ブラウン運動のシミュレーション可視化

以前ここで試した単純な粒子の中に大きいサイズの粒子を放り込む。周囲から無数の粒子がぶつかりランダムに動くブラウン運動のような動きをみることができる。

■結果
ブラウン運動の可視化

import random
import math
from OpenGL.GL import *
from OpenGL.GLU import *
from OpenGL.GLUT import *

from PIL import Image
from PIL import ImageOps

a  = 2
Dt = 0.01
CUT = 5
#Define xy index
PX = 0
PY = 1
VX = 2
VY = 3
FX = 4
FY = 5
pot = [0,0]
perticle_num = 1000
xy = [[0 for i in range(6)] for j in range(perticle_num)]
BP = [0 for i in range(6)]
Radi  = 0.1

step = 1

def capture():
  global step
  pad_step = '{0:04d}'.format(step)
  print pad_step

  width = glutGet(GLUT_WINDOW_WIDTH)
  height = glutGet(GLUT_WINDOW_HEIGHT)

  glReadBuffer(GL_FRONT)
  glPixelStorei(GL_UNPACK_ALIGNMENT, 1)
  data = glReadPixels(0, 0, width, height, GL_RGBA, GL_UNSIGNED_BYTE)

  image = Image.fromstring("RGBA", (width, height), data)
  image = ImageOps.flip(image)
  image.save("test"+pad_step+".png")

def find_pair():
  global Radi
  particle_num = len(xy)
  pnum = 0
  w_ratio = 0.1
  while pnum < particle_num:
    dx = xy[pnum][PX] - BP[PX]
    dy = xy[pnum][PY] - BP[PY]

    if dx > 0.5*a:
      dx = dx + a
    if dy > 0.5*a:
      dy = dy + a

    rr = math.sqrt(dx*dx + dy*dy)

    if rr < Radi:
      v2 = math.sqrt(xy[pnum][VX]**2 + xy[pnum][VY]**2)
      cos = (xy[pnum][VX]*dx + xy[pnum][VY]*dy)/(v2*rr)
      sin = math.sqrt(1 - cos**2)

      tmpx= xy[pnum][VX]*(cos**2 - sin**2) - xy[pnum][VY]*(2*cos*sin)
      tmpy= xy[pnum][VX]*(2*cos*sin) + xy[pnum][VY]*(cos**2 - sin**2)

      xy[pnum][VX] =  abs(tmpx) * dx / (abs(dx))
      xy[pnum][VY] =  abs(tmpy) * dy / (abs(dy))
      BP[VX] =  BP[VX] - w_ratio * abs(tmpx) * dx / (abs(dx))
      BP[VY] =  BP[VY] - w_ratio * abs(tmpy) * dy / (abs(dy))

    pnum += 1

def integ():
  find_pair()

  particle_num = len(xy)

  BP[PX] = BP[PX] + Dt*BP[VX]
  BP[PY] = BP[PY] + Dt*BP[VY]

  #boundary condition
  if BP[PX] > a:
     BP[PX] -= a
  if BP[PY] > a:
     BP[PY] -= a
  if BP[PX] < 0:
     BP[PX] += a
  if BP[PY] < 0:
     BP[PY] += a

  pnum = 0
  while pnum < particle_num:
    #update position
    xy[pnum][PX] = xy[pnum][PX] + Dt*xy[pnum][VX]
    xy[pnum][PY] = xy[pnum][PY] + Dt*xy[pnum][VY]

    if xy[pnum][PX] > a:
       xy[pnum][PX] -= a
    if xy[pnum][PY] > a:
       xy[pnum][PY] -= a
    if xy[pnum][PX] < 0:
       xy[pnum][PX] += a
    if xy[pnum][PY] < 0:
       xy[pnum][PY] += a
    pnum += 1


def calc_ena():
    ena = 0.0

    particle_num = len(xy)
    for i in range(0,particle):
       vx2 = xy[i][VX]*xy[i][VX]
       vy2 = xy[i][VY]*xy[i][VY]
       ena = ena + vx2 + vy2

    ena = 0.5*ena
    return ena


def update():
    global Radi
    PI = 3.14159263
    global step

    step = step + 1

    # If you want to get image...
    #capture()

    integ()

    #print step
    nnum = 0
    while nnum < len(xy):
       glPointSize(3.0)
       glColor3f(0.3, 0.3, 1.0)
       glBegin(GL_POINTS)
       glVertex2d(xy[nnum][PX], xy[nnum][PY])
       glEnd()
       nnum = nnum + 1

