercatore. 16 | 17 | \end{document} 18 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/03dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Tue Dec 03 2019} 5 | 6 | For italians going to study in North America: there exists the ``Italian Scientists and Scholars in North America Foundation'' or ISSNAF. 7 | 8 | You can get an advisor there, in order to get into a PhD school in the Bay area. 9 | 10 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/04dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/05nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Tue Nov 05 2019} 5 | 6 | We start by analyzing the data from CHANDRA. 7 | 8 | Then, we start to talk about \emph{grazing angles}: 9 | they depend on \(\delta \), where 10 | % 11 | \begin{align} 12 | \delta \sim \frac{1}{2 \pi } N_e r_e \lambda^2 13 | \,, 14 | \end{align} 15 | % 16 | which is of the order of one degree, and allows us to 17 | build detectors with more effective area. 18 | 19 | The effective area is: 20 | % 21 | \begin{align} 22 | A _{\text{eff}} = A _{\text{geom}} R(E) V(E, x, y) Q(E, x, y) 23 | \,. 24 | \end{align} 25 | % 26 | 27 | The vignetting \(V\) accounts for the fact that the outermost pixels are less bright than the innermost ones; 28 | the quantum efficiency \(Q\) is\dots 29 | 30 | 31 | 32 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/06nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Wed Nov 06 2019} 5 | 6 | Presentation by Bottacini like we will do for the exam. 7 | 8 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/10dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/11dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Wed Dec 11 2019} 5 | 6 | There will not be the exam on the last day of lecture. 7 | There will not be theoretical questions on the exam, but there will be questions on the stuff covered during lectures, in connection to what we did in the research. 8 | 9 | cflux to calculate the flux of a line. 10 | 11 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/13nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/16oct.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Wed Oct 16 2019} 5 | 6 | Or galaxy might have had a jet perpendicular to it in the past. 7 | 8 | Seeing galaxies at very high redshift is difficult: \(\gamma \) ray astronomy is useful that way, since it can tell very low FOV (optical?) telescopes where to look. 9 | 10 | We look at different wavelengths detected for 3C 279: a blazar. 11 | 12 | AGNs are Active Galactic Nuclei. They are best seen through X-rays, which can pierce the dusty accretion disc. 13 | 14 | Iron is the final state of fusion: we expect to see iron lines near SMBHs. 15 | When looking at a BH accretion disc at a high inclination, we see the region \emph{behind} the BH, since light is curved. 16 | 17 | Mrk 876 iron line: it seems \emph{too} reshifted, cosmological redshift alone does not explain it. We need to account for gravitational reshift from the SMBH, and tell what the distance from the center is. 18 | 19 | \begin{greenbox} 20 | Also, we can use Doppler redshift to measure the speed of rotation around the SMBH: how does this work? It seems like the two effects should combine\dots 21 | \end{greenbox} 22 | 23 | About INTEGRAL: it has 4 instruments, a \(\gamma \) ray telescope, an X ray telescope, an optical monitoring camera (and...?). 24 | 25 | It has a huge FOV (\SI{20}{\degree} by \SI{20}{\degree}), but the angular resolution is only 12'. 26 | 27 | We talk about the \SI{}{MeV} gap. 28 | 29 | 30 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/17dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/18dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/19nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Tue Nov 19 2019} 5 | 6 | Orbital motion: under Newtonian gravity we have \(T = 2 \pi \sqrt{a^{3} / \mu }\), where \(a\) is the semimajor axis of the ellipse and \(\mu = G (m_1 + m_2 )\). 7 | 8 | The inner Van Allen (not Eddie Van Halen!) bands reach down to \SI{200}{km} over the Earth's surface, especially over the South Atlantic: the region is about \(0 \divisionsymbol \SI{60}{\degree} \) W longitude and \(2 \divisionsymbol \SI{50}{\degree} \) S longitude. 9 | 10 | Satellites shut down when passing there. Astronauts in the ISS get \emph{shooting stars} in their eyes. 11 | 12 | The Lagrange points are \(L1\) between Sun and Earth, \(L2\) behind the Earth, \(L3\) on the other side of the Sun, \(L4\) and \(L5\) on the vertices of equilateral triangles with two vertices on S and E. 13 | 14 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/22oct.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Tue Oct 22 2019} 5 | [Missing. To recover.] 6 | 7 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/23oct.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | 5 | \section*{Wed Oct 23 2019} 6 | [Missing. To recover.] 7 | 8 | How does Fermi work? what are CRs? Compact Remnants? 9 | 10 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/26nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/27nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/29oct.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Tue Oct 29 2019} 5 | 6 | In the second part of the course we will look at a certain dataset in groups, analyze it, research it (with a couple weeks or a month to do it); then do a presentation for around 10 minutes each. 7 | 8 | The exam can be done even the last lecture: we just have to notify him a week in advance. 9 | 10 | We will analyze data either from CHANDRA or NUSTAR. 11 | 12 | Exercise: best fit in the 3 to \SI{79}{keV} and plot spectrum \(E^2 \dv{N}{E}\). 13 | Verify that the parametrs of the centroid of the iron line and the temperature are independently derived. 14 | Verify that the iron line is statistically significant. 15 | 16 | Steppar: to create a contour plot. 17 | 18 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/30oct.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Wed Oct 30 2019} 5 | 6 | Line emission: the light from the corona illuminates the accretion disk, and we see the spectral lines from the various elements in it. 7 | 8 | When looking at a disk edge-on, we have several effects: we see 9 | \begin{enumerate} 10 | \item Doppler shift (Newtonian): the outer annulus has a faster tangential velocity since the accretion disk rotates approximately rigidly; 11 | \item Beaming (special relativistic); 12 | \item Transverse Doppler (special relativistic); 13 | \item Gravitational redshift (general relativistic). 14 | \end{enumerate} 15 | 16 | We can simulate the spectra due to a line emission at different angles with respect to the accretion plane, and with respect to either a Schwarzschild or Kerr BH. 17 | 18 | Exercise. 19 | 20 | We assume that the matter in the accretion disk basically orbits in circular paths, regulated by 21 | % 22 | \begin{equation} 23 | \frac{v^2}{r} = \frac{GM}{r^2} 24 | \,, 25 | \end{equation} 26 | % 27 | with energy given by 28 | % 29 | \begin{equation} 30 | E = \frac{1}{2} m v^2 - \frac{GmM}{r} 31 | \,. 32 | \end{equation} 33 | 34 | We get the luminosity of the disk by assuming that the heat is dissipated through viscosity, 35 | % 36 | \begin{equation} 37 | L = \int _{r_{*}}^{\infty} - \dv{E}{T} 2 \pi r \dd{r} = \frac{G \dot{m} M}{2 r_{*}} 38 | \,, 39 | \end{equation} 40 | % 41 | where \(T\) is time, and \(\dot{m} = \dv*{m}{T}\). 42 | 43 | The temperature is increasing as \(r\) decreases. The total spectrum is the sum of several blackbodies, at each temperature. 44 | 45 | Instead, we see a blackbody component, and a powerlaw coming from the reflection of the accretion disk, plus an iron line. 46 | 47 | 48 | 49 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/30sep.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{30 september 2019} 5 | \section{A-L laboratory} 6 | 7 | Teacher: Roberto Ragazzoni, Gabriele Umbriaco et al. 8 | 9 | \url{roberto.ragazzoni@inaf.it} 10 | 11 | \begin{equation} 12 | \text{Lab Course} = \text{Course} (\lambda) 13 | \end{equation} 14 | 15 | Objective of this course: \emph{how to build an astronomical instrument} which will push the limits of astrophysical knowledge and technology. 16 | 17 | \subsection{Orders of magnitude} 18 | 19 | Diameters: in the future \SI{24}{m}, \SI{37}{m}. 20 | 21 | Resolution: \SI{0.04}{\arcsec} for the HST. 22 | 23 | Collected photons: \SI{2700}{Hz} for an eye at \(V=6\). 24 | 25 | For a galaxy at redshift \(z=10\), the Lyman break at \SI{91.4}{nm} is shifted. 26 | The Lyman break is the Rydberg constant: the limit of the Rydberg line, which is the hydrogen emission series corresponding to the electron dropping to its lowest energy level. 27 | 28 | In the background: magnitude 18 (with moon), 21 (no moon) per arcsec square. 29 | 30 | 10 meters, ``seeing limited'': \SI{1}{arcsec}; 1 meter, ``diffraction limited'': \SI{0.1}{arcsec}. Collection ratio: 100X, but the size of the background in which the unresolved source is located is also 100X. 31 | 32 | We have a great school of \emph{adaptive optics}. 33 | 34 | 35 | 36 | \end{document} 37 | -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/astrophysics_lab/main.pdf -------------------------------------------------------------------------------- /ap_first_semester/astrophysics_lab/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Astrophysics lab notes} 5 | 6 | \usepackage{subfiles} 7 | 8 | \begin{document} 9 | 10 | \maketitle 11 | 12 | \subfile{30sep} 13 | \subfile{01oct} 14 | \subfile{02oct} 15 | 16 | \subfile{08oct} 17 | \subfile{09oct} 18 | 19 | \subfile{15oct} 20 | \subfile{16oct} 21 | 22 | \subfile{22oct} 23 | \subfile{23oct} 24 | 25 | \subfile{29oct} 26 | \subfile{30oct} 27 | 28 | \subfile{05nov} 29 | \subfile{06nov} 30 | 31 | \subfile{12nov} 32 | \subfile{13nov} 33 | 34 | \subfile{19nov} 35 | 36 | \subfile{26nov} 37 | \subfile{27nov} 38 | 39 | \subfile{03dec} 40 | \subfile{04dec} 41 | 42 | \subfile{10dec} 43 | \subfile{11dec} 44 | 45 | \subfile{17dec} 46 | \subfile{18dec} 47 | 48 | 49 | \end{document} 50 | -------------------------------------------------------------------------------- /ap_first_semester/general_relativity.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/general_relativity.pdf -------------------------------------------------------------------------------- /ap_first_semester/general_relativity/figures/fixed_L_orbits.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/general_relativity/figures/fixed_L_orbits.pdf -------------------------------------------------------------------------------- /ap_first_semester/general_relativity/figures/kruskal.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | from matplotlib import rc 5 | from scipy.optimize import fsolve 6 | rc('text', usetex=True) 7 | rc('font',**{'family':'serif','serif':['Palatino']}) 8 | rc('text.latex', preamble=r'''\usepackage{amsmath} 9 | \usepackage{physics} 10 | \usepackage{siunitx} 11 | ''') 12 | 13 | plt.close() 14 | 15 | R = np.linspace(0, 3, num=200) 16 | f = lambda x: (x-1) * np.exp(x) 17 | # fig = plt.figure(1) 18 | # plt.plot(R, f(R)) 19 | # plt.grid() 20 | # plt.show() 21 | # plt.close() 22 | 23 | @np.vectorize 24 | def r(U, V, hint=None): 25 | """ 26 | a numerical solution to 27 | U**2 - V**2 = (r-1) * exp(r/2) 28 | """ 29 | 30 | LHS = U ** 2 - V ** 2 31 | if (LHS < 0): 32 | return (0) 33 | function = lambda x: (x-1)*np.exp(x) - LHS 34 | if(not hint): 35 | hint = max(np.log(LHS), 0) 36 | 37 | return fsolve(function, x0=hint) 38 | 39 | def U_from_r(r, V): 40 | return( (r-1)*np.exp(r) + V**2) 41 | 42 | # Us = np.linspace(-10, 10, num=200) 43 | for V0 in range(4): 44 | # rs = r(Us, V0) 45 | if (V0 == 0): 46 | lab = f"$V_0 = $ {V0}" 47 | else: 48 | lab= f"$V_0 = \pm$ {V0}" 49 | # plt.plot(rs, Us, label=lab) 50 | rs = np.linspace(0, 2, num=200) 51 | Us = U_from_r(rs, V0) 52 | positive_U = np.nonzero(Us>0) 53 | rs = rs[positive_U] 54 | Us = Us[positive_U] 55 | plt.plot(np.append(np.flip(rs), rs), np.append(np.flip(Us), -Us), label=lab) 56 | plt.xlabel("$r(U^2 - V^2) / 2GM$") 57 | plt.ylabel("$U$") 58 | plt.legend() 59 | plt.savefig('kruskal_constant_V.pdf', format='pdf') 60 | plt.close() -------------------------------------------------------------------------------- /ap_first_semester/general_relativity/figures/kruskal_constant_V.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/general_relativity/figures/kruskal_constant_V.pdf -------------------------------------------------------------------------------- /ap_first_semester/general_relativity/figures/rindlerU2-V2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/general_relativity/figures/rindlerU2-V2.pdf -------------------------------------------------------------------------------- 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33 | 34 | \subfile{28nov} 35 | \subfile{29nov} 36 | 37 | \subfile{05dec} 38 | \subfile{06dec} 39 | 40 | \subfile{12dec} 41 | \subfile{13dec} 42 | 43 | \subfile{19dec} 44 | \subfile{20dec} 45 | 46 | \subfile{09jan} 47 | \subfile{10jan} 48 | 49 | \end{document} 50 | 51 | -------------------------------------------------------------------------------- /ap_first_semester/gr_exercises.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/gr_exercises.pdf -------------------------------------------------------------------------------- /ap_first_semester/gr_exercises/figures/Visualization of accelerational time dilation.ggb: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/gr_exercises/figures/Visualization of 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\titleformat{\section} 12 | {\normalfont\Large\bfseries} % The style of the section title 13 | {} % a prefix 14 | {0pt} % How much space exists between the prefix and the title 15 | {} % How the section is represented 16 | 17 | % Starred variant 18 | \titleformat{name=\section,numberless} 19 | {\normalfont\Large\bfseries} 20 | {} 21 | {0pt} 22 | {} 23 | 24 | \numberwithin{equation}{section} 25 | 26 | \begin{document} 27 | 28 | \maketitle 29 | 30 | \tableofcontents 31 | 32 | \vspace{1cm} 33 | 34 | \subfile{sheet1} 35 | \subfile{sheet2} 36 | \subfile{sheet3} 37 | \subfile{sheet4} 38 | \subfile{sheet5} 39 | \subfile{sheet6} 40 | \subfile{sheet7} 41 | \subfile{sheet8} 42 | \subfile{sheet9} 43 | \subfile{sheet10} 44 | \subfile{sheet11} 45 | \subfile{sheet12} 46 | 47 | \end{document} 48 | 49 | 50 | -------------------------------------------------------------------------------- /ap_first_semester/gr_exercises/python/allowed_angular_velocities_Kerr.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | plt.style.use(astropy_mpl_style) 5 | from matplotlib import rc 6 | rc('font',**{'family':'serif','serif':['Palatino']}) 7 | rc('text', usetex=True) 8 | rc('text.latex', preamble=r'''\usepackage{amsmath} 9 | \usepackage{physics} 10 | \usepackage{siunitx} 11 | ''') 12 | 13 | def omega1(r): 14 | omega1 = (2 - r) / (2 - r + r ** 2) 15 | return(omega1) 16 | 17 | def omega2(r): 18 | omega2 = 1 / (1 + r) 19 | return (omega2) 20 | 21 | rs = np.linspace(1, 6, num=200) 22 | plt.plot(rs, omega1(rs), label="$\\Omega_{-}$") 23 | plt.plot(rs, omega2(rs), label="$\\Omega_{+}$") 24 | plt.xlabel("$R = r/GM$") 25 | plt.ylabel("$O = \\Omega GM$") 26 | plt.legend() 27 | plt.savefig(fname='../figures/allowed_velocities.pdf', format = 'pdf') -------------------------------------------------------------------------------- /ap_first_semester/gr_exercises/python/sheet7_1.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | from matplotlib import rc 5 | rc('text', usetex=True) 6 | rc('font',**{'family':'serif','serif':['Palatino']}) 7 | rc('text.latex', preamble=r'''\usepackage{amsmath} 8 | \usepackage{physics} 9 | \usepackage{siunitx} 10 | ''') 11 | 12 | R = np.linspace(1, 5, num=200) 13 | 14 | f = lambda x: x ** (-2) - x ** (-3) 15 | 16 | fig = plt.figure(1) 17 | plt.plot(R, f(R)) 18 | plt.xlabel('$R = r/r_s$') 19 | plt.grid() 20 | plt.savefig(fname="../figures/photon_effective_potential.pdf", format="pdf") 21 | plt.close() -------------------------------------------------------------------------------- /ap_first_semester/gr_exercises/python/sheet7_2.