-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathmind.py
237 lines (211 loc) · 7.41 KB
/
mind.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
################################################################################
# ,--. ,--. ,--. ,--. #
# | `.' | `--' ,--,--, ,-| | #
# | |'.'| | ,--. | \ ' .-. | #
# | | | | | | | || | \ `-' | #
# `--' `--' `--' `--''--' `---' #
# #
# ** A Minimal Lennard-Jones Fluid Molecular Dynamics Python Program ** #
# #
# #
# #
# Author: Pu Du #
# Website: pudu.io #
# Email: [email protected] #
################################################################################
import time
import numpy as np
from numba import jit
def initialize(N, L, rx, ry, rz):
"""put N particles in a box"""
n3 = int(N ** (1 / 3.)) + 1
iix = iiy = iiz = 0
for i in range(N):
rx[i] = (iix + 0.5) * L / n3
ry[i] = (iiy + 0.5) * L / n3
rz[i] = (iiz + 0.5) * L / n3
iix += 1
if iix == n3:
iix = 0
iiy += 1
if iiy == n3:
iiy = 0
iiz += 1
def velocity_verlet(dt, rx, ry, rz, vx, vy, vz, i):
"""verloctiy verlet algorithm"""
dt2 = dt * dt
rx[i] += vx[i] * dt + 0.5 * dt2 * fx[i]
ry[i] += vy[i] * dt + 0.5 * dt2 * fy[i]
rz[i] += vz[i] * dt + 0.5 * dt2 * fz[i]
vx[i] += 0.5 * dt * fx[i]
vy[i] += 0.5 * dt * fy[i]
vz[i] += 0.5 * dt * fz[i]
def wrap_into_box(L, rx, ry, rz, i):
"""wrap the coordinates"""
if rx[i] < 0.0:
rx[i] += L
if rx[i] > L:
rx[i] -= L
if ry[i] < 0.0:
ry[i] += L
if ry[i] > L:
ry[i] -= L
if rz[i] < 0.0:
rz[i] += L
if rz[i] > L:
rz[i] -= L
@jit
def potential_energy(N, L, rc2, rx, ry, rz, fx, fy, fz):
"""calculate the potential energy"""
fx.fill(0)
fy.fill(0)
fz.fill(0)
hL = L / 2.0
e = 0.0
for i in range(N-1):
for j in range(i+1, N):
dx = rx[i] - rx[j]
dy = ry[i] - ry[j]
dz = rz[i] - rz[j]
if dx > hL:
dx -= L
if dx < -hL:
dx += L
if dy > hL:
dy -= L
if dy < -hL:
dy += L
if dz > hL:
dz -= L
if dz < -hL:
dz += L
r2 = dx * dx + dy * dy + dz * dz
if r2 < rc2:
r6i = 1.0 / (r2 * r2 * r2)
e += 4 * (r6i * r6i - r6i)
f = 48 * (r6i * r6i - 0.5 * r6i)
fx[i] += dx * f / r2
fx[j] -= dx * f / r2
fy[i] += dy * f / r2
fy[j] -= dy * f / r2
fz[i] += dz * f / r2
fz[j] -= dz * f / r2
return e
@jit
def kinetic_energy(N, dt, vx, vy, vz, fx, fy, fz):
"""calculate the kinetic energy"""
e = 0.0
for i in range(N):
vx[i] += 0.5 * dt * fx[i]
vy[i] += 0.5 * dt * fy[i]
vz[i] += 0.5 * dt * fz[i]
e += vx[i] * vx[i] + vy[i] * vy[i] + vz[i] * vz[i]
e *= 0.5
return e
def berendsen_thermostat(N, dt, KE, vx, vy, vz):
"""berendsen thermostat algorithm"""
lamb = np.sqrt(1 + dt / tau * (T / (2.0 * KE / 3.0 / N) - 1.0))
for i in range(N):
vx[i] *= lamb
vy[i] *= lamb
vz[i] *= lamb
def thermostat(KE, T, N, vx, vy, vz):
"""velocity scaling algorithm"""
t = KE / N * 2. / 3.
