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2025-01-19 18:09:01 +01:00
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commit 503017ac91
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67
Source/TODEL_area.py
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@@ -1,67 +0,0 @@
import numpy as np
import matplotlib.pyplot as plt
import potentials as pot
import integrator as itg
import initial_conditions as init
# Parameters
h = 0.01 # Step size for integrator
N_inter = 500 # Number of iterations for distance calculation
eps = 1e-3 # Perturbation distance
mu_c = 0.6 # Threshold for classifying ergodic vs regular
energy_values = np.array([0.01, 0.02, 0.04, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18])
N_PART = 100
def classify_point(P1, P1_prime):
pos_t1, positions1 = itg.rk4(0, P1, h, N_inter, pot.hh_evolution)
pos_t2, positions2 = itg.rk4(0, P1_prime, h, N_inter, pot.hh_evolution)
# Compute the sum of squared distances (μ)
mu = 0
for i in range(N_inter):
y1, y_dot1 = positions1[i, 0, 1], positions1[i, 1, 1]
y2, y_dot2 = positions2[i, 0, 1], positions2[i, 1, 1]
x1, x_dot1 = positions1[i, 0, 0], positions1[i, 1, 0]
x2, x_dot2 = positions2[i, 0, 0], positions2[i, 1, 0]
squared_distance = (np.sqrt((x2 - x1)**2 + (y2 - y1) ** 2 + (x_dot2 - x_dot1) ** 2 +(y_dot2 - y_dot1) ** 2))**2
mu += squared_distance
return mu
# Analyze for different energy values
relative_areas = []
for E in energy_values:
# Generate initial conditions for the given energy level
initial_conditions = init.n_energy_part(pot.hh_potential, N=N_PART, E=E)
initial_conditions_eps = initial_conditions.copy()
initial_conditions_eps[0,1] += eps
n_regular = 0
# Loop through each initial condition
for i in range(N_PART):
P1 = initial_conditions[:, :, i]
# Perturb the initial point slightly
P1_prime = initial_conditions_eps[:,:,i]
# Classify the point based on the evolution
mu = classify_point(P1, P1_prime)
np.nan_to_num(mu, copy=False, nan=1.0)
print(f"the mu value is {mu}")
if mu < mu_c:
n_regular += 1
# Compute the relative area covered by regular points
relative_area = n_regular / N_PART
relative_areas.append(relative_area)
# Plot the results
plt.figure()
plt.plot(energy_values, relative_areas, marker='o', color='C0')
plt.xlabel("Energy (E)")
plt.ylabel("Relative Area Covered by Regular Curves")
plt.title("Transition from Ergodic to Stable Regime")
plt.grid()
plt.show()

17
Source/TODEL_equations.py
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@@ -1,17 +0,0 @@
from sympy import *
# Forces
X, Y, U, V = symbols("X, Y, U, V")
POT = (X**2 + Y**2 + 2*X**2*Y - 2*Y**3/3)/2
KIN = (U**2 + V**2)/2
TOT = KIN + POT
DX = diff(POT, X)
DY = diff(POT, Y)
FX = -DX
FY = -DY
print(FX)
print(FY)