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | from matplotlib import rc 5 | rc('text', usetex=True) 6 | rc('font',**{'family':'serif','serif':['Palatino']}) 7 | rc('text.latex', preamble=r'''\usepackage{amsmath} 8 | \usepackage{physics} 9 | \usepackage{siunitx} 10 | ''') 11 | R = np.linspace(1, 1.5, num=200) 12 | f = lambda x: np.arcsin(np.sqrt(27/4/x**2 * (1 - 1/x))) / (np.pi/2) 13 | fig = plt.figure(1) 14 | plt.plot(R, f(R)) 15 | plt.grid() 16 | # plt.show() 17 | plt.xlabel('$R = r / 2GM$') 18 | plt.ylabel('$\psi_{\\text{critical}} / (\\pi/2)$') 19 | plt.savefig('../figures/critical_psi.pdf', format = 'pdf') 20 | plt.close() -------------------------------------------------------------------------------- /ap_first_semester/gr_exercises/python/sheet7_3.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | from matplotlib import rc 5 | rc('text', usetex=True) 6 | rc('font',**{'family':'serif','serif':['Palatino']}) 7 | rc('text.latex', preamble=r'''\usepackage{amsmath} 8 | \usepackage{physics} 9 | \usepackage{siunitx} 10 | ''') 11 | R = np.linspace(1.5, 5, num=200) 12 | f = lambda x: np.sqrt(1 + 1/(2*x-3))/np.sqrt(1 - 1/x) 13 | fg = lambda x: 1 / np.sqrt(1 - 1 / x) - 1 14 | fd = lambda x: np.sqrt(1 + 1/(2*x-3))- 1 15 | fig = plt.figure(1) 16 | # plt.plot(R, f(R)) 17 | # plt.plot(R, f2(R)) 18 | plt.plot(R, fg(R)/fd(R)) 19 | plt.grid() 20 | # plt.close() 21 | -------------------------------------------------------------------------------- /ap_first_semester/gr_exercises/python/sheet9_1.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | from astropy.visualization import astropy_mpl_style 3 | plt.style.use(astropy_mpl_style) 4 | 5 | from matplotlib import rc 6 | rc('font',**{'family':'serif','serif':['Palatino']}) 7 | rc('text', usetex=True) 8 | rc('text.latex', preamble=r'''\usepackage{amsmath} 9 | \usepackage{physics} 10 | \usepackage{siunitx} 11 | ''') 12 | 13 | import numpy as np 14 | 15 | def V(e, r): 16 | t1 = 3/(8*r**2) - 1/(8*r**3) 17 | t2 = - 1/(2*r) + 1/(8*r**2) 18 | return(e**2 * t1 + t2) 19 | 20 | x= np.linspace(1/3, 3, num=300) 21 | 22 | for e in np.arange(1, 3, .5): 23 | plt.plot(x, V(e, x) - (e**2-1)/2, label=f"$e =$ {e}") 24 | plt.legend() 25 | plt.xlabel("$R$") 26 | plt.ylabel("$ V _{\\text{eff}} (R, e) - (e^2-1)/2$") 27 | 28 | plt.savefig('../figures/potential_barrier.pdf', format='pdf') 29 | plt.close() -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/numerical_methods.pdf -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/05dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Thu Dec 05 2019} 5 | 6 | Numerical integration! 7 | 8 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/06dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/07nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Thu Nov 07 2019} 5 | 6 | \section{Sorting} 7 | 8 | Useful for astrophysics since we often deal with large files. 9 | 10 | \paragraph{Bubble sort} 11 | We loop through the file, and swap each pair if it is not ordered. 12 | 13 | It is \(O(n^2)\) in general. 14 | 15 | \paragraph{Selection sort} 16 | We look for the minimum and put it at the beginning, then scan the remaining array. 17 | 18 | It is \(O(n^2)\) in general. 19 | 20 | \paragraph{Quicksort} 21 | 22 | \begin{enumerate} 23 | \item We pick an element, the \emph{pivot}; 24 | \item we reorder the array so that all elements less than the pivot come before it; 25 | \item we do this recursively to the subarrays to the left and right of the pivot. 26 | \end{enumerate} 27 | 28 | It is \(O(n^2)\) in the worst case, \(O(n \log n )\) usually. 29 | 30 | \paragraph{Merge sort} 31 | 32 | We divide the array into small subarrays, and merge them to produce larger subarrays. 33 | 34 | It is \(O(n^2)\) in the worst case, \(O(n \log n )\) usually. 35 | 36 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/08nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Fri Nov 08 2019} 5 | 6 | One can time a bash command using 7 | 8 | \begin{lstlisting}[language=bash] 9 | time [Command] 10 | \end{lstlisting} 11 | 12 | \section{Linear systems} 13 | 14 | We want to solve a linear system, in the form \(A \vec{x} = \vec{b}\), with unknown \(\vec{x}\). 15 | How do we solve this numerically? 16 | We can transform our system to an equivalent one, by 17 | \begin{enumerate} 18 | \item exchanging two rows; 19 | \item multiplying an equation by a nonzero constant; 20 | \item adding an equation to another. 21 | \end{enumerate} 22 | 23 | These allow us to do Gaussian elimination, and LU decomposition. These are \emph{direct methods}. 24 | 25 | Another class is that of \emph{indirect methods}: we start with an \emph{ansatz} and refine it. These are easier to implement, more generally applicable, more efficient if the matrix is sparse. 26 | They, however, do not always converge. 27 | 28 | An example is the Gauss-Seidel method. 29 | 30 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/12dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/13dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/14nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Thu Nov 14 2019} 5 | 6 | \subsection{Gauss-Seidel} 7 | 8 | We can rewrite \(\sum _{j} A_{ij} x_{j} = b_i\) as 9 | % 10 | \begin{align} 11 | x_{i} = \frac{1}{A_{ii}} \qty(b_{i} - \sum _{j \neq i} A_{ij}x_{j}) 12 | \,, 13 | \end{align} 14 | % 15 | and the algorithm works by starting with and \emph{ansatz}, updating it with this formula, and iterating. 16 | The update can be written more generally as 17 | % 18 | \begin{align} 19 | x_{i}^{n+1} = \frac{\omega }{A_{ii}} \qty(b_{i} - \sum _{j \neq i} A_{ij}x_{j}^{n}) + (1-\omega) x_{i}^{n} 20 | \,, 21 | \end{align} 22 | % 23 | with the \emph{relaxation parameter} \(\omega \). 24 | Do note that \(n\) is not an exponent but an iteration number. 25 | 26 | A good choice for \(\omega \) after the \(5\)th iteration: 27 | % 28 | \begin{align} 29 | \omega _{\text{opt}} = \frac{2}{1 + \sqrt{1- (\Delta x^{k+p} / \Delta x^{k})^{1/p}}} 30 | \,, 31 | \end{align} 32 | % 33 | 34 | 35 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/15nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Fri Nov 15 2019} 5 | 6 | Implementation of Gauss-Seidel. 7 | 8 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/19dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/20dec.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/21nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | 5 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/22nov.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_first_semester/numerical_methods/main.pdf -------------------------------------------------------------------------------- /ap_first_semester/numerical_methods/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Numerical methods notes} 5 | 6 | \usepackage{subfiles} 7 | 8 | \begin{document} 9 | 10 | \maketitle 11 | 12 | The course is held by Michela Mapelli: a team leader in GW astronomy. 13 | 14 | The first lessons are about basic Linux and Python, I will not take notes now, I will start later on. 15 | 16 | 17 | \subfile{07nov} 18 | \subfile{08nov} 19 | \subfile{14nov} 20 | \subfile{15nov} 21 | 22 | \subfile{21nov} 23 | \subfile{22nov} 24 | 25 | \subfile{28nov} 26 | \subfile{29nov} 27 | 28 | \subfile{05dec} 29 | \subfile{06dec} 30 | 31 | \subfile{12dec} 32 | \subfile{13dec} 33 | 34 | \subfile{19dec} 35 | \subfile{20dec} 36 | 37 | 38 | \end{document} 39 | -------------------------------------------------------------------------------- /ap_first_semester/subeq_align.py: -------------------------------------------------------------------------------- 1 | import os 2 | import re 3 | 4 | align_start = "\\begin{align}" 5 | align_end = "\\end{align}" 6 | subeq_start = "\\begin{subequations}" 7 | subeq_end = "\\end{subequations}" 8 | align_newline = "\\\\" 9 | 10 | folder_names = [ 11 | "advanced_astrophysics", 12 | "astrophysics_lab", 13 | "general_relativity", 14 | "numerical_methods", 15 | "astrophysics_cosmology", 16 | "gr_exercises" 17 | ] 18 | filenames_regex = "(\\d{2}\\w{3}|\\w{5}\\d{1,2})\\.tex" 19 | 20 | def cpars(s): 21 | return(s.count('{') == s.count('}')) 22 | 23 | def make_subeq_align(filename): 24 | 25 | with open(filename, 'r') as f: 26 | lines = f.readlines() 27 | 28 | for i, line in enumerate(lines): 29 | if (align_start in line 30 | and 31 | subeq_start not in lines[i - 1]): 32 | 33 | newline = False 34 | for pnumber, pline in enumerate(lines[i:]): 35 | if align_newline in pline: 36 | newline = True 37 | if align_end in pline: 38 | j = pnumber + i 39 | break 40 | if (not newline): 41 | pass 42 | else: 43 | lines[i] = subeq_start + '\n' + lines[i] 44 | if (cpars(lines[j])): 45 | lines[j] = lines[j] + subeq_end + '\n' 46 | else: 47 | l = lines[j].split('}') 48 | line = '}'.join(l[:-1]) 49 | lines[j] = line + '\n' + subeq_end + '}' + l[-1] + '\n' 50 | 51 | with open(filename, 'w') as f: 52 | f.writelines(lines) 53 | 54 | for folder in folder_names: 55 | for fname in os.listdir(folder): 56 | if re.match(filenames_regex, fname): 57 | make_subeq_align(os.path.join(folder, fname)) 58 | -------------------------------------------------------------------------------- /ap_second_semester/astroparticle_physics.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/astroparticle_physics.pdf -------------------------------------------------------------------------------- /ap_second_semester/astroparticle_physics/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \usepackage[ 5 | backend=biber, 6 | style=alphabetic, 7 | sorting=nyt, 8 | urldate=iso8601, 9 | backref=true 10 | ]{biblatex} 11 | 12 | \addbibresource{astroparticle_physics.bib} 13 | \title{Astroparticle physics notes} 14 | 15 | \usepackage{subfiles} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | \tableofcontents 21 | 22 | \subfile{mar10} 23 | \subfile{mar11} 24 | 25 | \subfile{mar17} 26 | \subfile{mar18} 27 | 28 | \subfile{mar24} 29 | \subfile{mar25} 30 | 31 | \subfile{mar31} 32 | \subfile{apr01} 33 | 34 | \subfile{apr07} 35 | \subfile{apr08} 36 | 37 | \subfile{apr15} 38 | 39 | \subfile{apr21} 40 | \subfile{apr22} 41 | 42 | \subfile{apr28} 43 | \subfile{apr29} 44 | 45 | \subfile{may05} 46 | \subfile{may06} 47 | 48 | \subfile{may12} 49 | \subfile{may13} 50 | 51 | \subfile{may19} 52 | \subfile{may20} 53 | 54 | \subfile{may26} 55 | \subfile{may27} 56 | 57 | \subfile{jun03} 58 | 59 | \printbibliography 60 | 61 | \end{document} 62 | 63 | -------------------------------------------------------------------------------- /ap_second_semester/gravitational_physics.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/gravitational_physics.pdf -------------------------------------------------------------------------------- /ap_second_semester/gravitational_physics/figures/amplitude_estimation.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from astropy.constants import codata2018 as ac 3 | import astropy.units as u 4 | 5 | m1 = 36 * u.Msun 6 | m2 = 29 * u.Msun 7 | m = (m1 * m2 ) / (m1 + m2) 8 | M = m1 + m2 9 | 10 | f_gw = 35 * u.Hz 11 | omega_s = (2 * np.pi * f_gw) / 2 12 | 13 | r = 410 * u.Mpc 14 | A = (4 * ac.G**(5/3) * (omega_s)**(2/3) * m * M**(2/3) / r / ac.c**4).to(1) 15 | -------------------------------------------------------------------------------- /ap_second_semester/gravitational_physics/figures/binary_angular_GW_spectrum.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | plt.style.use(astropy_mpl_style) 5 | import matplotlib.animation as animation 6 | from matplotlib import rc 7 | rc('font',**{'family':'serif','serif':['Palatino']}) 8 | rc('text', usetex=True) 9 | rc('text.latex', preamble=r'''\usepackage{amsmath} 10 | \usepackage{physics} 11 | \usepackage{siunitx} 12 | ''') 13 | 14 | NMAX = 200 15 | 16 | thetas = np.linspace(0, 2 * np.pi, num=1000) 17 | 18 | plus_polarization_amplitude = (1 + np.cos(thetas)**2)/2 19 | cross_polarization_amplitude = np.cos(thetas) 20 | 21 | fig = plt.figure() 22 | ax = fig.add_subplot(projection='polar') 23 | ax.set_theta_zero_location("N") 24 | # line, = ax.plot([], []) 25 | 26 | def init(): 27 | ax.set_ylim((0,1.1)) 28 | line.set_data([], []) 29 | return (line,) 30 | 31 | def total_amplitude(time, Nmax=NMAX): 32 | t = np.pi * time / Nmax 33 | amplitude = (((plus_polarization_amplitude * np.sin(t))** 2 + (cross_polarization_amplitude * np.cos(t))** 2)) 34 | 35 | line.set_data(thetas, amplitude) 36 | 37 | def averaged_amplitude(): 38 | amplitude = (((plus_polarization_amplitude)** 2 + (cross_polarization_amplitude)** 2)) 39 | return(amplitude) 40 | 41 | # anim = animation.FuncAnimation(fig, total_amplitude, range(NMAX), init_func=init, interval=50) 42 | 43 | # anim.save('angular_spectrum_no_sin.gif', writer='imagemagick', fps=60, dpi=200) 44 | 45 | ax.plot(thetas, averaged_amplitude()) 46 | ax.set_title('$r(\\theta) \\propto \\dv{E}{\\Omega}$') 47 | 48 | plt.show(block=False) 49 | -------------------------------------------------------------------------------- /ap_second_semester/gravitational_physics/figures/binary_averaged_angular_spectrum.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/gravitational_physics/figures/binary_averaged_angular_spectrum.pdf -------------------------------------------------------------------------------- /ap_second_semester/gravitational_physics/figures/binary_averaged_angular_spectrum_no_sin.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/gravitational_physics/figures/binary_averaged_angular_spectrum_no_sin.pdf -------------------------------------------------------------------------------- /ap_second_semester/gravitational_physics/jun01.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{Overview of GW detections and science} 5 | 6 | \marginpar{Monday\\ 2020-6-1, \\ compiled \\ \today} 7 | 8 | % Discussion on current GW detections and prospects for the future. 9 | Did not write this part down. 10 | 11 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/gravitational_physics/jun05.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/gravitational_physics/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \title{Gravitational physics notes} 5 | 6 | \usepackage[ 7 | backend=biber, 8 | style=alphabetic, 9 | sorting=nyt, 10 | urldate=iso8601 11 | ]{biblatex} 12 | 13 | \addbibresource{gravitational_physics.bib} 14 | 15 | \usepackage{subfiles} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | \tableofcontents 21 | 22 | \subfile{mar09} 23 | \subfile{mar13} 24 | 25 | \subfile{mar16} 26 | \subfile{mar20} 27 | 28 | \subfile{mar23} 29 | \subfile{mar27} 30 | 31 | \subfile{mar30} 32 | \subfile{apr03} 33 | 34 | \subfile{apr06} 35 | \subfile{apr10} 36 | 37 | \subfile{apr17} 38 | 39 | \subfile{apr20} 40 | \subfile{apr24} 41 | 42 | \subfile{apr27} 43 | \subfile{may01} 44 | 45 | \subfile{may04} 46 | \subfile{may08} 47 | 48 | \subfile{may11} 49 | \subfile{may15} 50 | 51 | \subfile{may18} 52 | \subfile{may22} 53 | 54 | \subfile{may29} 55 | 56 | \subfile{jun01} 57 | \subfile{jun05} 58 | 59 | \printbibliography 60 | 61 | \end{document} 62 | -------------------------------------------------------------------------------- /ap_second_semester/gravitational_physics/may29.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/gravitational_wave_astrophysics.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/gravitational_wave_astrophysics.pdf -------------------------------------------------------------------------------- /ap_second_semester/gravitational_wave_astrophysics/apr01.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Wednesday\\ 2020-4-1, \\ compiled \\ \today} 5 | 6 | Hulse-Taylor pulsars. 7 | We have many ways to measure masses of binary NS systems. 8 | 9 | \end{document} 10 | 11 | -------------------------------------------------------------------------------- /ap_second_semester/gravitational_wave_astrophysics/apr03.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{Binary neutron stars and GW emission} 5 | 6 | \marginpar{Friday\\ 2020-4-3, \\ compiled \\ \today} 7 | 8 | The sensitivity curves of ground-based detectors have three edges, from thermal (brownian) noise, seismic noise, and photon shot noise. 9 | 10 | The predictions for the yields of r-process elements match the observed solar composition well. 11 | 12 | LISA could detect NS-WD binaries. 13 | 14 | \end{document} 15 | -------------------------------------------------------------------------------- /ap_second_semester/gravitational_wave_astrophysics/figures/Eddington_alpha_dependence.