fac = np.sqrt( T / t)
for i in range(N):
vx[i] *= fac
vy[i] *= fac
vz[i] *= fac
def output_welcome(N, L, dt, nSteps, T):
"""print welcome information"""
mind = '''
,--. ,--. ,--. ,--.
| `.' | `--' ,--,--, ,-| |
| |'.'| | ,--. | \ ' .-. |
| | | | | | | || | \ `-' |
`--' `--' `--' `--''--' `---'
'''
print(mind)
print('** A Minimal Lennard-Jones Fluid Molecular Dynamics Python Program **')
print('\nSystem information:\n')
print(' ** ALL UNITS ARE IN REDUCED UNITS **\n')
print(' Simulation type:\tNVT')
print(' Number of particles in the box:\t{:d}'.format(N))
print(' Box length:\t{:f}'.format(L))
print(' Time step:\t{:f}'.format(dt))
print(' Total number of steps:\t{:d}'.format(nSteps))
print(' Target temperature:\t{:f}'.format(T))
print('\nOutput format:\n')
print ( 'Step Potential Kinetic Total' )
print ( ' Energy PE Energy KE Energy TE\n' )
def output_thermo(s, PE, KE, TE):
"""print thermo information"""
print('Step: {:9d} PE = {:12.4f} KE = {:12.4f} TE = {:12.4f}'.format(s+1, PE, KE, TE))
def output_xyz(N, rx, ry, rz):
"""xyz output"""
with open('output.xyz', 'a+') as f:
f.write(str(N) + '\n\n')
for i in range(N):
f.write('{:s} {:.8f} {:.8f} {:.8f}'.format('Pu', rx[i], ry[i], rz[i]))
f.write('\n')
def output_end(t_start, t_end):
"""print time information"""
print('-' * 70)
print ('Total looping time = {:.2f} seconds.'.format(t_end - t_start))
art = '''
.
":"
___:____ |"\/"|
,' `. \ /
| O \___/ |
~^~^~^~^~^~^~^~^~^~^~^~^~
'''
print(art)
def mdrun(N, L, rc2, dt, nSteps, T, rx, ry, rz, vx, vy, vz, fx, fy, fz):
"""main MD function"""
print('-' * 70)
for s in range(nSteps):
for i in range(N):
velocity_verlet(dt, rx, ry, rz, vx, vy, vz,i)
wrap_into_box(L, rx, ry, rz, i)
PE = potential_energy(N, L, rc2, rx, ry, rz, fx, fy, fz)
KE = kinetic_energy(N, dt, vx, vy, vz, fx, fy, fz)
TE = PE + KE
berendsen_thermostat(N, dt, KE, vx, vy, vz)
output_thermo(s, PE, KE, TE)
output_xyz(N, rx, ry, rz)
if (__name__ == '__main__'):
############################################
# parameters can be changed (reduced unit)
# L : box length
# N : number of particles
# dt : time step
# rc2 : squared cutoff distance
# nSteps : number of steps of simulation
# T : temperature
L = 7.55952
N = 216
dt = 0.001
rc2 = 1.e20
nSteps = 10000
T = 1.0
tau = 0.1
Tdamp = 1
############################################
rx = np.zeros(N)
ry = np.zeros(N)
rz = np.zeros(N)
vx = np.zeros(N)
vy = np.zeros(N)
vz = np.zeros(N)
fx = np.zeros(N)
fy = np.zeros(N)
fz = np.zeros(N)
output_welcome(N, L, dt, nSteps, T)
initialize(N, L, rx, ry, rz)
output_xyz(N, rx, ry, rz)
t_start = time.clock()
mdrun(N, L, rc2, dt, nSteps, T, rx, ry, rz, vx, vy, vz, fx, fy, fz)
t_end = time.clock()
output_end(t_start, t_end)