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94 lines
3.1 KiB
Python
94 lines
3.1 KiB
Python
#!/usr/bin/env python
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"""
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Main: Compute Relative Area
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Computes the relative area covered bu the curves for different energies, to
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study ordered and chaotic regimes.
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@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
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@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
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de Strasbourg, UMR 7550, F-67000 Strasbourg, France
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@ Date: 2025-01-01
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Licence:
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Order and Chaos in a 2D potential
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Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
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Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
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main_area.py
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Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
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Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see https://www.gnu.org/licenses/.
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"""
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import numpy as np
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from scipy.optimize import curve_fit
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import potentials as pot
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import energies as ene
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import integrator as itg
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import initial_conditions as init
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import poincare_sections as pcs
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OUT_DIR = "./Output/"
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FILENAME_PREFIX = "phase_separation_"
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EXTENSION = ".csv"
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DEFAULT_N_iter = int(1e5)
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DEFAULT_N_part = 200
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DEFAULT_h = 0.005
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E_all = np.linspace(1/100, 1/6, 20)
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def compute_mu(E: float,
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N_iter: int = DEFAULT_N_iter,
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N_part: int = DEFAULT_N_part,
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h: float = DEFAULT_h) -> tuple:
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"""
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Computes the phase-space squared distances for particles of given energy E.
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@params:
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- E: the total energy of each particles
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- N_iter: the number of iteration
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- N_part: the number of particles
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- h: integration steps
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@returns:
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- mu: phase-space squared distance
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"""
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W_1, W_2 = init.n_energy_2part(pot.hh_potential, N_part, E)
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t_1, positions_1 = itg.rk4(0, W_1, h, N_iter, pot.hh_evolution)
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x_1 = positions_1[:, 0, 0]
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y_1 = positions_1[:, 0, 1]
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u_1 = positions_1[:, 1, 0]
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v_1 = positions_1[:, 1, 1]
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t_2, positions_2 = itg.rk4(0, W_2, h, N_iter, pot.hh_evolution)
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x_2 = positions_2[:, 0, 0]
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y_2 = positions_2[:, 0, 1]
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u_2 = positions_2[:, 1, 0]
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v_2 = positions_2[:, 1, 1]
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dist_sq = (x_2[-25:] - x_1[-25:])**2 \
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+ (y_2[-25:] - y_1[-25:])**2 \
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+ (u_2[-25:] - u_1[-25:])**2 \
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+ (v_2[-25:] - v_1[-25:])**2
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mu = np.sum(dist_sq, axis=0)
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return mu
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if __name__ == "__main__":
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mu_all = []
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for i in range(len(E_all)):
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mu = compute_mu(E_all[i])
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filename = OUT_DIR + FILENAME_PREFIX\
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+ str(i) + EXTENSION
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np.savetxt(filename, mu)
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