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/gravitational_wave_astrophysics/figures/Eddington_alpha_dependence.pdf -------------------------------------------------------------------------------- /ap_second_semester/gravitational_wave_astrophysics/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \usepackage[ 5 | backend=biber, 6 | style=alphabetic, 7 | sorting=nyt, 8 | urldate=iso8601 9 | ]{biblatex} 10 | 11 | \addbibresource{gravitational_wave_astrophysics.bib} 12 | 13 | \title{Gravitational wave astrophysics notes} 14 | 15 | \usepackage{subfiles} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | \tableofcontents 21 | 22 | 23 | 24 | \subfile{mar23} 25 | \subfile{mar24} 26 | \subfile{mar25} 27 | \subfile{mar27} 28 | 29 | \subfile{mar30} 30 | \subfile{mar31} 31 | \subfile{apr01} 32 | \subfile{apr03} 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | \printbibliography 44 | 45 | \end{document} 46 | -------------------------------------------------------------------------------- /ap_second_semester/multimessenger_astrophysics.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/multimessenger_astrophysics.pdf -------------------------------------------------------------------------------- /ap_second_semester/path_integral.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/path_integral.pdf -------------------------------------------------------------------------------- /ap_second_semester/path_integral/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Path integrals and non-Gaussianity in cosmology} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso 10 | ]{biblatex} 11 | 12 | \addbibresource{../theoretical_cosmology/theoretical_cosmology.bib} 13 | 14 | \usepackage{subfiles} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | \tableofcontents 20 | 21 | \subfile{intro} 22 | \subfile{statistical_methods} 23 | \subfile{path_integral} 24 | % \subfile{applications} 25 | 26 | \printbibliography 27 | 28 | \end{document} 29 | -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/radiative_processes.pdf -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/figures/compton-sigma.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/radiative_processes/figures/compton-sigma.pdf -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/figures/compton-sigma.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/radiative_processes/figures/compton-sigma.png -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/jun03.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/jun04.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \title{Radiative processes in astrophysics notes} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | \addbibresource{radiative_processes.bib} 13 | 14 | \usepackage{subfiles} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | \tableofcontents 20 | 21 | \subfile{mar11} 22 | \subfile{mar12} 23 | 24 | \subfile{mar18} 25 | \subfile{mar19} 26 | 27 | \subfile{mar25} 28 | \subfile{mar26} 29 | 30 | \subfile{apr01} 31 | \subfile{apr02} 32 | 33 | \subfile{apr08} 34 | \subfile{apr09} 35 | 36 | \subfile{apr15} 37 | \subfile{apr16} 38 | 39 | \subfile{apr22} 40 | \subfile{apr23} 41 | 42 | \subfile{apr29} 43 | \subfile{apr30} 44 | 45 | \subfile{may06} 46 | \subfile{may07} 47 | 48 | \subfile{may13} 49 | \subfile{may14} 50 | 51 | \subfile{may20} 52 | \subfile{may21} 53 | 54 | \subfile{may27} 55 | \subfile{may28} 56 | 57 | \subfile{jun03} 58 | \subfile{jun04} 59 | 60 | \printbibliography 61 | 62 | \end{document} 63 | -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/may14.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/may20.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/may21.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/may27.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/may28.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/radiative_processes/radiative_processes.bib: -------------------------------------------------------------------------------- 1 | 2 | @book{rybickiRadiativeProcessesAstrophysics1979, 3 | title = {Radiative {{Processes}} in {{Astrophysics}}}, 4 | author = {Rybicki, G. B. and Lightman, A. P.}, 5 | date = {1979}, 6 | publisher = {{John Wiley and Sons}}, 7 | url = {http://www.bartol.udel.edu/~owocki/phys633/RadProc-RybLightman.pdf}, 8 | isbn = {978-0-471-82759-7}, 9 | file = {/home/jacopo/zotero/storage/FL3U4N52/Rybicki and Lightman - 1979 - Radiative Processes in Astrophysics.pdf} 10 | } 11 | 12 | 13 | -------------------------------------------------------------------------------- /ap_second_semester/subeq_align.py: -------------------------------------------------------------------------------- 1 | import os 2 | import re 3 | 4 | align_start = "\\begin{align}" 5 | align_end = "\\end{align}" 6 | subeq_start = "\\begin{subequations}" 7 | subeq_end = "\\end{subequations}" 8 | align_newline = "\\\\" 9 | 10 | folder_names = [ 11 | "astroparticle_physics", 12 | "gravitational_physics", 13 | "gravitational_wave_astrophysics", 14 | "multimessenger_astrophysics", 15 | "radiative_processes", 16 | "theoretical_cosmology", 17 | "theoretical_physics" 18 | ] 19 | filenames_regex = "(\\w{3}\\d{2}|\\w{5}\\d{1,2})\\.tex" 20 | 21 | def cpars(s): 22 | return(s.count('{') == s.count('}')) 23 | 24 | def make_subeq_align(filename): 25 | 26 | with open(filename, 'r') as f: 27 | lines = f.readlines() 28 | 29 | for i, line in enumerate(lines): 30 | if (align_start in line 31 | and 32 | subeq_start not in lines[i - 1]): 33 | 34 | newline = False 35 | for pnumber, pline in enumerate(lines[i:]): 36 | if align_newline in pline: 37 | newline = True 38 | if align_end in pline: 39 | j = pnumber + i 40 | break 41 | if (not newline): 42 | pass 43 | else: 44 | lines[i] = subeq_start + '\n' + lines[i] 45 | if (cpars(lines[j])): 46 | lines[j] = lines[j] + subeq_end + '\n' 47 | else: 48 | l = lines[j].split('}') 49 | line = '}'.join(l[:-1]) 50 | lines[j] = line + '\n' + subeq_end + '}' + l[-1] + '\n' 51 | 52 | with open(filename, 'w') as f: 53 | f.writelines(lines) 54 | 55 | for folder in folder_names: 56 | for fname in os.listdir(folder): 57 | if re.match(filenames_regex, fname): 58 | make_subeq_align(os.path.join(folder, fname)) 59 | -------------------------------------------------------------------------------- /ap_second_semester/theoretical_cosmology.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/theoretical_cosmology.pdf -------------------------------------------------------------------------------- /ap_second_semester/theoretical_cosmology/apr03.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Friday\\ 2020-4-3, \\ compiled \\ \today} 5 | 6 | 7 | 8 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/theoretical_cosmology/apr16.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Thursday\\ 2020-4-16, \\ compiled \\ \today} 5 | 6 | Plot: figure 1 from \cite[]{planckcollaborationPlanck2018Results2019}, the power spectrum. Error bars seem small, but consider the factor \(\ell (\ell+1)\) (?). 7 | 8 | The resolution could go to \(\ell = 3000\). 9 | 10 | Temperature anisotropies map, also from Planck: the grey part is reconstructed from galactic absorption. 11 | Helpix: software to reconstruct the whole sky, which allows us to calculate the power spectrum. 12 | 13 | We can include the polarization, to distinguish E and B-modes. 14 | B-modes are divergence-free, E-modes are curl-free. 15 | 16 | We would like to take a statistical average over all observers, so we must average over the angles. 17 | 18 | We define the quantity \(\zeta = - \frac{3}{2} \Phi \), which is gauge invariant and connected to inflation. 19 | 20 | Sachs-Wolfe, Doppler term, integrated Sachs-Wolfe. 21 | 22 | We have 23 | % 24 | \begin{align} 25 | \expval{ \delta (\vec{k}) \delta (\vec{k}')} 26 | = (2 \pi )^3 \delta^{(3)} (\vec{k} + \vec{k}') P(k) 27 | \,, 28 | \end{align} 29 | % 30 | where we have plus since we are computing the average of \(\delta \delta \) instead of \(\delta^{*} \delta \). 31 | 32 | The fluctuation of CDM, \(\delta \), is proportional to \(k^2 \Phi \). This is conventional. 33 | 34 | A powerlaw is scale-invariant: if we multiply by \(\lambda \) the powerlaw is multiplied by \(\lambda^{n}\), but it is not distorted. 35 | 36 | \subsection{The free-streaming term} 37 | 38 | Dark energy changes \(\Phi \) and \(\Psi \), making them decrease. 39 | 40 | 41 | 42 | \end{document} 43 | -------------------------------------------------------------------------------- /ap_second_semester/theoretical_cosmology/jun04.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Thursday\\ 2020-6-4, \\ compiled \\ \today} 5 | 6 | More primordial GW. 7 | 8 | \end{document} -------------------------------------------------------------------------------- /ap_second_semester/theoretical_cosmology/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \title{Theoretical cosmology notes} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso 10 | ]{biblatex} 11 | 12 | \addbibresource{theoretical_cosmology.bib} 13 | 14 | \usepackage{subfiles} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | \tableofcontents 20 | 21 | \subfile{mar12} 22 | \subfile{mar13} 23 | 24 | \subfile{mar19} 25 | \subfile{mar20} 26 | 27 | \subfile{mar26} 28 | \subfile{mar27} 29 | 30 | \subfile{apr02} 31 | \subfile{apr03} 32 | 33 | \subfile{apr09} 34 | \subfile{apr10} 35 | 36 | \subfile{apr16} 37 | \subfile{apr17} 38 | 39 | \subfile{apr23} 40 | \subfile{apr24} 41 | 42 | \subfile{apr30} 43 | 44 | \subfile{may07} 45 | \subfile{may08} 46 | 47 | \subfile{may14} 48 | \subfile{may15} 49 | 50 | \subfile{may21} 51 | \subfile{may22} 52 | 53 | \subfile{may20-extra} 54 | 55 | \subfile{may28} 56 | \subfile{may29} 57 | 58 | \subfile{jun04} 59 | 60 | \printbibliography 61 | 62 | \end{document} 63 | -------------------------------------------------------------------------------- /ap_second_semester/theoretical_cosmology/may22.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Friday\\ 2020-5-22, \\ compiled \\ \today} 5 | 6 | We have found that the functional \(Z\), which is the partition function, can be expressed as the functional integral of the exponential of the double integral of the bilinear form \(K^{-1}\) applied to the linear term. 7 | 8 | The average of a functional is given by the expression 9 | % 10 | \begin{align} 11 | \expval{ F [q]} = \int \mathcal{D}q \qty(P [q] F[q]) 12 | \,. 13 | \end{align} 14 | 15 | We can calculate this for any functional if we know its functional derivatives and the \(n\)-point correlation function. 16 | 17 | Plus, we can express the correlation function as a functional derivative of the partition function. 18 | This can be expressed compactly as 19 | % 20 | \begin{align} 21 | \expval{F[q]} = \eval{F[-i \fdv{}{J}] Z[J] }_{J=0} 22 | \,. 23 | \end{align} 24 | 25 | We define the \emph{connected} correlation function by 26 | % 27 | \begin{align} 28 | W[J] = \sum _{n} \frac{i^{n}}{n!} \int \dd{x_1 } \dots \dd{x_{n}} C^{(n)}_{C} (x_1 , \dots, x_{n}) J(x_1) \dots J(x_{n}) 29 | \,, 30 | \end{align} 31 | 32 | where \(W[J] = \log Z[J]\). 33 | From the classical field \(q _{\text{cl}} \) we define \(\Gamma \), and then this gives us the classical equation of motion: 34 | % 35 | \begin{align} 36 | J(x) = - \fdv{\Gamma [q _{\text{cl}}]}{q _{\text{cl}}} 37 | \,. 38 | \end{align} 39 | 40 | Now, we want to make the discussion concrete: from a probability functional to a probability density function. 41 | 42 | We want to compute the probability density \(\dd{P}_{\alpha }\) that the field \(q\) at a point \(\overline{x}\) takes a value between \(\alpha \) and \(\alpha + \dd{\alpha }\). We can compute it as the average of \(\expval{q (\vec{x}) - \alpha }_{q}\). 43 | 44 | 45 | 46 | \end{document} 47 | -------------------------------------------------------------------------------- /ap_second_semester/theoretical_cosmology/may29.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{GW perturbations} 5 | 6 | \marginpar{Friday\\ 2020-5-29, \\ compiled \\ \today} 7 | 8 | We have a background FLRW metric, and a perturbation to this spacetime. 9 | 10 | We need to be careful about the distinction between \emph{gauge} and \emph{coordinate} transformations. 11 | The former are the identity on the background spacetime, the latter are not. 12 | 13 | We classify the perturbations according to how they transform with respect to coordinate transformations in the background spacetime. 14 | 15 | \end{document} 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LL, ls =':') 22 | ax.plot(thetas, LR, ls = '--') 23 | 24 | # ax.legend() 25 | ax.get_yaxis().set_visible(False) 26 | plt.tight_layout() 27 | fig.savefig('angular_distribution.png', format = 'png', dpi=300) -------------------------------------------------------------------------------- /ap_second_semester/theoretical_physics/figures/primed_momentum_potential.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_second_semester/theoretical_physics/figures/primed_momentum_potential.pdf -------------------------------------------------------------------------------- /ap_second_semester/theoretical_physics/figures/primed_momentum_potential.py: -------------------------------------------------------------------------------- 1 | M = .5 2 | omegak=.7 3 | V0 = np.linspace(0, 2*(M+omegak), num=1000) 4 | k = abs(((omegak-V0)**2 - M**2))**(1/2) 5 | plt.plot(V0, k) 6 | plt.xlabel('$V_0$') 7 | plt.ylabel('$\\abs{k_x^{\\prime}}$') 8 | plt.axvline(x=M, label='$M$', ls=':', c='red') 9 | plt.axvline(x=omegak, label='$\\omega_k$', ls=':', c='orange') 10 | plt.legend() 11 | plt.show(block=False) 12 | lsave('primed_momentum_potential') 13 | -------------------------------------------------------------------------------- /ap_second_semester/theoretical_physics/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \title{Theoretical physics notes} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601, 10 | backref=true 11 | ]{biblatex} 12 | 13 | \addbibresource{theoretical_physics.bib} 14 | 15 | \usepackage{subfiles} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | \tableofcontents 21 | 22 | \subfile{mar09} 23 | \subfile{mar10} 24 | 25 | \subfile{mar16} 26 | \subfile{mar17} 27 | 28 | \subfile{mar23} 29 | \subfile{mar24} 30 | 31 | \subfile{mar30} 32 | \subfile{mar31} 33 | 34 | \subfile{apr06} 35 | \subfile{apr07} 36 | 37 | 38 | \subfile{apr20} 39 | \subfile{apr21} 40 | 41 | \subfile{apr27} 42 | \subfile{apr28} 43 | 44 | \subfile{may04} 45 | \subfile{may05} 46 | \subfile{sheet11b} 47 | 48 | \subfile{may11} 49 | \subfile{may12} 50 | 51 | \subfile{sheet14} 52 | \subfile{sheet15} 53 | \subfile{sheet16} 54 | \subfile{sheet17} 55 | 56 | \subfile{exercises7} 57 | 58 | \printbibliography 59 | 60 | \end{document} 61 | -------------------------------------------------------------------------------- /ap_third_semester/astrostat_homework.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_third_semester/astrostat_homework.pdf -------------------------------------------------------------------------------- /ap_third_semester/astrostat_homework/__pycache__/MCMC.cpython-37.pyc: 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import numpy as np 2 | import matplotlib.pyplot as plt 3 | from matplotlib import rc 4 | rc('font',**{'family':'serif','serif':['Palatino']}) 5 | rc('text', usetex=True) 6 | rc('text.latex', preamble=r'''\usepackage{amsmath} 7 | \usepackage{physics} 8 | \usepackage{siunitx} 9 | ''') 10 | 11 | N = 500 12 | ts = np.arange(N) 13 | omegas = np.logspace(-4, 2, num=10000) 14 | h = np.average(np.sin(2 * omegas[:, np.newaxis] * ts[np.newaxis,:]), axis=1) 15 | c = np.average(np.cos(omegas[:, np.newaxis] * ts[np.newaxis,:])**2, axis=1) 16 | s = np.average(np.sin(omegas[:, np.newaxis] * ts[np.newaxis,:])**2, axis=1) 17 | plt.semilogx(omegas, c, lw=.7, label='$c/N$') 18 | plt.semilogx(omegas, h, lw=.7, label='$h/N$') 19 | plt.semilogx(omegas, s, lw=.7, label='$s/N$') 20 | plt.xlabel('$\\omega$') 21 | plt.grid('on') 22 | # plt.axvline(1, label='$\\Delta^{-1}$', c='black', ls=':') 23 | plt.axvline(2 * np.pi / 2, label='$\\pi \\Delta^{-1}$ = Nyquist pulsation', c='black', ls=':', lw=.7) 24 | plt.axvline(1/N, c='black', ls='--', label='$1/(N\\Delta )$', lw=.7) 25 | # plt.axvspan(1/np.pi, np.pi, color='blue', alpha=.1, label='Approximation works well') 26 | plt.legend() 27 | plt.savefig('large_pulsation.pdf') 28 | plt.close() 29 | -------------------------------------------------------------------------------- /ap_third_semester/astrostat_homework/figures/marginalization.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_third_semester/astrostat_homework/figures/marginalization.pdf -------------------------------------------------------------------------------- /ap_third_semester/astrostat_homework/figures/signal.