/
SimulateCollisions.py
206 lines (179 loc) · 9.63 KB
/
SimulateCollisions.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
import scipy as sp
from scipy.stats import uniform as uni
import CalculateConserved as CalcConsd
import time
import matplotlib.pyplot as plt
# Creates elastic collision between two particles for arbitrary masses, center of mass velocities, and
# center of momentum angles with respect to horizontal. First generates 1D collision along x-axis, with
# particle 1 on +x-axis and particle 2 on -x-axis. The particles are rotated arbitrarily around the collision point,
# and then a center of mass velocity is added to both velocities. The frame in which the center of mass moves is
# the laboratory frame. All important physical quantity arrays are saved to LabValuesTrain.npz
# and LabValuesIntermediate.py for later retrieval by other programs.
# Author: Lawson Fuller
start_time = time.time()
numTrials = 10000
# Notation:
# Letter "a" in variable name means quantity is in aligned (mass 1 on +x axis) CM frame
# Letter "n" is "not aligned"/unaligned frame
# Letter "L" is lab frame (CM velocity nonzero)
#===========================================
#
# CM Aligned Frame
#
#===========================================
print("Beginning Aligned Center of Mass Phase: ")
print(str(time.time() - start_time)+" seconds")
# min and max of sampled values
m_min = 0.01
m_max = 6
x_min = 0.01
x_max = 10
v1ax_min = 0.001
v1ax_max = 3
vcm_min = -10
vcm_max = 10
for trainOrIntermediateFile in [0,1]:
# Random physical initial states for all trials with dimension (numTrials)
m1_Arr = uni.rvs(m_min, m_max, size=numTrials)
m2_Arr = uni.rvs(m_min, m_max, size=numTrials)
x1a_Arr = uni.rvs(x_min, x_max, size=numTrials)
v1ax_Arr = sp.multiply(-1,uni.rvs(v1ax_min, v1ax_max, size=numTrials))
vcm_x_Arr = uni.rvs(vcm_min, vcm_max, size=numTrials)
vcm_y_Arr = uni.rvs(vcm_min, vcm_max, size=numTrials)
# Always zero quantities with dimension (numTrials)
y1a_Arr = sp.zeros(numTrials)
y2a_Arr = sp.zeros(numTrials)
v1ay_Arr = sp.zeros(numTrials)
v2ay_Arr = sp.zeros(numTrials)
# Time until collision
t_col = sp.fabs(sp.divide(x1a_Arr,v1ax_Arr))
# Velocity of particle 2 with dimension (numTrials)
v2ax_Arr = sp.fabs(sp.multiply(v1ax_Arr,sp.divide(m1_Arr,m2_Arr)))
# Initial placement of particle 2 with dimension (numTrials)
x2a_Arr = sp.multiply(-1,sp.multiply(v2ax_Arr,t_col))
# Full aligned vectors with dimensions (2, numTrials)
v1a = sp.array([v1ax_Arr,v1ay_Arr])
v2a = sp.array([v2ax_Arr,v2ay_Arr])
InitialPosition1a = sp.array([x1a_Arr,y1a_Arr])
InitialPosition2a = sp.array([x2a_Arr,y2a_Arr])
# Initial energy in CM frame
E_i = CalcConsd.energy(m1_Arr,m2_Arr,sp.transpose(v1a),sp.transpose(v2a))
# Final states (after collision) with vector dimension (numTrials):
m2Overm1Times2 = sp.multiply(2,sp.divide(m2_Arr,m1_Arr))
v1a_total_f = sp.sqrt( sp.divide(sp.multiply(m2Overm1Times2,E_i),(m1_Arr+m2_Arr)) )
v2a_total_f = sp.multiply(-1,sp.multiply(sp.divide(m1_Arr,m2_Arr),v1a_total_f))
# Final x velocities in CM Frame with dimension (2, numTrials)
v1a_f = sp.array( [v1a_total_f, sp.zeros(numTrials)])