    N_t = 30
    glColor3f(1.0, 0.0, 0.0)
    glBegin(GL_POLYGON)
    for j in range(0,N_t):
       glVertex2d(Radi*math.cos(2.0*PI*j/N_t)+BP[PX],
                  Radi*math.sin(2.0*PI*j/N_t)+BP[PY])

    glEnd()

def init_set():
  pnum = 0
  xv_sum = 0
  yv_sum = 0
  particle_num = len(xy)
  while pnum < particle_num:
    xy[pnum][PX] = 0  # 0 x-position 
    xy[pnum][PY] = 0  # 1 y-position
    xy[pnum][VX] = random.uniform(-1,1) # 2 x-velocity
    xy[pnum][VY] = random.uniform(-1,1) # 3 y-velocity
    xv_sum += xy[pnum][VX]
    yv_sum += xy[pnum][VY]
    pnum += 1

  xv_sum = xv_sum / particle_num
  yv_sum = yv_sum / particle_num
  pnum = 0

  while pnum < particle_num:
    xy[pnum][VX] = xy[pnum][VX] - xv_sum
    xy[pnum][VY] = xy[pnum][VY] - yv_sum
    pnum += 1

  BP[PX] = a/2
  BP[PY] = a/2
  BP[VX] = random.uniform(-0.5,0.5)
  BP[VY] = random.uniform(-0.5,0.5)


def draw():
    glClearColor(0.0, 0.0, 0.0, 0.0)
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)

    glLoadIdentity()
    glColor3f(1.0,1.0,0.0)
    gluLookAt(a/2, a/2, 4.0  ,a/2 ,a/2 ,0 , 0, 1.0, 0.0)

    glBegin(GL_LINE_LOOP)
    glVertex2d(0,0)
    glVertex2d(0,a)
    glVertex2d(a,a)
    glVertex2d(a,0)
    glEnd()

    update()
    glutSwapBuffers()

def resize(w, h):
    glViewport(0, 0, w, h)
    glLoadIdentity()
    glOrtho(0, a, 0, a, -a, a)

def init():
    glClearColor(0.7, 0.7, 0.7, 0.7)

def idle():
    glutPostRedisplay()

def reshape(w, h):
    glViewport(0, 0,w,h)
    glMatrixMode(GL_PROJECTION)
    glLoadIdentity()
    gluPerspective(30.0, w/h, 1.0, 100.0)
    glMatrixMode (GL_MODELVIEW)


if __name__ == "__main__":

    init_set()

    glutInitWindowPosition(50, 50);
    glutInitWindowSize(340, 340);
    glutInit(sys.argv)
    glutInitDisplayMode(GLUT_RGBA | GLUT_DOUBLE )
    glutCreateWindow("pyOpenGL TEST")
    glutDisplayFunc(draw)
    glutReshapeFunc(reshape)
    init()

    glutIdleFunc(idle)
    glutMainLoop()

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import random

import math

from OpenGL.GL import *

from OpenGL.GLU import *

from OpenGL.GLUT import *

from PIL import Image

from PIL import ImageOps

a = 2

Dt = 0.01

CUT = 5

#Define xy index

PX = 0

PY = 1

VX = 2

VY = 3

FX = 4

FY = 5

pot = [0,0]

perticle_num = 1000

xy = [[0 for i in range(6)] for j in range(perticle_num)]

BP = [0 for i in range(6)]

Radi = 0.1

step = 1

def capture():

global step

pad_step = '{0:04d}'.format(step)

print pad_step

width = glutGet(GLUT_WINDOW_WIDTH)

height = glutGet(GLUT_WINDOW_HEIGHT)

glReadBuffer(GL_FRONT)

glPixelStorei(GL_UNPACK_ALIGNMENT, 1)

data = glReadPixels(0, 0, width, height, GL_RGBA, GL_UNSIGNED_BYTE)

image = Image.fromstring("RGBA", (width, height), data)

image = ImageOps.flip(image)

image.save("test"+pad_step+".png")

def find_pair():

global Radi

particle_num = len(xy)

pnum = 0

w_ratio = 0.1

while pnum < particle_num:

dx = xy[pnum][PX] - BP[PX]

dy = xy[pnum][PY] - BP[PY]

if dx > 0.5*a:

dx = dx + a

if dy > 0.5*a:

dy = dy + a

rr = math.sqrt(dx*dx + dy*dy)

if rr < Radi:

v2 = math.sqrt(xy[pnum][VX]**2 + xy[pnum][VY]**2)

cos = (xy[pnum][VX]*dx + xy[pnum][VY]*dy)/(v2*rr)

sin = math.sqrt(1 - cos**2)

tmpx= xy[pnum][VX]*(cos**2 - sin**2) - xy[pnum][VY]*(2*cos*sin)

tmpy= xy[pnum][VX]*(2*cos*sin) + xy[pnum][VY]*(cos**2 - sin**2)

xy[pnum][VX] = abs(tmpx) * dx / (abs(dx))

xy[pnum][VY] = abs(tmpy) * dy / (abs(dy))