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_third_semester/astrostat_homework/figures/signal.pdf -------------------------------------------------------------------------------- /ap_third_semester/astrostat_homework/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{AstroStatistics and Cosmology Homework} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | \addbibresource{../astrostatistics_cosmology/AstroStatistics_and_Cosmology.bib} 13 | 14 | \usepackage{subfiles} 15 | \setcounter{secnumdepth}{1} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | % \tableofcontents 21 | 22 | % Exercises 1--3 and 7\footnote{It is not finished yet.} are in Jupyter notebooks in the folder \texttt{astrostat\_homework}. 23 | % They can be most easily accessed through the following links: 24 | % \begin{enumerate} 25 | % \item \url{https://nbviewer.jupyter.org/github/jacopok/notes/blob/master/ap_third_semester/astrostat_homework/exercises_123.ipynb} 26 | % \item \url{https://nbviewer.jupyter.org/github/jacopok/notes/blob/master/ap_third_semester/astrostat_homework/exercise_7.ipynb}. 27 | % \end{enumerate} 28 | 29 | \subfile{exercises_456} 30 | \subfile{exercises_89} 31 | \subfile{exercise_10} 32 | 33 | \printbibliography 34 | 35 | \end{document} 36 | -------------------------------------------------------------------------------- /ap_third_semester/astrostatistics_cosmology.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_third_semester/astrostatistics_cosmology.pdf -------------------------------------------------------------------------------- /ap_third_semester/astrostatistics_cosmology/dec21.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Monday\\ 2020-12-21, \\ compiled \\ \today} 5 | 6 | There will be a couple of optional additional lectures uploaded to the Moodle. 7 | 8 | Today we will discuss \cite[]{hobsonCombiningCosmologicalDatasets2002}. 9 | The idea is to combine the \(\chi^2\) for the various experiments with various weights, which are our hyperparameters. 10 | 11 | Do we actually need these hyperparameters, or can we avoid using them by simply adding the \(\chi^2\)? This is a model selection problem. 12 | 13 | In the hyperparameter model the likelihood is not a Gaussian anymore. 14 | The weights must be larger than \(0\), we can take them to be larger than 1 if the corresponding experiment was overestimating its errorbars. 15 | 16 | 17 | \end{document} 18 | -------------------------------------------------------------------------------- /ap_third_semester/astrostatistics_cosmology/dec22.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Tuesday\\ 2020-12-22, \\ compiled \\ \today} 5 | 6 | We discuss \cite[]{heavensModelSelectionForecasting2007}. 7 | 8 | \end{document} 9 | -------------------------------------------------------------------------------- /ap_third_semester/astrostatistics_cosmology/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \title{AstroStatistics and Cosmology} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601, 10 | backref=true 11 | ]{biblatex} 12 | 13 | \addbibresource{AstroStatistics_and_Cosmology.bib} 14 | 15 | \usepackage{subfiles} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | \tableofcontents 21 | 22 | 23 | \subfile{sep28} 24 | \subfile{sep29} 25 | 26 | \subfile{oct05} 27 | \subfile{oct06} 28 | 29 | \subfile{oct12} 30 | \subfile{oct13} 31 | 32 | \subfile{oct19} 33 | \subfile{oct20} 34 | 35 | \subfile{oct26} 36 | \subfile{oct27} 37 | 38 | \subfile{nov02} 39 | \subfile{nov03} 40 | 41 | \subfile{nov09} 42 | \subfile{nov10} 43 | 44 | \subfile{nov16} 45 | \subfile{nov17} 46 | 47 | \subfile{nov23} 48 | \subfile{nov24} 49 | 50 | \subfile{nov30} 51 | \subfile{dec01} 52 | 53 | 54 | \subfile{dec14} 55 | \subfile{dec15} 56 | 57 | \subfile{dec21} 58 | \subfile{dec22} 59 | 60 | 61 | \printbibliography 62 | 63 | \end{document} 64 | 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4, 22 | "nbformat_minor": 2, 23 | "cells": [ 24 | { 25 | "cell_type": "code", 26 | "execution_count": null, 27 | "metadata": {}, 28 | "outputs": [], 29 | "source": [ 30 | "{r,t,\\phi,\\theta}::Coordinate;\n", 31 | "{\\mu,\\nu,\\sigma,\\lambda,\\kappa,\\chi,\\gamma,\\xi}::Indices(values={t,r,\\phi,\\theta}, position=fixed);\n", 32 | "\\partial{#}::PartialDerivative;\n", 33 | "g_{\\mu\\nu}::Metric.\n", 34 | "g^{\\mu\\nu}::InverseMetric.\n", 35 | "T_{\\mu\\nu}::Symmetric.\n", 36 | "{A, B, \\rho, P}::Depends(r)" 37 | ] 38 | }, 39 | { 40 | "cell_type": "code", 41 | "execution_count": null, 42 | "metadata": {}, 43 | "outputs": [], 44 | "source": [] 45 | } 46 | ] 47 | } -------------------------------------------------------------------------------- /ap_third_semester/compact_objects/calculations/quick_calculations.py: -------------------------------------------------------------------------------- 1 | #%% 2 | 3 | import numpy as np 4 | 5 | print(1 - np.sqrt(8 / 9)) 6 | print(1 / 12) 7 | 8 | #%% 9 | 10 | theta = np.linspace(0, 2* np.pi) 11 | Cs = np.linspace(0, 2, num=10) 12 | 13 | ax = plt.subplot(projection='polar') 14 | ax.set_theta_zero_location('N') 15 | 16 | for C in Cs: 17 | ax.plot(theta, C * np.sin(theta)**2) 18 | 19 | # %% 20 | 21 | -------------------------------------------------------------------------------- /ap_third_semester/compact_objects/dec22.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_third_semester/compact_objects/figures/NS-interior.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_third_semester/compact_objects/figures/NS-interior.png -------------------------------------------------------------------------------- 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np.sqrt(1 + 3 * np.cos(theta)** 2) 16 | 17 | plt.plot(theta, np.sqrt(np.abs(cos_big_theta))) 18 | plt.xlabel('$\\theta$') 19 | plt.ylabel('$T / T_P$') 20 | plt.savefig('NS-temperature.pdf') -------------------------------------------------------------------------------- /ap_third_semester/compact_objects/figures/Rcirc_vs_R1.py: -------------------------------------------------------------------------------- 1 | @np.vectorize 2 | def R1(qtest): 3 | if(.05<=qtest<=2): 4 | return(.38 - .2 * np.log(qtest)) 5 | elif(qtest>2): 6 | return(.426 / (1+qtest)**(1/3)) 7 | else: 8 | return(0) 9 | 10 | q = np.logspace(-1, 1) 11 | 12 | Rcirc = (.5 - .227 * np.log(q) )**4 * (1+q) 13 | plt.plot(q, R1(q), label='R1') 14 | plt.plot(q, Rcirc, label = 'Rcirc') 15 | plt.legend() 16 | plt.show() 17 | -------------------------------------------------------------------------------- /ap_third_semester/compact_objects/figures/alfven-accretion.png: 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preamble=r'''\usepackage{amsmath} 8 | \usepackage{physics} 9 | \usepackage{siunitx} 10 | ''') 11 | import scipy.constants as sc 12 | from astropy.constants import codata2018 as ac 13 | from astropy.constants import iau2015 as aa 14 | import astropy.units as u 15 | from astropy.cosmology import Planck15 as cosmo 16 | import astropy.uncertainty as aun 17 | 18 | x_n = np.logspace(-2.5, 2.5) 19 | Q = (ac.m_n - ac.m_p) 20 | m_n = ac.m_n 21 | m_e = ac.m_e 22 | 23 | R_np = x_n ** 3 * (4 * (1 + x_n ** 2) / (x_n ** 4 + 4 * Q / m_n + 4 * (Q ** 2 - m_e ** 2) / m_n ** 2))**(3 / 2) 24 | 25 | # plt.loglog(x_n, x_n**3 * (1/R_np + 1)) 26 | # plt.loglog(x_n**3 * (1/R_np + 1), R_np) 27 | plt.grid() 28 | plt.loglog(x_n, R_np) 29 | plt.xlabel('$x_n$') 30 | plt.ylabel('$R_{\\text{np}}$') 31 | # plt.savefig('neutron-proton-ratio.pdf') 32 | plt.show() 33 | # %% 34 | 35 | density_unit = u.g/ u.cm**3 36 | 37 | const = (ac.m_p * 8 * np.pi / 3 * (ac.m_p * ac.c / ac.hbar)** 3).to(density_unit) 38 | 39 | rho = const * x_n**3 * (1/R_np + 1) 40 | plt.loglog(rho, R_np) 41 | plt.grid() 42 | plt.xlabel('$\\rho$ (logarithmic, units of g/cm$^3$)') 43 | plt.ylabel('$R_{\\text{np}}$') 44 | plt.savefig('neutron-proton-ratio-density.pdf') 45 | plt.show() 46 | 47 | # %% 48 | -------------------------------------------------------------------------------- /ap_third_semester/compact_objects/figures/p-pdot-diagram.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_third_semester/compact_objects/figures/p-pdot-diagram.png -------------------------------------------------------------------------------- /ap_third_semester/compact_objects/figures/relativisticity_degeneracy.pdf: -------------------------------------------------------------------------------- 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9 | rc('text', usetex=True) 10 | rc('text.latex', preamble=r'''\usepackage{amsmath} 11 | \usepackage{physics} 12 | \usepackage{siunitx} 13 | ''') 14 | 15 | log_T = np.linspace(4, 15) 16 | 17 | urca = 27 + 6 * (log_T - 9) 18 | murca = 21 + 8 * (log_T - 9) 19 | 20 | plt.plot(log_T, urca, label='URCA process') 21 | plt.plot(log_T, murca, label='MURCA process') 22 | plt.xlabel('$\\log_{10} T$ [K]') 23 | plt.ylabel('$\\log_{10} \\epsilon_\\nu $ [erg / cm$^3$ / s]') 24 | plt.legend() 25 | plt.savefig('urca-murca.pdf') -------------------------------------------------------------------------------- /ap_third_semester/compact_objects/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \title{Compact Object Astrophysics} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | \addbibresource{Compact_Objects.bib} 13 | 14 | \usepackage{subfiles} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | \tableofcontents 20 | 21 | 22 | \subfile{sep29} 23 | \subfile{sep30} 24 | 25 | \subfile{oct06} 26 | \subfile{oct07} 27 | 28 | \subfile{oct13} 29 | \subfile{oct14} 30 | 31 | \subfile{oct20} 32 | \subfile{oct21} 33 | 34 | \subfile{oct27} 35 | \subfile{oct28} 36 | 37 | \subfile{nov03} 38 | \subfile{nov04} 39 | 40 | \subfile{nov10} 41 | \subfile{nov11} 42 | 43 | \subfile{nov17} 44 | \subfile{nov18} 45 | 46 | \subfile{nov24} 47 | \subfile{nov25} 48 | 49 | \subfile{dec01} 50 | \subfile{dec02} 51 | 52 | \subfile{dec09} 53 | 54 | \subfile{dec15} 55 | \subfile{dec16} 56 | 57 | \subfile{dec22} 58 | \subfile{dec23} 59 | 60 | 61 | \printbibliography 62 | 63 | \end{document} 64 | -------------------------------------------------------------------------------- /ap_third_semester/compact_objects/sep29.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Tuesday\\ 2020-9-29, \\ compiled \\ \today} 5 | 6 | \subsection*{Introduction} 7 | 8 | Tuesdays and Wednesday at 14.30 PM in room P1A, Paolotti building. 9 | 22 people. 10 | 11 | This course overlaps with ``Computational Astrophysics'' by professor Mapelli. 12 | 13 | The examination is an oral one, done either online or live. 14 | 15 | We start with a brief overview of the final fates of massive stars. 16 | We have white dwarfs, neutron stars and black holes under the category of ``compact objects'', but white dwarfs are not really that compact. 17 | 18 | We then discuss accretion onto compact objects, and neutron stars. 19 | An open question: what is the EOS of ultradense neutron matter? 20 | 21 | ``Accretion power in astrophysics'', ``The physics of Compact Objects'', ``Astrofisica Relativistica I \& II'', ``Astrofisica delle Alte Energie''. 22 | 23 | \end{document} 24 | -------------------------------------------------------------------------------- /ap_third_semester/early_universe.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/ap_third_semester/early_universe.pdf -------------------------------------------------------------------------------- /ap_third_semester/early_universe/dec23.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_third_semester/early_universe/jan13.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_third_semester/early_universe/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{report} 2 | 3 | \input{../header.tex} 4 | \title{Early Universe Cosmology} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | \addbibresource{Early_Universe.bib} 13 | 14 | \usepackage{subfiles} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | \tableofcontents 20 | 21 | 22 | \subfile{sep28} 23 | \subfile{sep30} 24 | 25 | \subfile{oct05} 26 | \subfile{oct07} 27 | 28 | \subfile{oct12} 29 | \subfile{oct14} 30 | 31 | \subfile{oct19} 32 | \subfile{oct21} 33 | 34 | \subfile{oct26} 35 | \subfile{oct28} 36 | 37 | \subfile{nov02} 38 | \subfile{nov04} 39 | 40 | \subfile{nov09} 41 | \subfile{nov11} 42 | 43 | \subfile{nov16} 44 | \subfile{nov18} 45 | 46 | \subfile{nov23} 47 | \subfile{nov25} 48 | 49 | \subfile{nov30} 50 | \subfile{dec02} 51 | 52 | \subfile{dec09} 53 | 54 | \subfile{dec14} 55 | \subfile{dec16} 56 | 57 | \subfile{dec21} 58 | \subfile{dec22} 59 | \subfile{dec23} 60 | 61 | \subfile{jan11} 62 | \subfile{jan13} 63 | 64 | \printbibliography 65 | 66 | \end{document} 67 | -------------------------------------------------------------------------------- /ap_third_semester/early_universe/sep28.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /ap_third_semester/subeq_align.py: -------------------------------------------------------------------------------- 1 | import os 2 | import re 3 | 4 | align_start = "\\begin{align}" 5 | align_end = "\\end{align}" 6 | subeq_start = "\\begin{subequations}" 7 | subeq_end = "\\end{subequations}" 8 | align_newline = "\\\\" 9 | 10 | folder_names = [ 11 | "astroparticle_physics", 12 | "gravitational_physics", 13 | "gravitational_wave_astrophysics", 14 | "multimessenger_astrophysics", 15 | "radiative_processes", 16 | "theoretical_cosmology", 17 | "theoretical_physics" 18 | ] 19 | filenames_regex = "(\\w{3}\\d{2}|\\w{5}\\d{1,2})\\.tex" 20 | 21 | def cpars(s): 22 | return(s.count('{') == s.count('}')) 23 | 24 | def make_subeq_align(filename): 25 | 26 | with open(filename, 'r') as f: 27 | lines = f.readlines() 28 | 29 | for i, line in enumerate(lines): 30 | if (align_start in line 31 | and 32 | subeq_start not in lines[i - 1]): 33 | 34 | newline = False 35 | for pnumber, pline in enumerate(lines[i:]): 36 | if align_newline in pline: 37 | newline = True 38 | if align_end in pline: 39 | j = pnumber + i 40 | break 41 | if (not newline): 42 | pass 43 | else: 44 | lines[i] = subeq_start + '\n' + lines[i] 45 | if (cpars(lines[j])): 46 | lines[j] = lines[j] + subeq_end + '\n' 47 | else: 48 | l = lines[j].split('}') 49 | line = '}'.join(l[:-1]) 50 | lines[j] = line + '\n' + subeq_end + '}' + l[-1] + '\n' 51 | 52 | with open(filename, 'w') as f: 53 | f.writelines(lines) 54 | 55 | for folder in folder_names: 56 | for fname in os.listdir(folder): 57 | if re.match(filenames_regex, fname): 58 | make_subeq_align(os.path.join(folder, fname)) 59 | -------------------------------------------------------------------------------- /astronomy/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/astronomy/main.pdf -------------------------------------------------------------------------------- /astronomy/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{header.tex} 4 | \title{Interdisciplinary Astronomy} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | \addbibresource{Interdisciplinary_Astronomy.bib} 13 | 14 | \usepackage{subfiles} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | 20 | \subfile{apr07} 21 | \subfile{apr08} 22 | \subfile{apr09} 23 | \subfile{apr15} 24 | \subfile{apr16} 25 | 26 | \subfile{may05} 27 | \subfile{may06} 28 | 29 | \subfile{may12} 30 | 31 | \printbibliography 32 | 33 | \end{document} 34 | -------------------------------------------------------------------------------- /astronomy/project.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/astronomy/project.pdf -------------------------------------------------------------------------------- /astronomy/project/data/farnese.csv: -------------------------------------------------------------------------------- 1 | DEVIATION 2 | 0.5 3 | 9.1 4 | 1.4 5 | 0.1 6 | 2.6 7 | -4.9 8 | 2.5 9 | 7 10 | 0.9 11 | 3.1 12 | 0.5 13 | 0.2 14 | 4.8 15 | -2.1 16 | -4.4 17 | 1.3 18 | 2.3 19 | -6.8 20 | -5.5 21 | -4.8 22 | -1.1 23 | -0.6 24 | -3 25 | 5.3 26 | 2.5 27 | -3.2 28 | 3.4 29 | 0.3 30 | -4.8 31 | 1.6 32 | -3.5 33 | 4.7 34 | -1.5 35 | -1.3 36 | 2.7 37 | 0.3 38 | -1.9 39 | -5.7 40 | -0.5 41 | -1.7 42 | 1 43 | -0.5 44 | 3.4 45 | 4.6 46 | -1 47 | 0.3 48 | 1.7 49 | -------------------------------------------------------------------------------- /astronomy/project/figures/Ursa.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/astronomy/project/figures/Ursa.pdf -------------------------------------------------------------------------------- /astronomy/project/figures/aries_on_colure_184_BC.