Code and data associated with the paper "Non-reciprocal phase transitions"

This record contains the code needed to reproduce the main results of the paper Non-reciprocal phase transitions, Michel Fruchart, Ryo Hanai, Peter B. Littlewood, Vincenzo Vitelli, Nature (2021) [ doi:10.1038/s41586-021-03375-9 ] [ arXiv:2003.13176 ]

The scripts use Mathematica (Mathematica 12.2.0, WolframScript 1.5.0), Julia (version 1.5.0), and Python (version 3.8.8).
Some of the numerical simulations are performed using Dedalus (version 2.1810 ; https://dedalus-project.org).

All code is released under the 2-clause BSD license (see LICENSE), except the file complex_derivative.wl (CC BY-SA 4.0, see details in the file).

Below, we give a list of the files corresponding to each figure.

Main text

• Fig. 1:
  •  - ab: nothing
  •  - cd: vicsek/* [ plot: same directory ]
  •  - ef: nothing
  •  - ghi: nothing
• Fig. 2:
  •  - abc: compute_phase_diagram.wl and analytical_phase_boundaries.wl [ plot: figure_phase_diagram.ipynb ]
  •  - de: nothing
  •  - fg: compute_spectrogram.wl [ plot: figure_frequencies_steady_state.ipynb ]
• Fig. 3:
  •  - a: compute_chiral_stability_diagram.wl [ plot: figure_stability_diagram_with_chiral.ipynb ]
  •  - b: nothing
  •  - c: growth_rate_momentum_space.wl [ plot: figure_growth_rate_kspace.ipynb ]
  •  - def: dedalus_cluster/* [ plot: figure_movie_patterns_data_analysis_dedalus.ipynb ]
• Fig. 4: nothing

Methods

• EDF1: nothing
• EDF2: kuramoto_sqrtn/* [ plot: figure_kuramoto_sqrtN.ipynb ]
• EDF3: nothing
• EDF4: kuramoto_ao_Lop.nb [ plot: figure_kuramoto_phase_diagram.ipynb ]
• EDF5: kuramoto_ao_hysteresis.nb [ plot: figure_kuramoto_hysteresis.ipynb ]
• EDF6: coupled_swift_hohenberg.py [ plot: figure_coupled_sh.ipynb ]
• EDF7: parity_breaking_fingering.nb [ plot: figure_si_exceptional_point_jacobian_fingering.ipynb ]

SI

• S1: nothing
• S2: same as main Fig. 1cd
• S3: nothing
• S4: generalized_system_phase_diagram.wl [ plot: figure_si_effect_perturbations_O2.ipynb ]
• S5: nothing
• S6: nothing
• S7: flocking_aligned_chiral_growth_rate_si_fig_data.wl [ plot: figure_growth_rate_chiral_transition.ipynb ]
• S8: swap_transition_growth_rates.wl [ plot: figure_si_growth_rate_swap_transition.ipynb ]
• S9: simplified_bifurcation_diagram_compute_data.nb [ plot: figures_si_bifurcation_diagram.ipynb ]
• S10: same as S7
• S11: kuramoto_comparison_mean_field/* [ plot: same directory ]
• S12: same as EDF2
• S13: same as S11
• S14: nothing
• S15: dynamical_system_3D_O3.nb [ plot: figure_si_EP_O3.ipynb ]
• S16: laser_ep.nb [ plot: figure_si_EP_laser.ipynb ]
• S17: nothing
• S18: same as main Fig. 3def
• S19: linear_stability_hydro_simus.wl [ plot: figure_si_linear_stability_hydro_simus.ipynb ]