v2a_f = sp.array( [v2a_total_f, sp.zeros(numTrials)])
E_i = CalcConsd.energy(m1_Arr,m2_Arr,sp.transpose(v1a),sp.transpose(v2a))
E_f = CalcConsd.energy(m1_Arr,m2_Arr,sp.transpose(v1a_f),sp.transpose(v2a_f))
p_x_i = CalcConsd.x_momentum(m1_Arr,m2_Arr,sp.transpose(v1a),sp.transpose(v2a))
p_y_i = CalcConsd.y_momentum(m1_Arr,m2_Arr,sp.transpose(v1a),sp.transpose(v2a))
p_x_f = CalcConsd.x_momentum(m1_Arr,m2_Arr,sp.transpose(v1a_f),sp.transpose(v2a_f))
p_y_f = CalcConsd.y_momentum(m1_Arr,m2_Arr,sp.transpose(v1a_f),sp.transpose(v2a_f))
#===========================================
#
# CM Unaligned Frame
#
#===========================================
print("Beginning Rotation Phase")
print(str(time.time() - start_time)+" seconds")
# Rotation angles:
phi = sp.multiply(sp.random.uniform(0,1,size=numTrials),2*sp.pi) #remove the zero
# Rotation matrix with dimensions (2 , 2 , numTrials)
R = sp.array([[sp.cos(phi), sp.sin(phi)],[-sp.sin(phi), sp.cos(phi)]])
v1n = sp.empty(shape=(numTrials, 2))
v2n = sp.empty(shape=(numTrials, 2))
v1n_f = sp.empty(shape=(numTrials, 2))
v2n_f = sp.empty(shape=(numTrials, 2))
InitialPosition1n = sp.empty(shape=(numTrials, 2))
InitialPosition2n = sp.empty(shape=(numTrials, 2))
# Rotating initial vectors of particles 1 and 2 with dimensions (numTrials, 2)
for trial in range(numTrials):
v1n[trial] = sp.matmul(R[:,:,trial], v1a[:,trial])
v2n[trial] = sp.matmul(R[:,:,trial], v2a[:,trial])
v1n_f[trial] = sp.matmul(R[:,:,trial], v1a_f[:,trial])
v2n_f[trial] = sp.matmul(R[:,:,trial], v2a_f[:,trial])
InitialPosition1n[trial] = sp.matmul(R[:,:,trial], InitialPosition1a[:,trial])
InitialPosition2n[trial] = sp.matmul(R[:,:,trial], InitialPosition2a[:,trial])
#===========================================
#
# Lab Frame Velocities
#
#===========================================
print("Beginning Lab Phase: ")
print(str(time.time() - start_time)+" seconds")
# Full center of mass velocity in lab frame. Dimension (numTrials , 2)
vcm = sp.transpose(sp.array([vcm_x_Arr, vcm_y_Arr]))
# Particle velocities in lab frame. Dimension (numTrials, 2)
v1L = v1n + vcm
v2L = v2n + vcm
v1L_f = v1n_f + vcm
v2L_f = v2n_f + vcm
# Initial positions in lab frame:
InitialPosition1L = InitialPosition1n
InitialPosition2L = InitialPosition2n
#===========================================
#
# Lab Frame Conserved Quantities
#
#===========================================
E_i = CalcConsd.energy(m1_Arr,m2_Arr,v1L,v2L)
E_f = CalcConsd.energy(m1_Arr,m2_Arr,v1L_f,v2L_f)
p_x_i = CalcConsd.x_momentum(m1_Arr,m2_Arr,v1L,v2L)
p_y_i = CalcConsd.y_momentum(m1_Arr,m2_Arr,v1L,v2L)
p_x_f = CalcConsd.x_momentum(m1_Arr,m2_Arr,v1L_f,v2L_f)
p_y_f = CalcConsd.y_momentum(m1_Arr,m2_Arr,v1L_f,v2L_f)
#===========================================
#
# Lab Frame Collision Time Series
#
#===========================================
print("Beginning Path Phase: ")
print(str(time.time() - start_time)+" seconds")
timeStepOfCollision = 2+1
timeSteps = 2*(timeStepOfCollision) - 1
# Dimension (timeSteps)
t = sp.linspace(0, sp.multiply(2,t_col), timeSteps)