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/astronomy/project/figures/aries_on_colure_184_BC.png 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\usepackage{subfiles} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | 21 | \subfile{content} 22 | 23 | \printbibliography 24 | 25 | \end{document} 26 | -------------------------------------------------------------------------------- /info_Q/montangero/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/info_Q/montangero/main.pdf -------------------------------------------------------------------------------- /info_Q/montangero/main_montangero.tex: -------------------------------------------------------------------------------- 1 | \documentclass{article} 2 | 3 | \input{../header.tex} 4 | \usepackage{subfiles} 5 | 6 | \title{Montangero's lectures} 7 | \author{Notes taken by Jacopo Tissino} 8 | \date{June 2019} 9 | 10 | \begin{document} 11 | 12 | \maketitle 13 | 14 | \subfile{montangero1.tex} 15 | 16 | \subfile{montangero2.tex} 17 | 18 | \subfile{12-6-19.tex} 19 | 20 | \end{document} 21 | -------------------------------------------------------------------------------- /info_Q/zanardi/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/info_Q/zanardi/main.pdf -------------------------------------------------------------------------------- /info_Q/zanardi/main_zanardi.tex: -------------------------------------------------------------------------------- 1 | \documentclass{article} 2 | 3 | \input{../header.tex} 4 | 5 | \usepackage{subfiles} 6 | 7 | \title{Zanardi's lectures} 8 | \author{Notes taken by Jacopo Tissino} 9 | \date{June 2019} 10 | 11 | \begin{document} 12 | 13 | \maketitle 14 | 15 | \subfile{zanardi1.tex} 16 | 17 | \subfile{zanardi2.tex} 18 | 19 | \subfile{zanardi3.tex} 20 | 21 | \subfile{zanardi4.tex} 22 | 23 | \end{document} 24 | -------------------------------------------------------------------------------- /phd_courses/experimental_gravitation_cosmology.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_gravitation_cosmology.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_gravitation_cosmology/feb02.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{Einstein Telescope} 5 | 6 | \marginpar{Wednesday\\ 2022-2-2} 7 | 8 | It's like a xylophone: in each cavity we have several interferometers. 9 | 10 | While it improves a lot when working in a network, 11 | it can also work alone. 12 | 13 | It is now considered to be a priority for Europe. 14 | The main sites in competitions are Italy and the Netherlands, and the decision 15 | will be made three years from now. 16 | 17 | Cosmic Explorer is behind Europe, but the Americans are typically fast once 18 | they get their funding. 19 | 20 | This instrument will allow us to look at the Early Universe! 21 | 22 | The rate of BNS mergers \emph{heavily} depends on how efficient the common envelope 23 | phase is at ejecting mass. 24 | 25 | High latitude emission, from components emitted not along the line of sight! 26 | 27 | In GR, GW luminosity distance and EM luminosity distance are the same; 28 | this may not be true in modified gravity models. 29 | 30 | \todo[inline]{The main uncertainty in this will be on the intrinsic luminosity 31 | of the GW and EM signals, right? } 32 | 33 | LGWA would have been able to detect GW170817 one year before! 34 | 35 | \end{document} -------------------------------------------------------------------------------- /phd_courses/experimental_gravitation_cosmology/feb03.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /phd_courses/experimental_gravitation_cosmology/figures/__pycache__/make_all_figures.cpython-38.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_gravitation_cosmology/figures/__pycache__/make_all_figures.cpython-38.pyc -------------------------------------------------------------------------------- /phd_courses/experimental_gravitation_cosmology/figures/husini.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_gravitation_cosmology/figures/husini.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_gravitation_cosmology/figures/make_all_figures.py: -------------------------------------------------------------------------------- 1 | from tqdm import tqdm 2 | import matplotlib.pyplot as plt 3 | from matplotlib import rc 4 | rc('font',**{'family':'serif','serif':['Palatino']}) 5 | rc('text', usetex=True) 6 | rc('text.latex', preamble=r'''\usepackage{amsmath} 7 | \usepackage{physics} 8 | \usepackage{siunitx} 9 | ''') 10 | rc('figure', dpi=150) 11 | 12 | 13 | def plot_and_save(plotting_func): 14 | plotting_func() 15 | plt.savefig(str(plotting_func.__name__).split(sep='.')[0] + '.pdf', bbox_inches='tight', pad_inches = 0) 16 | 17 | 18 | if __name__ == "__main__": 19 | from polarization import polarization 20 | from squeezing import husini 21 | 22 | plotter_list = [ 23 | polarization, 24 | husini, 25 | ] 26 | 27 | for plotting_func in tqdm(plotter_list): 28 | plot_and_save(plotting_func) -------------------------------------------------------------------------------- /phd_courses/experimental_gravitation_cosmology/figures/polarization.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_gravitation_cosmology/figures/polarization.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_gravitation_cosmology/figures/polarization.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | 4 | def vector_field(x, y, h_p=1, h_c=0): 5 | 6 | # x_new = x * (1 + h_p * expon) + y * h_c * expon 7 | # y_new = y * (1 - h_p * expon) + x * h_c * expon 8 | 9 | matrix = np.array([ 10 | [h_p, h_c], 11 | [h_c, - h_p] 12 | ]) 13 | 14 | return np.einsum('ij, jkl->ikl', matrix, np.stack((x, y), axis=0)) 15 | 16 | def polarization(): 17 | 18 | xs = np.linspace(-1, 1) 19 | ys = np.linspace(-1, 1) 20 | 21 | X, Y = np.meshgrid(xs, ys) 22 | 23 | vectors = vector_field(X, Y) 24 | 25 | plt.streamplot(X, Y, *vectors, density=1.4, color=np.linalg.norm(vectors, axis=0), cmap = plt.get_cmap('inferno')) 26 | plt.xlabel('$x$ [arbitrary units]') 27 | plt.ylabel('$y$ [arbitrary units]') 28 | plt.xticks(ticks=None) 29 | plt.yticks(ticks=None) 30 | 31 | 32 | if __name__ == "__main__": 33 | from make_all_figures import plot_and_save 34 | plot_and_save(polarization) -------------------------------------------------------------------------------- /phd_courses/experimental_gravitation_cosmology/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Experimental Gravitation and Cosmology} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | \addbibresource{GW.bib} 13 | 14 | \usepackage{subfiles} 15 | \setcounter{secnumdepth}{1} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | % \tableofcontents 21 | 22 | \subfile{nov17} 23 | 24 | \subfile{nov22} 25 | \subfile{nov23} 26 | 27 | \subfile{dec03} 28 | 29 | \subfile{dec06} 30 | 31 | 32 | \subfile{dec20} 33 | \subfile{dec21} 34 | \subfile{dec22} 35 | 36 | \subfile{jan10} 37 | \subfile{jan11} 38 | \subfile{jan13} 39 | \subfile{jan14} 40 | 41 | \subfile{jan17} 42 | \subfile{jan21} 43 | 44 | \subfile{jan25} 45 | 46 | \subfile{feb02} 47 | \subfile{feb03} 48 | 49 | \printbibliography 50 | 51 | \end{document} 52 | -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle.pdf: -------------------------------------------------------------------------------- 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u.cm**3 9 | 10 | n = (ac.N_A * Z * rho / A / ac.u).si 11 | z = 1 12 | 13 | 14 | def bethe_bloch_func(beta): 15 | gamma = 1/ np.sqrt(1 - beta**2) 16 | 17 | prefactor = ( 18 | 4 * np.pi 19 | / (ac.m_e * ac.c**2) 20 | * n * z**2 21 | / beta**2 22 | * (ac.e**2 23 | / (4 * np.pi * ac.eps0) 24 | )**2 25 | ).si 26 | 27 | return prefactor * 28 | 29 | def bethe_bloch(): 30 | beta = np.logspace(.1, 3) 31 | 32 | 33 | def energy_loss(): 34 | pass 35 | 36 | if __name__ == "__main__": 37 | from make_all_figures import plot_and_save 38 | plot_and_save(bethe_bloch) 39 | plot_and_save(energy_loss) -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/figures/cosmic_ray_diffusion.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_high_energy_astroparticle/figures/cosmic_ray_diffusion.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/figures/cosmic_rays_energies.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_high_energy_astroparticle/figures/cosmic_rays_energies.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/figures/cosmic_rays_energies.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | 4 | energies = np.logspace(-1, 11) 5 | THR = 1e6 6 | SCALING = 1.8e4 7 | 8 | # Formula from PDG 2020, page 219 9 | 10 | @np.vectorize 11 | def flux(E): 12 | if E < THR: 13 | return E**(-2.7) * (THR)**(2.7-3) * SCALING 14 | else: 15 | return E**(-3) * SCALING 16 | 17 | def cosmic_rays_energies(): 18 | plt.loglog(energies, flux(energies)) 19 | plt.grid('on') 20 | plt.xlabel('Energy [GeV]') 21 | plt.ylabel('Flux [$\SI{}{\meter^{-2}\ \second^{-1}\ \steradian^{-1}\ \GeV^{-1}}$]') 22 | 23 | if __name__ == "__main__": 24 | 25 | from make_all_figures import plot_and_save 26 | plot_and_save(cosmic_rays_energies) 27 | -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/figures/make_all_figures.py: -------------------------------------------------------------------------------- 1 | from tqdm import tqdm 2 | import matplotlib.pyplot as plt 3 | from matplotlib import rc 4 | rc('font',**{'family':'serif','serif':['Palatino']}) 5 | rc('text', usetex=True) 6 | rc('text.latex', preamble=r'''\usepackage{amsmath} 7 | \usepackage{physics} 8 | \usepackage{siunitx} 9 | ''') 10 | rc('figure', dpi=150) 11 | 12 | 13 | def plot_and_save(plotting_func): 14 | plotting_func() 15 | plt.savefig(str(plotting_func.__name__).split(sep='.')[0] + '.pdf', bbox_inches='tight', pad_inches = 0) 16 | 17 | if __name__ == "__main__": 18 | 19 | from cosmic_rays_energies import cosmic_rays_energies 20 | from angular_distribution_shift import angular_distribution_shift 21 | from rapidity import rapidity 22 | from bethe_bloch import bethe_bloch 23 | 24 | plotter_list = [ 25 | cosmic_rays_energies, 26 | angular_distribution_shift, 27 | rapidity, 28 | bethe_bloch 29 | ] 30 | 31 | for plotting_func in tqdm(plotter_list): 32 | plot_and_save(plotting_func) -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/figures/rapidity.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_high_energy_astroparticle/figures/rapidity.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/figures/rapidity.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | 4 | NUM = int(1e4) 5 | 6 | def pseudo_rapidity(theta: np.ndarray): 7 | return - np.log(np.arctan(theta / 2)) 8 | 9 | def rapidity(): 10 | thetas = np.linspace(0, np.pi, num=NUM) 11 | plt.plot(thetas, pseudo_rapidity(thetas)) 12 | plt.grid('on') 13 | 14 | if __name__ == "__main__": 15 | from make_all_figures import plot_and_save 16 | plot_and_save(rapidity) -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/jan19.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \subsection{Neutrino telescopes} 5 | 6 | \marginpar{Wednesday\\ 2022-1-19} 7 | 8 | \begin{enumerate} 9 | \item Muon neutrinos: hadronic shower + muon track; 10 | \item electron neutrinos: hadronic and electromagnetic shower; 11 | \item tau neutrinos: two separate hadronic showers; 12 | \end{enumerate} 13 | 14 | If the neutrino spectrum has a slope \(E^{-2}\), we expect a neutrino rate 15 | % 16 | \begin{align} 17 | R = \int _{E_{\text{min}}}^{ \infty } k E^{-2} \sigma (E) \rho N_A \dd{E} 18 | \,, 19 | \end{align} 20 | % 21 | and we would like \(R V \SI{1}{yr}\) to be at least a few. 22 | The required size comes out to be a few hundred meters. 23 | 24 | We will not be able to distinguish neutrinos from antineutrinos: there 25 | is no way to have such a large magnetic field. 26 | 27 | IceCube saw an excess compared to the expected neutrino background. 28 | 29 | The low-energy regime is up to \SI{100}{GeV}, then up to \SI{0.1}{TeV} is the mid-energy regime, while up from there is high-energy. 30 | 31 | How to distinguish ultra high-energy neutrino-induced events from proton-induced ones? 32 | The idea is to look near the horizon: a proton or nucleus could not have 33 | crossed that much atmosphere. 34 | 35 | \subsection{Hadrons} 36 | 37 | \dots 38 | 39 | \end{document} 40 | -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/jan21.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{Ultra High Energy Cosmic Rays} 5 | 6 | \marginpar{Friday\\ 2022-1-21} 7 | 8 | Current experiments include the Telescope Array and the Pierre Auger observatory. 9 | 10 | The flux is ultra-low: on the order of 1 particle per kilometer squared per 11 | century per year. 12 | The mean free path of a photon as a function of energy rises after the cutoff. 13 | 14 | The modification of the trajectories of ultra-high energy cosmic rays 15 | by galactic magnetic fields becomes very small around \(E \gtrsim \SI{e19}{eV}\). 16 | 17 | The galactic magnetic field is about 3 orders of magnitude larger than the extra-galactic one. 18 | 19 | There are experiments with very high area. 20 | 21 | One can estimate the position of the shower core, and from it get a 22 | determination of the primary energy. 23 | This is done passing through the value of the lateral particle distribution 24 | at a certain lateral distance. 25 | 26 | If we have two ``eyes'' observing fluorescence from the same shower we can get a better 27 | shower reconstruction. 28 | 29 | Auger has both fluorescence detectors and particle detectors. 30 | The particle detectors can be calibrated in energy using the subset of events 31 | which were taken at night. 32 | 33 | The depth of the shower maximum scales logarithmically with the energy; 34 | if we fix the energy the depth changes with \(\log A\). 35 | 36 | Auger detected a large scale anisotropy above \SI{8e18}{eV}! 37 | 38 | 39 | 40 | \end{document} -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{High Energy Experimental Astroparticle Physics} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | \addbibresource{../High Energy Astrophysics.bib} 13 | 14 | \usepackage{subfiles} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | % \tableofcontents 20 | 21 | \subfile{nov08} 22 | \subfile{nov09} 23 | \subfile{nov11} 24 | 25 | \subfile{nov16} 26 | \subfile{nov18} 27 | 28 | \subfile{nov23} 29 | 30 | \subfile{dec02} 31 | 32 | 33 | \subfile{dec16} 34 | 35 | \subfile{dec20} 36 | \subfile{dec21} 37 | 38 | \subfile{jan13} 39 | 40 | \subfile{jan17} 41 | \subfile{jan18} 42 | \subfile{jan19} 43 | \subfile{jan20} 44 | \subfile{jan21} 45 | 46 | 47 | 48 | \printbibliography 49 | 50 | \end{document} 51 | -------------------------------------------------------------------------------- /phd_courses/experimental_high_energy_astroparticle/nov18.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_low_energy_astroparticle.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/calculations/neutron_dipole.py: -------------------------------------------------------------------------------- 1 | from astropy.constants import codata2018 as ac 2 | import astropy.units as u 3 | from astropy.cosmology import Planck15 as cosmo 4 | import numpy as np 5 | 6 | m_u = 2.16 * u.MeV 7 | m_d = 4.67 * u.MeV 8 | m_n = 939.57 * u.MeV 9 | m_p = 938.27 * u.MeV 10 | f = 132 * u.MeV 11 | 12 | alpha = (m_n - m_p) / (m_d - m_u) / 2 13 | g_A = 1.26 14 | 15 | print((m_u * m_d / (m_u + m_d) / m_n**2 * ac.hbar * ac.c).to(u.cm)) 16 | 17 | # from https://arxiv.org/pdf/hep-lat/0508009.pdf 18 | 19 | print(((g_A * alpha / 2 / np.pi**2 / f**2 * (2 *np.log(140 * u.MeV / u.GeV)) + 1/(u.GeV)**2)* (m_u * m_d / (m_u + m_d)) * ac.hbar * ac.c).cgs) 20 | 21 | -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/dec01a.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \subsubsection{Crystal-based experiments} 5 | 6 | \marginpar{Wednesday\\ 2021-12-1} 7 | 8 | % Baracchini 9 | 10 | Crystals are dense, and typically have a large light yield. 11 | 12 | The light they emit is at reasonable wavelengths. 13 | 14 | It is easier to have contamination when the crystals are grown, though. 15 | 16 | The bandgap for these crystals is very large (\SI{5}{eV} to \SI{10}{eV}), 17 | so they are typically doped. 18 | 19 | Pulse shape discrimination does not work at the relevant, low energies. 20 | 21 | DAMA saw an annual modulation, but they did not claim it was WIMPs. 22 | However, they are not sharing their data, which is fishy. 23 | 24 | The relevant unit is the \(\text{dru} = \SI{}{kg^{-1} d^{-1} KeV^{-1}}\). 25 | 26 | \subsection{Bolometers} 27 | 28 | These are detectors which measure the heat and phonons emitted by the nuclear recoil. 29 | 30 | Exams: present an experimental technique which was not discussed in detail in the course. 