BP[VX] = BP[VX] - w_ratio * abs(tmpx) * dx / (abs(dx))

BP[VY] = BP[VY] - w_ratio * abs(tmpy) * dy / (abs(dy))

pnum += 1

def integ():

find_pair()

particle_num = len(xy)

BP[PX] = BP[PX] + Dt*BP[VX]

BP[PY] = BP[PY] + Dt*BP[VY]

#boundary condition

if BP[PX] > a:

BP[PX] -= a

if BP[PY] > a:

BP[PY] -= a

if BP[PX] < 0:

BP[PX] += a

if BP[PY] < 0:

BP[PY] += a

pnum = 0

while pnum < particle_num:

#update position

xy[pnum][PX] = xy[pnum][PX] + Dt*xy[pnum][VX]

xy[pnum][PY] = xy[pnum][PY] + Dt*xy[pnum][VY]

if xy[pnum][PX] > a:

xy[pnum][PX] -= a

if xy[pnum][PY] > a:

xy[pnum][PY] -= a

if xy[pnum][PX] < 0:

xy[pnum][PX] += a

if xy[pnum][PY] < 0:

xy[pnum][PY] += a

pnum += 1

def calc_ena():

ena = 0.0

particle_num = len(xy)

for i in range(0,particle):

vx2 = xy[i][VX]*xy[i][VX]

vy2 = xy[i][VY]*xy[i][VY]

ena = ena + vx2 + vy2

ena = 0.5*ena

return ena

def update():

global Radi

PI = 3.14159263

global step

step = step + 1

# If you want to get image...

#capture()

integ()

#print step

nnum = 0

while nnum < len(xy):

glPointSize(3.0)

glColor3f(0.3, 0.3, 1.0)

glBegin(GL_POINTS)

glVertex2d(xy[nnum][PX], xy[nnum][PY])

glEnd()

nnum = nnum + 1

N_t = 30

glColor3f(1.0, 0.0, 0.0)

glBegin(GL_POLYGON)

for j in range(0,N_t):

glVertex2d(Radi*math.cos(2.0*PI*j/N_t)+BP[PX],

Radi*math.sin(2.0*PI*j/N_t)+BP[PY])

glEnd()

def init_set():

pnum = 0

xv_sum = 0

yv_sum = 0

particle_num = len(xy)

while pnum < particle_num:

xy[pnum][PX] = 0 # 0 x-position

xy[pnum][PY] = 0 # 1 y-position

xy[pnum][VX] = random.uniform(-1,1) # 2 x-velocity

xy[pnum][VY] = random.uniform(-1,1) # 3 y-velocity

xv_sum += xy[pnum][VX]

yv_sum += xy[pnum][VY]

pnum += 1

xv_sum = xv_sum / particle_num

yv_sum = yv_sum / particle_num

pnum = 0

while pnum < particle_num:

xy[pnum][VX] = xy[pnum][VX] - xv_sum

xy[pnum][VY] = xy[pnum][VY] - yv_sum

pnum += 1

BP[PX] = a/2

BP[PY] = a/2

BP[VX] = random.uniform(-0.5,0.5)

BP[VY] = random.uniform(-0.5,0.5)

def draw():

glClearColor(0.0, 0.0, 0.0, 0.0)

glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)

glLoadIdentity()

glColor3f(1.0,1.0,0.0)

gluLookAt(a/2, a/2, 4.0 ,a/2 ,a/2 ,0 , 0, 1.0, 0.0)

glBegin(GL_LINE_LOOP)

glVertex2d(0,0)

glVertex2d(0,a)

glVertex2d(a,a)

glVertex2d(a,0)

glEnd()

update()

glutSwapBuffers()

def resize(w, h):

glViewport(0, 0, w, h)

glLoadIdentity()

glOrtho(0, a, 0, a, -a, a)

def init():

glClearColor(0.7, 0.7, 0.7, 0.7)

def idle():

glutPostRedisplay()

def reshape(w, h):

glViewport(0, 0,w,h)

glMatrixMode(GL_PROJECTION)

glLoadIdentity()

gluPerspective(30.0, w/h, 1.0, 100.0)

glMatrixMode (GL_MODELVIEW)

if __name__ == "__main__":

init_set()

glutInitWindowPosition(50, 50);

glutInitWindowSize(340, 340);

glutInit(sys.argv)

glutInitDisplayMode(GLUT_RGBA | GLUT_DOUBLE )

glutCreateWindow("pyOpenGL TEST")

glutDisplayFunc(draw)

glutReshapeFunc(reshape)

init()

glutIdleFunc(idle)

glutMainLoop()

brownian motion simulation visualization by python and openGL

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