diff --git a/Jaslo/sheet3.py b/Jaslo/sheet3.py
index 30d6bafba3139c5a044a4eabe588c7d814a69039..cc34dfbee7df69a037d8c18362c0cc65c63d91d7 100644
--- a/Jaslo/sheet3.py
+++ b/Jaslo/sheet3.py
@@ -1,6 +1,8 @@
import numpy as np
from scipy.constants import Boltzmann as k_B
import matplotlib.pyplot as plt
+from tqdm import tqdm
+
def verlet(force, x0, p0, m, dt, N):
assert(x0.shape == p0.shape)
@@ -11,7 +13,7 @@ def verlet(force, x0, p0, m, dt, N):
x[0] = x0
p[0] = p0
- for i in range(1, N):
+ for i in tqdm(range(1, N)):
p[i] = p[i-1] + 1/2 * force(x[i-1]) * dt
x[i] = x[i-1] + p[i] / m * dt
p[i] = p[i] + 1/2 * force(x[i]) * dt
@@ -43,81 +45,87 @@ p0[-1] = -p0[0]
dt = 0.1
t = np.arange(0, 300, dt)
-x, p = verlet(force, x0, p0, m, dt, len(t))
+# x, p = verlet(force, x0, p0, m, dt, len(t))
-# fig, ax = plt.subplots()
+# # fig, ax = plt.subplots()
-for i in range(x.shape[1]):
- plt.plot(t, x[:,i], label=f"Bead {i+1}")
+# for i in range(x.shape[1]):
+# plt.plot(t, x[:,i], label=f"Bead {i+1}")
-plt.xlabel(r"$t / \tau$")
-plt.ylabel(r"$x / l$")
-plt.legend()
-plt.show()
+# plt.xlabel(r"$t / \tau$")
+# plt.ylabel(r"$x / l$")
+# plt.legend()
+# plt.show()
-# E = np.sum(p**2 / (2 * m), axis=1) + 1/2 * k * np.sum((x[:,1:] - x[:,:-1])**2, axis=1)
-# K = np.sum(p**2 / (2 * m), axis=1)
+# # E = np.sum(p**2 / (2 * m), axis=1) + 1/2 * k * np.sum((x[:,1:] - x[:,:-1])**2, axis=1)
+# # K = np.sum(p**2 / (2 * m), axis=1)
-# plt.plot(t, K)
-# plt.show()
+# # plt.plot(t, K)
+# # plt.show()
-# b)
-for N in (2, 3, 11, 100):
- m = np.full(N, 1)
- I = np.arange(1, N+1)
- x0 = l * I
- p0 = np.zeros(x0.shape)
- p0[0] = 1/2 * np.sqrt(m[0] * eps)
- p0[-1] = -p0[0]
+# # b)
+# for N in (2, 3, 11, 100):
+# m = np.full(N, 1)
+# I = np.arange(1, N+1)
+# x0 = l * I
+# p0 = np.zeros(x0.shape)
+# p0[0] = 1/2 * np.sqrt(m[0] * eps)
+# p0[-1] = -p0[0]
- x, p = verlet(force, x0, p0, m, dt, len(t))
- K = np.sum(p**2 / (2 * m), axis=1)
- K_l = np.average(K)
- T = 2 * K_l / N
+# x, p = verlet(force, x0, p0, m, dt, len(t))
+# K = np.sum(p**2 / (2 * m), axis=1)
+# K_l = np.average(K)
+# T = 2 * K_l / N
- print(f"<K> = {K_l}")
- print(f"k_B T = {T}")
+# print(f"<K> = {K_l}")
+# print(f"k_B T = {T}")
-# c)
-for N in (2, 3, 11, 100):
- for i in range(3):
- m = np.full(N, 1)
- I = np.arange(1, N+1)
- x0 = l * I
- p0 = np.random.normal(0, np.sqrt(m[0] * eps), N)
+# # c)
+# for N in (2, 3, 11, 100):
+# for i in range(3):
+# m = np.full(N, 1)
+# I = np.arange(1, N+1)
+# x0 = l * I
+# p0 = np.random.normal(0, np.sqrt(m[0] * eps), N)
- x, p = verlet(force, x0, p0, m, dt, len(t))
- R_l = np.abs(x[:,0] - x[:,-1])
+# x, p = verlet(force, x0, p0, m, dt, len(t))
+# R_l = np.abs(x[:,0] - x[:,-1])
- print(f"N = {N}, i = {i}: R_l = {np.average(R_l)}")
+# print(f"N = {N}, i = {i}: R_l = {np.average(R_l)}")
- plt.plot(t, R_l)
- plt.xlabel(r"$t / \tau$")
- plt.ylabel(r"$\overline{R_l} / l$")
- plt.show()
+# plt.plot(t, R_l)
+# plt.xlabel(r"$t / \tau$")
+# plt.ylabel(r"$\overline{R_l} / l$")
+# plt.show()
# d)
def d(x1, p1, x2, p2):
return np.sqrt(1 / (6 * x1.shape[0]) * np.sum(k * (x1 - x2)**2 + (p1 - p2)**2 / m))
+dt = 0.1
+t = np.arange(0, 1*10e3, dt)
-t = np.arange(0, 2e4, dt)
-
-for N in (10, 20):
+N_vals = [10,20]
+for N in N_vals:
m = np.full(N, 1)
I = np.arange(1, N+1)
x0 = l * I
- p0 = np.random.normal(0, np.sqrt(m[0] * eps), N)
+ # p0 = np.random.normal(0, np.sqrt(m[0] * eps), N)
+ p0 = np.zeros(x0.shape)
+ p0[0] = 1/2 * np.sqrt(m[0] * eps)
+ p0[-1] = -p0[0]
x, p = verlet(force, x0, p0, m, dt, len(t))
- ts = t[int(10 / dt):]
+ ts = t[int(10 / dt):]
ds = np.zeros(ts.shape)
- for i in range(len(ds)):
+ for i in tqdm(range(len(ds))):
ds[i] = d(x[int(10 / dt) + i], p[int(10 / dt) + i], x[int(10 / dt)], p[int(10 / dt)])
print(f"N = {N}: d_min = {np.min(ds)}")
+ plt.figure(figsize=(48, 6))
plt.xlabel(r"$t / \tau$")
plt.ylabel(r"$d / \sqrt{k l^2}$")
plt.plot(ts, ds)
- plt.show()
+ # plt.tight_layout()
+ plt.savefig(f'4c_N={N}.png')