31 | 32 | \end{document} 33 | -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/dec07.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{Bolometers} 5 | 6 | \marginpar{Tuesday\\ 2021-12-7} 7 | 8 | We need cryogenic detectors to be able to detect such small temperature increases. 9 | 10 | Thermistors are the most mature technology, but they have limited sensitivity. 11 | 12 | Transition edge sensor are operated at the edge of superconductivity. 13 | The readout from a TES can be accomplished with a Superconducting Quantum Interference Device. 14 | 15 | We look at COSINUS, at CRESST, at CDMS. 16 | 17 | Experiments are starting to give up the possibility to do particle identification 18 | and discrimination in order to lower the energy threshold for the DM particle. 19 | 20 | Neganov-Luke effect: while electron-hole pairs are separated by the \(\vec{E}\) field, 21 | and they start moving, they can radiate some energy as phonons. 22 | 23 | With this, they reach an energy threshold of \SI{50}{eV}, by raising the potential 24 | by a lot. As mentioned before, this means that particle identification cannot be done anymore. 25 | 26 | 27 | 28 | \end{document} 29 | -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/dec15.tex: -------------------------------------------------------------------------------- 1 | 2 | \documentclass[main.tex]{subfiles} 3 | \begin{document} 4 | 5 | \subsection{Bolometers} 6 | 7 | \marginpar{Wednesday\\ 2021-12-15} 8 | 9 | Bring down a crystal to very low temperature. 10 | 11 | They take a very long time, like \SI{1}{s}, to be restored to 12 | operating temperature, so they are only useful for rare event searches. 13 | 14 | With tellurium oxide at \SI{10}{mK} 15 | we can get a capacity of the order of \SI{1}{MeV} per \SI{100}{\micro K}. 16 | 17 | The thermometer must be made by doping a Germanium crystal by a very precise amount, 18 | what people typically do is to dope through a neutron beam from a nuclear reactor. 19 | 20 | Lead 210 is produced by cosmic rays, and it decays in \SI{22}{yr}. 21 | So, Roman lead! 22 | 23 | The plot of \(3 \sigma \) discovery against exposure, 24 | with a knee going from linear to square root: how does it come about? 25 | 26 | 27 | 28 | \end{document} 29 | -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/figures/__pycache__/make_all_figures.cpython-38.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_low_energy_astroparticle/figures/__pycache__/make_all_figures.cpython-38.pyc -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/figures/juno_flux.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_low_energy_astroparticle/figures/juno_flux.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/figures/low_background_statistics.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | 4 | N=int(1e5) 5 | 6 | def poisson(): 7 | rng = np.random.default_rng(seed=100) 8 | 9 | t = np.linspace(0, 100) 10 | 11 | rate_sig = 1 12 | rate_bkg = .1 13 | 14 | sig_events = rng.poisson(lam=t * rate_sig, size=(N,) + t.shape) 15 | bkg_events = rng.poisson(lam=t * rate_bkg, size=(N,) + t.shape) 16 | 17 | tot_events = sig_events + bkg_events 18 | 19 | bkg_dev = np.std(bkg_events, axis=0) 20 | sig_avg = np.average(sig_events, axis=0) 21 | 22 | signal_over_avg_bkg = tot_events - t[np.newaxis, :] * rate_bkg 23 | snr = np.average(signal_over_avg_bkg, axis=0) / np.std(signal_over_avg_bkg, axis=0) 24 | 25 | plt.plot(t, snr, label='SNR') 26 | plt.plot(t, t*rate_bkg, label='average $N_B$') 27 | 28 | plt.xlabel('Time') 29 | plt.title(f'Signal rate {rate_sig}, bkg rate {rate_bkg}') 30 | 31 | plt.legend() 32 | 33 | 34 | if __name__ == "__main__": 35 | from make_all_figures import plot_and_save 36 | plot_and_save(poisson) -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/figures/make_all_figures.py: -------------------------------------------------------------------------------- 1 | from tqdm import tqdm # type: ignore 2 | import matplotlib.pyplot as plt # type: ignore 3 | from matplotlib import rc 4 | rc('font',**{'family':'serif','serif':['Palatino']}) 5 | rc('text', usetex=True) 6 | rc('text.latex', preamble=r'''\usepackage{amsmath} 7 | \usepackage{physics} 8 | \usepackage{siunitx} 9 | ''') 10 | rc('figure', dpi=150) 11 | from typing import Callable 12 | 13 | 14 | def plot_and_save(plotting_func : Callable): 15 | plotting_func() 16 | plt.savefig(str(plotting_func.__name__).split(sep='.')[0] + '.pdf', bbox_inches='tight', pad_inches = 0) 17 | plt.close() 18 | 19 | if __name__ == "__main__": 20 | plotter_list : list[Callable] = [] 21 | for plotting_func in tqdm(plotter_list): 22 | plot_and_save(plotting_func) -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/figures/oscillations.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_low_energy_astroparticle/figures/oscillations.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/figures/poisson.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/experimental_low_energy_astroparticle/figures/poisson.pdf -------------------------------------------------------------------------------- /phd_courses/experimental_low_energy_astroparticle/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Low Energy Experimental Astroparticle Physics} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | \addbibresource{Dark Matter.bib} 13 | 14 | \usepackage{subfiles} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | % \tableofcontents 20 | 21 | % Baracchini 22 | 23 | \subfile{nov09} 24 | \subfile{nov11} 25 | 26 | \subfile{nov15} 27 | \subfile{nov16} 28 | 29 | \subfile{nov25} 30 | \subfile{dec01a} 31 | \subfile{dec07} 32 | 33 | \subfile{dec13} 34 | 35 | % Ferroni 36 | 37 | \subfile{nov18} 38 | \subfile{nov19} 39 | 40 | 41 | \subfile{nov29} 42 | \subfile{nov30} 43 | \subfile{dec01} 44 | 45 | \subfile{dec09} 46 | 47 | \subfile{dec15} 48 | 49 | 50 | 51 | 52 | 53 | 54 | \printbibliography 55 | 56 | \end{document} 57 | -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/BH.bib: -------------------------------------------------------------------------------- 1 | 2 | @article{isiTestingBlackholeArea2021, 3 | title = {Testing the Black-Hole Area Law with {{GW150914}}}, 4 | author = {Isi, Maximiliano and Farr, Will M. and Giesler, Matthew and Scheel, Mark A. and Teukolsky, Saul A.}, 5 | date = {2021-07-01}, 6 | journaltitle = {Physical Review Letters}, 7 | shortjournal = {Phys. Rev. Lett.}, 8 | volume = {127}, 9 | number = {1}, 10 | eprint = {2012.04486}, 11 | eprinttype = {arxiv}, 12 | primaryclass = {astro-ph, physics:gr-qc}, 13 | pages = {011103}, 14 | issn = {0031-9007, 1079-7114}, 15 | doi = {10.1103/PhysRevLett.127.011103}, 16 | url = {http://arxiv.org/abs/2012.04486}, 17 | urldate = {2022-06-24}, 18 | abstract = {We present observational confirmation of Hawking's black-hole area theorem based on data from GW150914, finding agreement with the prediction with 97\% (95\%) probability when we model the ringdown including (excluding) overtones of the quadrupolar mode. We obtain this result from a new time-domain analysis of the pre- and postmerger data. We also confirm that the inspiral and ringdown portions of the signal are consistent with the same remnant mass and spin, in agreement with general relativity.}, 19 | archiveprefix = {arXiv}, 20 | keywords = {Astrophysics - High Energy Astrophysical Phenomena,General Relativity and Quantum Cosmology}, 21 | file = {/home/jacopo/Zotero/storage/6MMKBRK6/Isi et al. - 2021 - Testing the black-hole area law with GW150914.pdf;/home/jacopo/Zotero/storage/8LCW92WG/2012.html} 22 | } 23 | 24 | 25 | -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/figures/__pycache__/make_all_figures.cpython-39.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/general_relativity_exercises/figures/__pycache__/make_all_figures.cpython-39.pyc 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-------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/figures/kruskal.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | 4 | def killing_kruskal(): 5 | r_range = np.linspace(-3, 3) 6 | t_range = np.linspace(-3, 3) 7 | 8 | R, T = np.meshgrid(r_range, t_range) 9 | 10 | V = T + R 11 | U = T - R 12 | 13 | plt.quiver(R, T, 0, 2*R) 14 | 15 | plt.plot(r_range, r_range, c='black') 16 | plt.plot(r_range, -r_range, c='black') 17 | 18 | plt.plot(r_range, np.sqrt(r_range**2 + 1), c='black') 19 | plt.plot(r_range, -np.sqrt(r_range**2 + 1), c='black') 20 | 21 | plt.gca().set_aspect('equal') 22 | 23 | plt.xlabel('$R = (V - U) / 2$') 24 | plt.ylabel('$T = (V + U) / 2$') 25 | 26 | if __name__ == "__main__": 27 | from make_all_figures import plot_and_save 28 | plot_and_save(killing_kruskal) -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/figures/make_all_figures.py: -------------------------------------------------------------------------------- 1 | from pathlib import Path 2 | from tqdm import tqdm 3 | import matplotlib.pyplot as plt 4 | from matplotlib import rc 5 | rc('font',**{'family':'serif','serif':['Palatino']}) 6 | rc('text', usetex=True) 7 | rc('text.latex', preamble=r'''\usepackage{amsmath} 8 | \usepackage{physics} 9 | \usepackage{siunitx} 10 | ''') 11 | rc('figure', dpi=150) 12 | 13 | 14 | def plot_and_save(plotting_func): 15 | plotting_func() 16 | this_folder = Path(__file__).parent 17 | plt.savefig(this_folder / (str(plotting_func.__name__).split(sep='.')[0] + '.pdf'), bbox_inches='tight', pad_inches = 0) 18 | plt.close() 19 | 20 | 21 | if __name__ == "__main__": 22 | plotter_list = [] 23 | for plotting_func in tqdm(plotter_list): 24 | plot_and_save(plotting_func) -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/figures/negative_mass_geodesics.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/general_relativity_exercises/figures/negative_mass_geodesics.pdf -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/figures/negative_mass_geodesics.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | cmap = plt.get_cmap('plasma') 4 | 5 | 6 | def negative_mass_geodesics(): 7 | rs = np.logspace(-1, 1, num=1000) 8 | 9 | M = -1 10 | 11 | V_null = lambda r : 1 / 2 / r**2 - M / r**3 12 | V_mass_l = lambda r : - M / r + 1/2/r**2 - M / r**3 13 | V_mass_nol = lambda r : - M / r 14 | 15 | plt.loglog(rs, V_null(rs), c=cmap(.1), label='Null, nonzero $l$') 16 | plt.loglog(rs, V_mass_l(rs), c=cmap(.5), label='Timelike, nonzero $l$') 17 | plt.loglog(rs, V_mass_nol(rs), c=cmap(.9), label='Timelike, zero $l$') 18 | 19 | 20 | plt.xlabel('Radius [units of $M$]') 21 | plt.ylabel('Potential [dimensionless]') 22 | plt.yticks(None) 23 | plt.legend() 24 | 25 | 26 | if __name__ == "__main__": 27 | from make_all_figures import plot_and_save 28 | plot_and_save(negative_mass_geodesics) -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/figures/photon_orbits.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | cmap = plt.get_cmap('plasma') 4 | 5 | def impact_parameter(Vmax): 6 | return 1/ (np.sqrt(Vmax*2)) 7 | 8 | # Vmax = e**2 / l**2 / 2 = 1/2 / b**2 9 | # b**2 = 1 / 2 / Vmax 10 | 11 | def effective_potential(): 12 | rs = np.linspace(2, 8, num=1000) 13 | 14 | V = lambda r : 1 / 2 / r**2 - 1 / r**3 15 | 16 | plt.plot(rs, V(rs), c='black') 17 | 18 | plt.plot(rs, np.ones_like(rs)*1.2*V(3), 19 | label=f'$b=${impact_parameter(1.2*V(3)):.2f}$M$', 20 | c=cmap(.1)) 21 | for r in [3, 5]: 22 | less_rs = np.linspace(r, 8) 23 | plt.plot(less_rs, np.ones_like(less_rs) * V(r), 24 | label=f'$b=${impact_parameter(V(r)):.2f}$M$', 25 | c=cmap(r/6)) 26 | 27 | plt.xlim(0, 8) 28 | plt.xlabel('Radius [units of $M$]') 29 | plt.ylabel('Potential divided by $l^2$ [units of $M^{-2}$]') 30 | plt.yticks(None) 31 | plt.legend() 32 | 33 | 34 | if __name__ == "__main__": 35 | from make_all_figures import plot_and_save 36 | plot_and_save(effective_potential) -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/figures/potential_barrier.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/general_relativity_exercises/figures/potential_barrier.pdf -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/figures/rho_radius.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | 4 | def rho_radius(): 5 | 6 | rho = np.linspace(1/4, 3) 7 | 8 | r = rho * (1 + 1 / 2 / rho)**2 9 | 10 | print(min(r)) 11 | print(min(rho)) 12 | 13 | plt.plot(r, rho) 14 | 15 | 16 | 17 | 18 | if __name__ == "__main__": 19 | from make_all_figures import plot_and_save 20 | plot_and_save(rho_radius) -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/figures/spacetime_ef.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/general_relativity_exercises/figures/spacetime_ef.pdf -------------------------------------------------------------------------------- /phd_courses/general_relativity_exercises/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Black Holes @ GSSI} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | % urldate=iso8601, 10 | backref=true 11 | ]{biblatex} 12 | \emergencystretch=2em 13 | 14 | \addbibresource{BH.bib} 15 | 16 | \usepackage{subfiles} 17 | \setcounter{secnumdepth}{1} 18 | % \numberwithin{equation}{subsection} 19 | \usepackage{chngcntr} 20 | \counterwithout{equation}{section} 21 | 22 | 23 | \begin{document} 24 | 25 | \maketitle 26 | % \tableofcontents 27 | 28 | Exercises for the Black Holes course by professor Sotiriou. 29 | 30 | % \subfile{sheet1} 31 | \subfile{sheet2} 32 | 33 | \printbibliography 34 | 35 | \end{document} 36 | -------------------------------------------------------------------------------- /phd_courses/gravitational_waves.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/gravitational_waves.pdf -------------------------------------------------------------------------------- /phd_courses/gravitational_waves/figures/Screenshot from 2021-06-29 14-16-02.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/gravitational_waves/figures/Screenshot from 2021-06-29 14-16-02.png -------------------------------------------------------------------------------- /phd_courses/gravitational_waves/jul14.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Wednesday\\ 2021-7-14, \\ compiled \\ \today} 5 | 6 | We can write the data as \(d(t) = s(t) + n(t)\); we use \(s\) to denote the \emph{true} signal, while \(h(t)\) is our \emph{model} for the signal. 7 | 8 | The matched-filtering SNR is \((d|h) / \sqrt{(h|h)}\), while the optimal SNR is \(\sqrt{(h|h)}\). 9 | The issue is that \(h\) is a function of many parameters, 10 | % 11 | \begin{align} 12 | h = h (t, \vec{\theta} ) 13 | \qquad \text{where} \qquad 14 | \vec{\theta} = (m_1, m_2, \vec{\chi}_1, \vec{\chi}_2, \Lambda_1 , \Lambda_2 , D_L, \alpha , \delta \dots) 15 | \,, 16 | \end{align} 17 | % 18 | so, how do we estimate \(\vec{\theta}\)? 19 | 20 | We need to introduce a probability density \(\mathbb{P}(\theta )\) which encodes the agreement between the observed signal \(d(t)\) and the prediction \(h(t, \vec{\theta})\). 21 | 22 | How do we define \(\mathbb{P}(\theta )\)? 23 | We start from the residuals, the least squares: we can define the residual as 24 | % 25 | \begin{align} 26 | \chi^2 = (d-h | d-h) 27 | \,. 28 | \end{align} 29 | 30 | The probability density for this reads 31 | % 32 | \begin{align} 33 | \mathbb{P}(\theta ) \propto e^{- \frac{1}{2} \chi^2} 34 | = \exp(- \frac{1}{2} (h-d | h-d)) 35 | \,. 36 | \end{align} 37 | % 38 | which is the probability of having that specific realization of the noise. 39 | 40 | In order to sample this likelihood we need to use some MCMC. 41 | 42 | 43 | 44 | \end{document} -------------------------------------------------------------------------------- /phd_courses/gravitational_waves/jul26.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /phd_courses/gravitational_waves/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Gravitational Waves @ Jena University} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | % \addbibresource{../astrostatistics_cosmology/AstroStatistics_and_Cosmology.bib} 13 | 14 | \usepackage{subfiles} 15 | \setcounter{secnumdepth}{1} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | % \tableofcontents 21 | 22 | % Exercises 1--3 and 7\footnote{It is not finished yet.} are in Jupyter notebooks in the folder \texttt{astrostat\_homework}. 23 | % They can be most easily accessed through the following links: 24 | % \begin{enumerate} 25 | % \item \url{https://nbviewer.jupyter.org/github/jacopok/notes/blob/master/ap_third_semester/astrostat_homework/exercises_123.ipynb} 26 | % \item \url{https://nbviewer.jupyter.org/github/jacopok/notes/blob/master/ap_third_semester/astrostat_homework/exercise_7.ipynb}. 