# Rework dimensions of initial position and velocity matrices during this step
# Dimension (2(the # of SpatialDimensions), numTrials, timeSteps)
Position1L_t_pre = sp.repeat(sp.transpose(InitialPosition1L)[:,:,sp.newaxis], timeSteps, axis=2)\
+ sp.multiply( sp.repeat(sp.transpose(v1L)[:, :, sp.newaxis], timeSteps, axis=2), sp.transpose(t) )
Position2L_t_pre = sp.repeat(sp.transpose(InitialPosition2L)[:,:,sp.newaxis], timeSteps, axis=2) \
+ sp.multiply( sp.repeat(sp.transpose(v2L)[:, :, sp.newaxis], timeSteps, axis=2), sp.transpose(t) )
Position1L_t_post = sp.repeat(Position1L_t_pre[:,:,timeStepOfCollision-1][:,:,sp.newaxis], timeSteps, axis=2) \
+ sp.multiply( sp.repeat(sp.transpose(v1L_f)[:, :, sp.newaxis], timeSteps, axis=2), sp.transpose(t) )
Position2L_t_post = sp.repeat(Position2L_t_pre[:,:,timeStepOfCollision-1][:,:,sp.newaxis], timeSteps, axis=2) \
+ sp.multiply( sp.repeat(sp.transpose(v2L_f)[:, :, sp.newaxis], timeSteps, axis=2), sp.transpose(t) )
Position1L_t = sp.concatenate((Position1L_t_pre[:,:,:timeStepOfCollision],Position1L_t_post[:,:,1:timeStepOfCollision]),2)
Position2L_t = sp.concatenate((Position2L_t_pre[:,:,:timeStepOfCollision],Position2L_t_post[:,:,1:timeStepOfCollision]),2)
Velocity1L_t_pre = sp.repeat(sp.transpose(v1L)[:, :, sp.newaxis], timeSteps, axis=2)
Velocity2L_t_pre = sp.repeat(sp.transpose(v2L)[:, :, sp.newaxis], timeSteps, axis=2)
Velocity1L_t_post = sp.repeat(sp.transpose(v1L_f)[:, :, sp.newaxis], timeSteps, axis=2)
Velocity2L_t_post = sp.repeat(sp.transpose(v2L_f)[:, :, sp.newaxis], timeSteps, axis=2)
Velocity1L_t = sp.concatenate((Velocity1L_t_pre[:,:,:timeStepOfCollision],Velocity1L_t_post[:,:,timeStepOfCollision:]),2)
Velocity2L_t = sp.concatenate((Velocity2L_t_pre[:,:,:timeStepOfCollision],Velocity2L_t_post[:,:,timeStepOfCollision:]),2)
# print(sp.shape(m1_Arr))
# print("Final X Array m1:" + str(Position1L_t[0,0,timeStepOfCollision-2:timeStepOfCollision+6]))
# print("Final X Array m2:" + str(Position2L_t[0,0,timeStepOfCollision-2:timeStepOfCollision+6]))
# print("Final Y Array m1:" + str(Position1L_t[1,0,timeStepOfCollision-2:timeStepOfCollision+6]))
# print("Final Y Array m2:" + str(Position2L_t[1,0,timeStepOfCollision-2:timeStepOfCollision+6]))
#
# print("Pre Array: "+ str(Position1L_t_pre[0,0,timeStepOfCollision-1:timeStepOfCollision+2]))
# print("Post Array: " + str(Position1L_t_post[0,0,:2]))
# print(sp.shape(Position1L_t))
# print(sp.shape(Velocity1L_t))
# Save arrays to file
print("Saving: ")
print(str(time.time() - start_time)+" seconds")
dt = sp.divide(sp.multiply(2,t_col), timeSteps-1)
if trainOrIntermediateFile==0:
# Training File
sp.savez("LabValuesTrain", v1L, v2L, v1L_f, v2L_f, E_i, E_f, p_x_i, p_x_f, p_y_i, p_y_f,
t, Position1L_t, Position2L_t, Velocity1L_t, Velocity2L_t, m1_Arr, m2_Arr, dt)
elif trainOrIntermediateFile==1:
# Validation File
sp.savez("LabValuesIntermediate", v1L, v2L, v1L_f, v2L_f, E_i, E_f, p_x_i, p_x_f, p_y_i, p_y_f,
t, Position1L_t, Position2L_t, Velocity1L_t, Velocity2L_t, m1_Arr, m2_Arr, dt)
print("Time to run: ")
print(str(time.time() - start_time)+" seconds")