update

Source/main_yael.py

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+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()
+
+
+
+