27 | % \end{enumerate} 28 | 29 | \subfile{apr12} 30 | 31 | \subfile{apr19} 32 | 33 | \subfile{apr26} 34 | 35 | \subfile{may03} 36 | 37 | \subfile{may10} 38 | 39 | \subfile{may17} 40 | 41 | \subfile{may24} 42 | 43 | \subfile{may31} 44 | 45 | \subfile{jun07} 46 | 47 | \subfile{jun14} 48 | 49 | \subfile{jun21} 50 | 51 | \subfile{jun28} 52 | \subfile{jul01} 53 | 54 | 55 | \subfile{jul05} 56 | 57 | \subfile{jul12} 58 | \subfile{jul14} 59 | 60 | \subfile{jul26} 61 | 62 | \printbibliography 63 | 64 | \end{document} 65 | -------------------------------------------------------------------------------- /phd_courses/gravitational_waves/may10.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{Quadrupole formula} 5 | 6 | \marginpar{Monday\\ 2021-5-10, \\ compiled \\ \today} 7 | 8 | The self-gravity is denoted as \(\sigma = 2 GM / c^2 R = R_S / R\). 9 | In order for the quadrupole formula to work, we need \(\sigma \ll 1\) (negligible self-gravity) as well as the weak-field limit. 10 | 11 | Hypothesis 1 is that we are far away from the source, compared to the source's linear scale. 12 | 13 | Hypothesis 2 is that the source is slow: 14 | % 15 | \begin{align} 16 | v \sim \frac{\abs{T_{0i}}}{\abs{T_{00} }} \ll c = 1 17 | \,. 18 | \end{align} 19 | 20 | The process is as follows: 21 | \begin{enumerate} 22 | \item we use the two hypotheses to simplify the Green equation; 23 | \item we use the conservation law of \(T_{\mu \nu }\) in flat spacetime \(0 = \partial^{\mu } T_{\mu \nu }\) to further express \(T_{ij} \) in the Green equation in terms of \(T_{00} = \rho c^2\) 24 | \item we project into the TT gauge. 25 | \end{enumerate} 26 | 27 | The retarded time is 28 | % 29 | \begin{align} 30 | u = t - \abs{\vec{x} - \vec{x}'} \approx t- r + \hat{n}\cdot \vec{x}' 31 | \,. 32 | \end{align} 33 | 34 | The far-field approximation is given by expanding \(T_{\mu \nu } (t_r + \hat{n} \cdot \vec{x}' / c)\) around \(t_r\). 35 | 36 | As for the slow-velocity expansion, we do a Fourier transform and expand the exponential 37 | % 38 | \begin{align} 39 | e^{i \omega \qty(t_r + \hat{n} \cdot \vec{x}' /c)} \approx e^{-i \omega t_r} \qty(1 - \frac{i \omega }{c} n_i x^{i} + \dots) 40 | \,. 41 | \end{align} 42 | 43 | Then, in the time domain time derivatives correspond to \(i \omega \) terms. 44 | 45 | \end{document} -------------------------------------------------------------------------------- /phd_courses/gravitational_waves/may24.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /phd_courses/gravitational_waves_exercises.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/gravitational_waves_exercises.pdf -------------------------------------------------------------------------------- /phd_courses/gravitational_waves_exercises/calculations/amplitude_estimation.py: -------------------------------------------------------------------------------- 1 | import astropy.units as u 2 | from astropy.constants import codata2018 as ac 3 | 4 | @u.quantity_input(M='mass', D='length', v='speed') 5 | def estimate_h(M, D, v) -> u.dimensionless_unscaled: 6 | h = ac.G * M / D / ac.c**2 * (v / ac.c)**2 7 | # the units system takes care of all the unit conversion for us 8 | # since we specified that we want the result to be a pure number 9 | return(h) 10 | 11 | print(f'Car crash: {estimate_h (1e3*u.kg, 10*u.m, 100* u.km/u.hr):.0e}') 12 | print(f'Supernova: {estimate_h (1*u.Msun , 2*u.kpc , .2 * ac.c):.0e}') 13 | print(f'Binary BH: {estimate_h (50*u.Msun , 400*u.Mpc , .1 * ac.c):.0e}') -------------------------------------------------------------------------------- /phd_courses/gravitational_waves_exercises/calculations/tidal_deformation.py: -------------------------------------------------------------------------------- 1 | from astropy.constants import codata2018 as ac 2 | import astropy.units as u 3 | import numpy as np 4 | 5 | M = 1.4 * u.Msun 6 | h = 1.6 * u.m 7 | R = 12 * u.km 8 | 9 | @u.quantity_input 10 | def acc_newt(r) -> u.m / u.s**2: 11 | return ac.G * M / r**2 12 | 13 | @u.quantity_input 14 | def acc_gr(r) -> u.m / u.s**2: 15 | return ac.G * M / r**2 / np.sqrt(1 - 2 * ac.G * M / ac.c**2 / r) 16 | 17 | print('Newtonian, approximated') 18 | print((2 * ac.G * M * h / R**3).to(u.m / u.s**2)) 19 | 20 | print('Newtonian, exact') 21 | print(acc_newt(R) - acc_newt(R+h)) 22 | 23 | print('GR, exact') 24 | print(acc_gr(R) - acc_gr(R + h)) 25 | 26 | print('Non-free-fall ratio') 27 | print((acc_gr(R) - acc_gr(R + h)) / (acc_newt(R) - acc_newt(R+h))) -------------------------------------------------------------------------------- /phd_courses/gravitational_waves_exercises/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Gravitational Wave Exercises @ Jena} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601, 10 | backref=true 11 | ]{biblatex} 12 | 13 | \addbibresource{../gravitational_waves/GW.bib} 14 | 15 | \usepackage{subfiles} 16 | \setcounter{secnumdepth}{1} 17 | 18 | \begin{document} 19 | 20 | \maketitle 21 | % \tableofcontents 22 | 23 | Exercises for the Gravitational Waves course. 24 | The exercise sheets can be found on the \href{http://sbernuzzi.gitpages.tpi.uni-jena.de/gw/}{webpage}. 25 | 26 | \subfile{sheet1} 27 | \subfile{sheet2} 28 | \subfile{sheet3} 29 | 30 | % \subfile{tutorial1} 31 | 32 | \printbibliography 33 | 34 | \end{document} 35 | -------------------------------------------------------------------------------- /phd_courses/gravitational_waves_exercises/sheet3.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{Projector properties} 5 | 6 | In order to prove all the properties of the projection tensor \(\Lambda_{ij, kl}\) we can once again make use of Cadabra. 7 | An HTML version of the whole notebook can be found \href{https://jacopok.github.io/projector.html}{here}. 8 | 9 | \end{document} 10 | -------------------------------------------------------------------------------- /phd_courses/gravitational_waves_exercises/tutorial1.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Thursday\\ 2021-4-22, \\ compiled \\ \today} 5 | 6 | We start from a linear approximation on a flat background; 7 | then we will see the GW energy, the quadrupole approximation, and the multipolar expansion. 8 | 9 | Sources are among BBH, general BCO, hyperbolic encounters, 10 | self-rotating objects, supernovae, cosmological background... 11 | 12 | \section{Inertia tensor} 13 | 14 | Free fall in Newtonian gravity: 15 | % 16 | \begin{align} 17 | \frac{1}{2} m \dot{r}^2 + \frac{GMm}{r} =0 18 | \, 19 | \end{align} 20 | % 21 | leads to 22 | % 23 | \begin{align} 24 | \dot{r} = - c \sqrt{ \frac{r_s}{r}} 25 | \,. 26 | \end{align} 27 | 28 | This is solved by 29 | % 30 | \begin{align} 31 | r(t) = r_s^{1/3} (t_0 - t)^{2/3} (3/2)^{2/3} c^{2/3} 32 | \,, 33 | \end{align} 34 | % 35 | so the component \(I_{11} \) can be calculated from the center of the planet: 36 | % 37 | \begin{align} 38 | I_{11} = m r^2 39 | \,, 40 | \end{align} 41 | % 42 | 43 | 44 | \end{document} 45 | -------------------------------------------------------------------------------- /phd_courses/gravitational_waves_exercises/tutorial3.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section*{Exercise 4.1} 5 | 6 | The detector frame is \emph{locally flat}: 7 | we choose coordinates so that \(g_{\mu \nu } (x_0 ) = \eta_{\mu \nu }\) and \(\Gamma^{\mu }_{\nu \rho } (x_0) = 0\). 8 | 9 | This is a \emph{non-relativistic} frame. 10 | The corrections around a point will be of the order (distance to that point) squared. 11 | 12 | By making all the approximations we get 13 | % 14 | \begin{align} 15 | \dv[2]{\xi^{i}}{\tau } = \xi^{\lambda } \partial_{\lambda } \Gamma^{i}_{00} \qty(\dv{x^{0}}{\tau })^2 = 0 16 | \,. 17 | \end{align} 18 | 19 | The Riemann tensor is \emph{invariant} under gauge transformations in linearized GR. 20 | 21 | In the TT gauge we have 22 | % 23 | \begin{align} 24 | R_{i0j0} = - \frac{1}{2 c^2} \ddot{h}_{ij} 25 | \,, 26 | \end{align} 27 | % 28 | so 29 | % 30 | \begin{align} 31 | \ddot{\xi}^{i} - \frac{\ddot{h}_{ij}}{2} \xi_{j} = 0 32 | \,, 33 | \end{align} 34 | % 35 | which is very similar to a Newtonian force, with 36 | % 37 | \begin{align} 38 | F_{i} = m \ddot{\xi}_{i} = \frac{m}{2} \ddot{h}_{j} \xi_{j} 39 | \,. 40 | \end{align} 41 | 42 | 43 | 44 | \end{document} 45 | -------------------------------------------------------------------------------- /phd_courses/numerical_relativity.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/numerical_relativity.pdf -------------------------------------------------------------------------------- /phd_courses/numerical_relativity/jul06.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /phd_courses/numerical_relativity/jul13.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /phd_courses/numerical_relativity/jul27.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /phd_courses/numerical_relativity/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Numerical Relativity @ Jena} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | % \addbibresource{../astrostatistics_cosmology/AstroStatistics_and_Cosmology.bib} 13 | 14 | \usepackage{subfiles} 15 | \setcounter{secnumdepth}{1} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | % \tableofcontents 21 | 22 | \subfile{apr13} 23 | 24 | \subfile{apr20} 25 | 26 | \subfile{apr27} 27 | 28 | \subfile{may04} 29 | 30 | \subfile{may11} 31 | 32 | \subfile{may18} 33 | 34 | \subfile{may25} 35 | 36 | \subfile{jun01} 37 | 38 | \subfile{jun08} 39 | 40 | \subfile{jun15} 41 | 42 | \subfile{jun22} 43 | 44 | \subfile{jun29} 45 | 46 | \subfile{jul06} 47 | 48 | \subfile{jul13} 49 | 50 | \subfile{jul27} 51 | 52 | \printbibliography 53 | 54 | \end{document} 55 | -------------------------------------------------------------------------------- /phd_courses/numerical_relativity_exercises/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Gravitational Wave Exercises @ Jena} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | % \addbibresource{../astrostatistics_cosmology/AstroStatistics_and_Cosmology.bib} 13 | 14 | \usepackage{subfiles} 15 | \setcounter{secnumdepth}{1} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | % \tableofcontents 21 | 22 | Exercises for the Gravitational Waves course. 23 | The exercise sheets can be found on the \href{http://sbernuzzi.gitpages.tpi.uni-jena.de/gw/}{webpage}. 24 | 25 | \subfile{sheet1} 26 | 27 | \printbibliography 28 | 29 | \end{document} 30 | -------------------------------------------------------------------------------- /phd_courses/numerical_relativity_exercises/tutorial2.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Thursday\\ 2021-4-29, \\ compiled \\ \today} 5 | 6 | Try out tridiagonal solvers for Poisson! 7 | 8 | \end{document} -------------------------------------------------------------------------------- /phd_courses/numerical_relativity_exercises/tutorial4.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | 5 | 6 | \end{document} -------------------------------------------------------------------------------- /phd_courses/subeq_align.py: -------------------------------------------------------------------------------- 1 | import os 2 | import re 3 | 4 | align_start = "\\begin{align}" 5 | align_end = "\\end{align}" 6 | subeq_start = "\\begin{subequations}" 7 | subeq_end = "\\end{subequations}" 8 | align_newline = "\\\\" 9 | 10 | from file_creator import folder_names 11 | 12 | folder_names = list(folder_names.values()) 13 | 14 | filenames_regex = "(\\w{3}\\d{2}|\\w{5}\\d{1,2})\\.tex" 15 | 16 | def cpars(s): 17 | return(s.count('{') == s.count('}')) 18 | 19 | def make_subeq_align(filename): 20 | 21 | with open(filename, 'r') as f: 22 | lines = f.readlines() 23 | 24 | for i, line in enumerate(lines): 25 | if (align_start in line 26 | and 27 | subeq_start not in lines[i - 1]): 28 | 29 | newline = False 30 | for pnumber, pline in enumerate(lines[i:]): 31 | if align_newline in pline: 32 | newline = True 33 | if align_end in pline: 34 | j = pnumber + i 35 | break 36 | if (not newline): 37 | pass 38 | else: 39 | lines[i] = subeq_start + '\n' + lines[i] 40 | if (cpars(lines[j])): 41 | lines[j] = lines[j] + subeq_end + '\n' 42 | else: 43 | l = lines[j].split('}') 44 | line = '}'.join(l[:-1]) 45 | lines[j] = line + '\n' + subeq_end + '}' + l[-1] + '\n' 46 | 47 | with open(filename, 'w') as f: 48 | f.writelines(lines) 49 | 50 | for folder in folder_names: 51 | for fname in os.listdir(folder): 52 | if re.match(filenames_regex, fname): 53 | make_subeq_align(os.path.join(folder, fname)) 54 | -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/theoretical_gravitation_cosmology.pdf -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/feb01.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/feb02.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Wednesday\\ 2022-2-2} 5 | 6 | Discussion on the gravitational instability, looking at the fluid velocity, 7 | which is the derivative of \(d = a r\), where \(r\) is comoving. 8 | 9 | Since the total time derivative of \(f(r, t)\) must be the same 10 | we would get with \(f(x, t)\), we must have 11 | % 12 | \begin{align} 13 | \eval{\pdv{f}{t}}_{x= \text{const}} = 14 | \eval{\pdv{f}{t}}_{r= \text{const}} - 15 | H (\vec{r} \cdot \vec{\nabla}_r) f 16 | \,. 17 | \end{align} 18 | 19 | 20 | 21 | \end{document} -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/figures/__pycache__/make_all_figures.cpython-39.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/theoretical_gravitation_cosmology/figures/__pycache__/make_all_figures.cpython-39.pyc -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/figures/hubble_rate.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/theoretical_gravitation_cosmology/figures/hubble_rate.pdf -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/figures/make_all_figures.py: -------------------------------------------------------------------------------- 1 | from tqdm import tqdm 2 | import matplotlib.pyplot as plt 3 | from matplotlib import rc 4 | rc('font',**{'family':'serif','serif':['Palatino']}) 5 | rc('text', usetex=True) 6 | rc('text.latex', preamble=r'''\usepackage{amsmath} 7 | \usepackage{physics} 8 | \usepackage{siunitx} 9 | ''') 10 | rc('figure', dpi=150) 11 | 12 | 13 | def plot_and_save(plotting_func): 14 | plotting_func() 15 | plt.savefig(str(plotting_func.__name__).split(sep='.')[0] + '.pdf', bbox_inches='tight', pad_inches = 0) 16 | plt.close() 17 | 18 | 19 | if __name__ == "__main__": 20 | plotter_list = [] 21 | for plotting_func in tqdm(plotter_list): 22 | plot_and_save(plotting_func) -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/figures/universe_composition.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/theoretical_gravitation_cosmology/figures/universe_composition.pdf -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/jan26.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Wednesday\\ 2022-1-26} 5 | 6 | Final examination: unified with the exam by Andrea Maselli, 7 | we will be given examples of questions which will be asked. 8 | 9 | In the 1980s people thought the universe was flat, 10 | then they thought it was open, 11 | then it came back to flat, 12 | nowadays we do not have that issue anymore. 13 | 14 | \end{document} -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/jan27.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \end{document} -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/jan28.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \marginpar{Friday\\ 2022-1-28} 5 | 6 | 7 | 8 | \end{document} -------------------------------------------------------------------------------- /phd_courses/theoretical_gravitation_cosmology/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Theoretical Gravitation and Cosmology} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | % \addbibresource{} 13 | 14 | \usepackage{subfiles} 15 | \setcounter{secnumdepth}{1} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | % \tableofcontents 21 | 22 | \subfile{nov10} 23 | 24 | \subfile{nov15} 25 | \subfile{nov17} 26 | 27 | \subfile{nov22} 28 | \subfile{nov24} 29 | 30 | \subfile{nov29} 31 | \subfile{dec01} 32 | 33 | \subfile{exercises} 34 | 35 | 36 | \subfile{dec17} 37 | 38 | 39 | 40 | 41 | \subfile{jan24} 42 | \subfile{jan25} 43 | \subfile{jan26} 44 | \subfile{jan27} 45 | \subfile{jan28} 46 | 47 | \subfile{jan31} 48 | \subfile{feb01} 49 | \subfile{feb02} 50 | 51 | \printbibliography 52 | 53 | \end{document} 54 | -------------------------------------------------------------------------------- /phd_courses/theoretical_high_energy_astroparticle.