114
Source/TODEL_main_yael.py
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@@ -1,114 +0,0 @@
import time
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import potentials as pot
import energies as ene
import integrator as itg
import initial_conditions as init
import poincare_sections as pcs
if "YII_light_1" in plt.style.available:
plt.style.use("YII_light_1")
# Loading matplotlib style...
# PARAM
N_grid = 1000
N_inter = int(1e5)
N_part = 200
#all_E = np.array([1/100, 1/12, 1/10, 1/8, 1/6])
all_E = np.linspace(1/100, 1/6, 20)
h = 0.005
mu_c = 1e-4
d_12 = 1e-7
# INIT
W_grid = init.mesh_grid(N_grid, xmin=-1, xmax=1, ymin=-1, ymax=1)
X_grid = W_grid[0]
Y_grid = W_grid[1]
potential = pot.hh_potential(W_grid, position_only=True)
# MAIN
def gen_mu(E):
pot_valid = np.ma.masked_where(potential > E, potential)
W_1 = init.n_energy_part(pot.hh_potential, N_part, E)
W_2 = np.zeros_like(W_1)
alpha = np.random.uniform(0, 2*np.pi, N_part)
W_2[0, 0] = W_1[0, 0] + d_12*np.cos(alpha)
W_2[0, 1] = W_1[0, 1] + d_12*np.sin(alpha)
W_2[1, 0] = W_1[1, 0]
W_2[1, 1] = W_1[1, 1]
t_1, positions_1 = itg.rk4(0, W_1, h, N_inter, pot.hh_evolution)
x_1 = positions_1[:, 0, 0]
y_1 = positions_1[:, 0, 1]
u_1 = positions_1[:, 1, 0]
v_1 = positions_1[:, 1, 1]
t_2, positions_2 = itg.rk4(0, W_2, h, N_inter, pot.hh_evolution)
x_2 = positions_2[:, 0, 0]
y_2 = positions_2[:, 0, 1]
u_2 = positions_2[:, 1, 0]
v_2 = positions_2[:, 1, 1]
dist_sq = (x_2[-25:] - x_1[-25:])**2 \
+ (y_2[-25:] - y_1[-25:])**2 \
+ (u_2[-25:] - u_1[-25:])**2 \
+ (v_2[-25:] - v_1[-25:])**2
mu = np.sum(dist_sq, axis=0)
return mu
A = np.zeros_like(all_E)
MU = []
ALL_E = []
for i in range(len(all_E)):
mu = gen_mu(all_E[i])
n_total = N_part
n_ergo = np.sum(mu < mu_c) # count how many times the condition is verified
A[i] = n_ergo/n_total
MU.append(mu)
ALL_E.append([all_E[i]]*len(mu))
MU = np.array(MU)
ALL_E = np.array(ALL_E)
# def lin(x, a, b):
# return a*x + b
# w_chaos = np.argwhere(A < 1).flatten()
# X = all_E[w_chaos]
# Y = A[w_chaos]
# popt, pcov = curve_fit(lin, X, Y)
# a, b = popt
# da, db = np.sqrt(np.diag(pcov))
fig, ax = plt.subplots(1)
ax.scatter(ALL_E, MU, s=1,
color="k", alpha=0.1, label="Data")
ax.scatter(all_E, np.mean(MU, axis=1), s=10,
color="C3", marker="*", label="Mean")
ax.scatter(all_E, np.median(MU, axis=1), s=10,
color="C2", marker="s", label="Median")
ax.hlines(mu_c, np.min(all_E), np.max(all_E), color="C4")
ax.legend()
ax.set_yscale("log")
ax.set_xlabel("energy E")
ax.set_ylabel("quantity mu")
fig.tight_layout()
# fig.savefig("mu")
fig, ax = plt.subplots(1)
ax.scatter(all_E, A, color="C0", s=5, marker="o", label="Data")
ax.set_xlabel("energy E")
ax.set_ylabel("area A")
ax.legend()
fig.tight_layout()
# fig.savefig("area")
plt.show()

58
Source/TODEL_poincare_test.py
View File

@@ -1,58 +0,0 @@
import numpy as np
import matplotlib.pyplot as plt
import potentials as pot
import energies as ene
import integrator as itg
import initial_conditions as init
import poincare_sections as pcs
h = 0.01
N_inter = 30000
eps = 1e-2
x_0 = 0.0
y_vals = np.linspace(0, 0.6, 50)
E = 0.125 # 1/12
# Initialize lists to store all Poincaré points across different initial conditions
all_pcs_pos_y = []
all_pcs_vel_y = []
for i in range(len(y_vals)):
y0 = y_vals[i]
W_part = init.one_part(x_0, y0, 0, 0)
POT = pot.hh_potential(W_part)[0]
u_0 = np.sqrt(2 * (E - POT))
v_0 = 0.0
W_part[1, 0] = u_0
W_part[1, 1] = v_0
# Perform integration
pos_t, positions = itg.rk4(0, W_part, h, N_inter, pot.hh_evolution)
# Extract positions and velocities
pos_x = positions[:, 0, 0]
pos_y = positions[:, 0, 1]
vel_x = positions[:, 1, 0]
vel_y = positions[:, 1, 1]
# Find Poincaré section points for the current initial condition
pcs_pos_y, pcs_vel_y = pcs.pcs_find(pos_x, pos_y, vel_x, vel_y)
# Append the current Poincaré section points to the overall lists
all_pcs_pos_y.extend(pcs_pos_y)
all_pcs_vel_y.extend(pcs_vel_y)
# Plotting all Poincaré section points on the same graph
fig, ax = plt.subplots()
ax.scatter(all_pcs_pos_y, all_pcs_vel_y, s=2, color="C4")
# Set labels and legend
ax.set_xlabel("coordinate y")
ax.set_ylabel("velocity v")
ax.set_title("Combined Poincaré Section for Multiple Initial y0 Values")
plt.show()

26
Source/YII_1.mplstyle
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@@ -1,3 +1,29 @@
#@ Author: Moussouni, Yaël (MSc student)
#@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
# de Strasbourg, UMR 7550, F-67000 Strasbourg, France
#@ Date: 2025-01-01
#
#Licence:
#Order and Chaos in a 2D potential
#Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
# Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
#
#YII_1.mplstyle
#Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
#
#This program is free software: you can redistribute it and/or modify
#it under the terms of the GNU General Public License as published by
#the Free Software Foundation; either version 3 of the License, or
#(at your option) any later version.
#
#This program is distributed in the hope that it will be useful,
#but WITHOUT ANY WARRANTY; without even the implied warranty of
#MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
#GNU General Public License for more details.
#
#You should have received a copy of the GNU General Public License
#along with this program. If not, see https://www.gnu.org/licenses/.
### Axes
axes.titlesize : large
axes.labelsize : large

26
Source/YII_light_1.mplstyle
View File

@@ -1,3 +1,29 @@
#@ Author: Moussouni, Yaël (MSc student)
#@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
# de Strasbourg, UMR 7550, F-67000 Strasbourg, France
#@ Date: 2025-01-01
#
#Licence:
#Order and Chaos in a 2D potential
#Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
# Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
#
#YII_light_1.mplstyle
#Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
#
#This program is free software: you can redistribute it and/or modify
#it under the terms of the GNU General Public License as published by
#the Free Software Foundation; either version 3 of the License, or
#(at your option) any later version.
#
#This program is distributed in the hope that it will be useful,
#but WITHOUT ANY WARRANTY; without even the implied warranty of
#MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
#GNU General Public License for more details.
#
#You should have received a copy of the GNU General Public License
#along with this program. If not, see https://www.gnu.org/licenses/.
### Axes
axes.titlesize : large
axes.labelsize : large

24
Source/energies.py
View File

@@ -7,7 +7,29 @@ Compute energies (kinetic or total)
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-12-13
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
energies.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np

24
Source/initial_conditions.py
View File

@@ -7,7 +7,29 @@ Generate initial conditions depending on different criteria
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
initial_conditions.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np

25
Source/integrator.py
View File

@@ -7,7 +7,30 @@ Integrate differential equations.
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
integrator.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np

25
Source/main_area.py
View File

@@ -8,7 +8,30 @@ study ordered and chaotic regimes.
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-12-13
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
main_area.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np
from scipy.optimize import curve_fit

25
Source/main_poincare_sections_linear.py
View File

@@ -8,7 +8,30 @@ Computes the Poincaré Sections with a linear algorithm
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
main_poincare_sections_linear.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np

25
Source/main_poincare_sections_parallel.py
View File

@@ -7,7 +7,30 @@ Computes the Poincaré Sections with a parallel algorithm (with Numpy)
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
main_poincare_sections_parallel.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np

25
Source/plot_area.py
View File

@@ -7,7 +7,30 @@ Plots areas
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
plot_area.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import os
import numpy as np

25
Source/plot_poincare_sections.py
View File

@@ -8,7 +8,30 @@ or parallel algorithms.
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
plot_poincare_sections.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import os
import numpy as np

24
Source/plot_poincare_sections_zoom.py
View File

@@ -8,7 +8,29 @@ or parallel algorithms.
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
plot_poincare_sections_zoom.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import os
import numpy as np

24
Source/poincare_sections.py
View File

@@ -7,7 +7,29 @@ Computes the Poincaré Sections
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
poincare_sections.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np

25
Source/potentials.py
View File

@@ -7,7 +7,30 @@ Functions of the different potentials (and their derivatives for the evolution)
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
potentials.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np

25
Source/test_evolution.py
View File

@@ -8,7 +8,30 @@ followed by the particle in a given time.
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
test_evolution.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np

25
Source/test_initial_E.py
View File

@@ -7,7 +7,30 @@ Sample random particles with the same given energy in a valid coordinates range.
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
test_initial_E.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np
import matplotlib.pyplot as plt

25
Source/test_potentials.py
View File

@@ -7,7 +7,30 @@ Draw the Kepler potential and the Hénon--Heils potential
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
test_potentials.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import numpy as np
import matplotlib.pyplot as plt

24
Source/time_poincare_sections.py
View File

@@ -7,7 +7,29 @@ Computes the running time between the linear and parallel algorithms.
@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
de Strasbourg, UMR 7550, F-67000 Strasbourg, France
@ Date: 2024-11-29
@ Date: 2025-01-01
Licence:
Order and Chaos in a 2D potential
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
time_poincare_sections.py
Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see https://www.gnu.org/licenses/.
"""
import time