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/theoretical_high_energy_astroparticle.pdf -------------------------------------------------------------------------------- /phd_courses/theoretical_high_energy_astroparticle/figures/__pycache__/make_all_figures.cpython-37.pyc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/theoretical_high_energy_astroparticle/figures/__pycache__/make_all_figures.cpython-37.pyc -------------------------------------------------------------------------------- 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rc('text', usetex=True) 6 | rc('text.latex', preamble=r'''\usepackage{amsmath} 7 | \usepackage{physics} 8 | \usepackage{siunitx} 9 | ''') 10 | rc('figure', dpi=150) 11 | 12 | 13 | def plot_and_save(plotting_func, *args, **kwargs): 14 | plotting_func(*args, **kwargs) 15 | plt.savefig(str(plotting_func.__name__).split(sep='.')[0] + '.pdf', bbox_inches='tight', pad_inches = 0) 16 | plt.close() 17 | 18 | 19 | if __name__ == "__main__": 20 | plotter_list = [] 21 | for plotting_func in tqdm(plotter_list): 22 | plot_and_save(plotting_func) -------------------------------------------------------------------------------- /phd_courses/theoretical_high_energy_astroparticle/figures/shock_acceleration_distribution.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/theoretical_high_energy_astroparticle/figures/shock_acceleration_distribution.pdf 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\input{../header.tex} 4 | \title{High Energy Theoretical Astroparticle Physics} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso, 10 | seconds=true, 11 | ]{biblatex} 12 | 13 | \addbibresource{../High Energy Astrophysics.bib} 14 | 15 | \usepackage{subfiles} 16 | 17 | \DeclareSIUnit\gauss{G} 18 | 19 | \begin{document} 20 | 21 | \maketitle 22 | % \tableofcontents 23 | 24 | \subfile{nov08} 25 | \subfile{nov10} 26 | 27 | \subfile{nov18} 28 | 29 | \subfile{nov24} 30 | \subfile{nov25} 31 | 32 | \subfile{nov30} 33 | 34 | 35 | \subfile{dec14} 36 | 37 | \subfile{dec22} 38 | 39 | \subfile{jan10} 40 | \subfile{jan11} 41 | \subfile{jan14} 42 | 43 | \subfile{jan18} 44 | \subfile{jan19} 45 | \subfile{jan20} 46 | 47 | \subfile{jan24} 48 | 49 | 50 | \printbibliography 51 | 52 | \end{document} 53 | -------------------------------------------------------------------------------- /phd_courses/theoretical_low_energy_astroparticle.pdf: 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import rc 4 | rc('font',**{'family':'serif','serif':['Palatino']}) 5 | rc('text', usetex=True) 6 | rc('text.latex', preamble=r'''\usepackage{amsmath} 7 | \usepackage{physics} 8 | \usepackage{siunitx} 9 | ''') 10 | rc('figure', dpi=150) 11 | 12 | 13 | def plot_and_save(plotting_func): 14 | plotting_func() 15 | plt.savefig(str(plotting_func.__name__).split(sep='.')[0] + '.pdf', bbox_inches='tight', pad_inches = 0) 16 | plt.close() 17 | 18 | 19 | if __name__ == "__main__": 20 | plotter_list = [] 21 | for plotting_func in tqdm(plotter_list): 22 | plot_and_save(plotting_func) -------------------------------------------------------------------------------- /phd_courses/theoretical_low_energy_astroparticle/figures/mass_plot_io.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/phd_courses/theoretical_low_energy_astroparticle/figures/mass_plot_io.pdf 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quantity_support 11 | 12 | m0 = np.logspace(-4, 0) * u.eV 13 | 14 | small_dm = 7.5e-5 * u.eV**2 15 | big_dm = 2.5e-3 * u.eV**2 16 | 17 | def mass_plot_no(): 18 | 19 | m2 = np.sqrt(m0**2 + small_dm) 20 | m3 = np.sqrt(m0**2 + big_dm) 21 | 22 | with quantity_support(): 23 | 24 | plt.loglog(m0, m0) 25 | plt.loglog(m0, m2) 26 | plt.loglog(m0, m3) 27 | plt.loglog(m0, np.sqrt(.7 * m0**2 + .3 * m2**2 + .02 * m3**2)) 28 | 29 | def mass_plot_io(): 30 | 31 | m1 = np.sqrt(m0**2 + big_dm) 32 | m2 = np.sqrt(m1**2 + small_dm) 33 | 34 | with quantity_support(): 35 | 36 | plt.loglog(m0, m0) 37 | plt.loglog(m0, m1) 38 | plt.loglog(m0, m2) 39 | plt.loglog(m0, np.sqrt(.7 * m1**2 + .3 * m2**2 + .02 * m0**2)) 40 | 41 | def majorana_mass(): 42 | 43 | pass 44 | 45 | if __name__ == "__main__": 46 | from make_all_figures import plot_and_save 47 | plot_and_save(mass_plot_no) 48 | plot_and_save(mass_plot_io) -------------------------------------------------------------------------------- /phd_courses/theoretical_low_energy_astroparticle/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{../header.tex} 4 | \title{Low Energy Theoretical Astroparticle Physics} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso8601 10 | ]{biblatex} 11 | 12 | % \addbibresource{} 13 | 14 | \usepackage{subfiles} 15 | \setcounter{secnumdepth}{1} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | % \tableofcontents 21 | 22 | 23 | 24 | 25 | \subfile{dec06} 26 | \subfile{dec07} 27 | \subfile{dec09} 28 | \subfile{dec10} 29 | 30 | \subfile{dec13} 31 | \subfile{dec14} 32 | \subfile{dec15} 33 | \subfile{dec16} 34 | 35 | 36 | 37 | 38 | \subfile{jan25} 39 | \subfile{jan26} 40 | \subfile{jan27} 41 | \subfile{jan28} 42 | 43 | \subfile{jan31} 44 | \subfile{feb01} 45 | \subfile{feb02} 46 | \subfile{feb03} 47 | 48 | \printbibliography 49 | 50 | \end{document} 51 | -------------------------------------------------------------------------------- /quantum_optics/figures/statistics_comparison.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | from astropy.visualization import astropy_mpl_style 4 | from scipy.special import factorial 5 | plt.style.use(astropy_mpl_style) 6 | 7 | def thermal(n, n_bar): 8 | return ((n_bar/(1+nbar)) ** n / (1 + n_bar)) 9 | 10 | def coherent(n, n_bar): 11 | return (np.exp(-n_bar) * n_bar ** n / factorial(n)) 12 | 13 | ns = np.arange(0, 40) 14 | nbars = [6] 15 | width = 0.35 16 | alpha = .8 17 | 18 | for nbar in nbars: 19 | plt.bar(ns, coherent(ns, nbar), label='coherent ' + str(nbar), alpha = alpha, width=width) 20 | plt.bar(ns+width, thermal(ns, nbar), label='thermal ' + str(nbar), alpha = alpha, width=width) 21 | plt.legend() 22 | plt.show() 23 | 24 | def moment(b, v, n): 25 | m = np.average(b, weights=v) 26 | if (n == 1): 27 | return(m) 28 | return (np.sum((b - m)**n * v) / np.sum(v)) 29 | 30 | def analyze(dist, ns, nbar): 31 | bins = dist(ns, nbar) 32 | moments = {'mean': 1, 'variance': 2, 'skewness': 3, 'kurtosis': 4} 33 | for m, num in moments.items(): 34 | print(m, ' = ', moment(ns, bins, num)) 35 | 36 | """ 37 | For a Poissonian (coherent): mean=variance=skewness=nu 38 | and kurtosis = nu*(1+3*nu) 39 | 40 | For the thermal distribution: nth moment is something like exp(n) 41 | """ 42 | -------------------------------------------------------------------------------- /quantum_optics/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/quantum_optics/main.pdf -------------------------------------------------------------------------------- /quantum_optics/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[11pt]{article} 2 | 3 | \input{header.tex} 4 | \title{Quantum optics} 5 | \usepackage[ 6 | backend=biber, 7 | style=alphabetic, 8 | sorting=nyt, 9 | urldate=iso 10 | ]{biblatex} 11 | 12 | \addbibresource{quantum_optics.bib} 13 | 14 | \usepackage{subfiles} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | 20 | \subfile{08jan} 21 | \subfile{10jan} 22 | \subfile{13jan} 23 | \subfile{17jan} 24 | 25 | \subfile{mar16} 26 | \subfile{mar20} 27 | 28 | \subfile{mar27} 29 | 30 | \subfile{apr03} 31 | 32 | \subfile{apr10} 33 | 34 | \subfile{may12} 35 | 36 | \printbibliography 37 | 38 | \end{document} 39 | -------------------------------------------------------------------------------- /quick_files/coulomb/figures/odd_A_fit.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/quick_files/coulomb/figures/odd_A_fit.pdf 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what condition is imposed on the nucleus by \(C<0\): if this is the case, the nucleus will gain energy by deforming. 20 | 21 | Recall \(R_0 = r_0 A^{1/3}\), then 22 | 23 | \begin{subequations} 24 | \begin{align} 25 | \frac{4 r_0^2 A^{2/3} a_s}{4 \pi r_0^2} &< \frac{3Z^2 e^2}{10 \pi r_0 A^{1/3}} \\ 26 | \frac{10 a_s r_0}{3 e^2} &< \frac{Z^2}{A} \\ 27 | 2a_s \qty(\frac{3e^2}{5r_0})^{-1} = \frac{2 a_s}{a_C} &< \frac{Z^2}{A} 28 | \end{align} 29 | \end{subequations} 30 | 31 | 32 | 33 | 34 | \begin{flushright} 35 | Jacopo Tissino, 21 june 2019 36 | \end{flushright} 37 | 38 | 39 | \end{document} 40 | -------------------------------------------------------------------------------- /quick_files/latex_testing/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/quick_files/latex_testing/main.pdf -------------------------------------------------------------------------------- /quick_files/latex_testing/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass{article} 2 | \newcommand{\tabitem}{~~\llap{\textbullet}~~} 3 | \usepackage{makecell} 4 | \renewcommand\theadalign{tl} 5 | \usepackage[margin=1cm]{geometry} 6 | 7 | \begin{document} 8 | 9 | \begin{table} 10 | \centering 11 | \begin{tabular}{llll} 12 | Method & Target & Advantages & Disadvantages \\ 13 | \hline 14 | Communism & The people & \thead{\tabitem Seizing \\ 15 | \tabitem The means of production} & None \\ 16 | Capitalism & Bourgeois filth & None & \thead{\tabitem Exploiting \\ 17 | \tabitem workers} 18 | \end{tabular} 19 | \end{table} 20 | 21 | \end{document} 22 | -------------------------------------------------------------------------------- /quick_files/qft/breit-wigner.png: -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{Astrophysics and detection of gravitational wave sources} 5 | 6 | \marginpar{Monday\\ 2021-2-1, \\ compiled \\ \today} 7 | 8 | Lecture by Alberto Sesana from Milan Bicocca. 9 | 10 | 11 | 12 | 13 | \end{document} -------------------------------------------------------------------------------- /quick_files/seminars/asteroid_bombardment.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{The earliest asteroidal bombardment of the Earth-Moon system} 5 | 6 | A talk by Simone Marchi from the Southwest Research Institute in Boulder, CO. 7 | 8 | \subsection{Bombardment} 9 | 10 | From the Earth's accretion to the Moon forming impact: 90Myr, no samples from this period. 11 | From 90Myr to 600Myr: \emph{late accretion}. The oldest rocks we have started at \(>\SI{600}{Myr} \) after the initial accretion. 12 | 13 | On the moon, we have samples on the surface from 90Myr after the Earth's accretion (will omit ``after the Earth's accretion'' from now on). 14 | This is due to the lack of geological activity. 15 | 16 | There are 2 orders of magnitude more large (r than \(\SI{50}{km}\)) impact craters on the Moon than on the Earth. 17 | 18 | Late heavy bombardment of the moon: there seems to be a spike in the number of asteroids flux. 19 | 20 | Siderophilic elements: stuff that is found in the core, there should be no more of it after the Moon's formation: we see more of it than expected, maybe it got here later? 21 | 22 | There are siderophilic elements in asteroids. 23 | 24 | Spike in Iridium corresponding to the K-T extinction event. 25 | 26 | (then I got tired of taking notes) 27 | 28 | \end{document} 29 | -------------------------------------------------------------------------------- /quick_files/seminars/main.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jacopok/notes/9ded82acbd71015d0fc5dd1da72810348c3f24c9/quick_files/seminars/main.pdf -------------------------------------------------------------------------------- /quick_files/seminars/main.tex: -------------------------------------------------------------------------------- 1 | \documentclass[12pt]{article} 2 | 3 | \input{../header.tex} 4 | 5 | \usepackage{subfiles} 6 | % \usepackage[italian]{babel} 7 | 8 | \title{Various seminars} 9 | % \author{Notes taken by Jacopo Tissino} 10 | 11 | \begin{document} 12 | 13 | \maketitle 14 | 15 | \subfile{svelare_l_universo} 16 | \subfile{gravitational_waves} 17 | \subfile{ice_cube} 18 | 19 | \end{document} 20 | -------------------------------------------------------------------------------- /quick_files/seminars/results_from_alpha_spectrometer.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | \section{The Latest Results from the Alpha Magnetic Spectrometer on the International Space Station} 5 | 6 | \marginpar{Wednesday\\ 2021-11-10, \\ compiled \\ \today} 7 | 8 | A lecture by Nobel Laureate Samuel C.\ C.\ Ting. 9 | 10 | The lecture starts with a history of AMS. 11 | 12 | It measures several properties of incoming cosmic rays. 13 | The largest systematic error is the uncertainty on the absolute scale of the momentum. 14 | 15 | They quantify the momentum uncertainty as \(1/ \abs{p} - 1 / E\), which is of the order of \SI{30}{TeV^{-1}}. 16 | 17 | \todo[inline]{Why is it expressed in this way?} 18 | 19 | AMS searches for DM by looking for annihilations, like \(\chi + \chi \to e^{+} + p + \gamma \dots\). 20 | 21 | The rest of the talk discusses the interpretation of the various spectra. 22 | 23 | Pulsars produce positrons but not antiprotons, yet we observe them in similar amounts. 24 | 25 | There is a cutoff in energy in the positron spectrum, at \(4 \sigma \). 26 | 27 | ``AMS will provide the definitive answer on the nature of dark matter''. 28 | 29 | \todo[inline]{What is the way they are doing non-uniform binning? Are they bins with the same amount of events inside them? Might be because of the \(E^3\) multiplication\dots} 30 | 31 | He puts Fluorine together with B, Be, Li as spallation products\dots is this correct? 32 | 33 | They always work in terms of rigidity, \(R = \text{momentum} / \text{charge}\). 34 | 35 | They measure increasing flux over the years. 36 | Improvement in the instrument? 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/quick_files/throwaway/mar22.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | We define the 4 events as in the figure, and impose: 5 | % 6 | \begin{align} 7 | \operatorname{dist} \qty(A_1, B_2 ) &= 0 \\ 8 | \operatorname{dist} \qty(B_1, A_2 ) &= 0 \\ 9 | \operatorname{dist} \qty(A_1, A_2 ) &= 10 | \operatorname{dist} \qty(B_1, B_2 ) = - \tau 11 | \marginnote{the timelines are time-like, and we are using the mostly plus signature} 12 | \,. 13 | \end{align} 14 | 15 | The velocities are approximated as \(u^{\mu }_A = u^{\mu }_{B} = (1, \vec{0}) \overset{\text{def}}{=} u^{\mu }\). So, for the \(2\) positions we have (to linear order): 16 | % 17 | \begin{align} 18 | x^{\mu }_{i, 2} = x^{\mu }_{i, 1} + \tau u^{\mu } 19 | \,, 20 | \end{align} 21 | % 22 | where \(i = A, B\). 23 | Also, we are assuming \(x^{\mu }_{B, 1} = x^{\mu }_{A, 1} + \dd{x^{\mu }}\). So, we get 24 | % 25 | \begin{align} 26 | \qty(x^{\mu }_{B, 2} - x^{\mu }_{A, 1})^2 &= \qty(x^{\mu }_{A, 1} + \dd{x^{\mu }} + \tau u^{\mu } - x^{\mu }_{A, 1})^2 \\ 27 | &= \qty(\dd{x^{\mu }} + \tau u^{\mu })^2 \\ 28 | &= \dd{x^{\mu }} \dd{x_{\mu }} + 2 \dd{x^{\mu }} \tau u_{\mu } + \tau^2 u^{\mu } u_{\mu } =0 29 | \,. 30 | \end{align} 31 | 32 | Now, for the other distance we have instead 33 | % 34 | \begin{align} 35 | \qty(x^{\mu }_{A, 2} - x^{\mu }_{B, 1})^2 &= 36 | \qty(x^{\mu }_{B, 1} - \dd{x^{\mu }} + \tau u^{\mu } - x^{\mu }_{B, 1})^2 \\ 37 | &= \qty(-\dd{x^{\mu }} + \tau u^{\mu })^2 \\ 38 | &= \dd{x^{\mu }} \dd{x_{\mu }} - 2 \dd{x^{\mu }} \tau u_{\mu } + \tau^2 u^{\mu } u_{\mu } =0 39 | \,, 40 | \end{align} 41 | % 42 | so subtracting the two we get 43 | % 44 | \begin{align} 45 | 4 \dd{x^{\mu }} u_{\mu } \tau = 0 46 | \,, 47 | \end{align} 48 | % 49 | which must hold for any (small) \(\tau \), so we must have \(u_{\mu }\dd{x^{\mu }}=u^{\mu } g_{\mu \nu } \dd{x^{\nu }} = 0\), therefore \(g_{0 \mu } \dd{x^{\mu }}= 0\). 50 | 51 | 52 | \end{document} -------------------------------------------------------------------------------- /quick_files/throwaway/test.tex: -------------------------------------------------------------------------------- 1 | \documentclass[main.tex]{subfiles} 2 | \begin{document} 3 | 4 | Nozione di base: \((A_{\mu \nu })^{\top} = A_{\nu \mu }\). Allora: 5 | % 6 | \begin{align} 7 | (AB)^{\top} \to \qty(A_{\mu \nu } B_{\nu \rho })^{\top} &= 8 | A_{\rho \nu } B_{\nu \mu } \\ 9 | &= \qty(A_{\nu \rho })^{\top} \qty(B_{\mu \nu })^{\top} \\ 10 | & \to B^{\top} A ^{\top} 11 | \,, 12 | \end{align} 13 | % 14 | e con gli aggiunti è la stessa cosa, aggiungi la coniugazione.. 15 | 16 | \end{document} --------------------------------------------------------------------------------