イオン粒子を座標原点向きに力を加えトラップしつつ速度をゆっくりと落としていくイオントラップの分子動力学シミュレーション。
粒子どうしはクーロン力により反発しつつ、中心向きの力を受け摂動しながら中央に集まっていく。分子動力学1ステップ毎に粒子の速度を減速させる。最終的には球体状の形状で安定構造となる。
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import random import math import itertools import time from OpenGL.GL import * from OpenGL.GLU import * from OpenGL.GLUT import * #from PIL import Image #from PIL import ImageOps #delta time Dt = 0.01 step = 0 #Define xyz index PX = 0 PY = 1 PZ = 2 VX = 3 VY = 4 VZ = 5 FX = 6 FY = 7 FZ = 8 FF = [FX, FY, FZ] PP = [PX, PY, PZ] #Coulomb's Force parameter CF = 1000.0 #mouse move mx = 0.0 my = 0.0 #lattice size lsize = 1.0 #number of particles in a line line_num = 8 #total particle num PN = line_num * line_num * line_num th = math.pi * 0.5 ph = math.pi * 0.5 #ready to 9 parameters for particle #(PX, PY, PZ, VX, VY, VZ, FX, FY, FZ) xyz = [[0 for i in range(9)] for j in range(PN)] def find_pair(): global PN for element in itertools.combinations(range(PN), 2): i = element[0] j = element[1] dx = xyz[i][PX] - xyz[j][PX] dy = xyz[i][PY] - xyz[j][PY] dz = xyz[i][PZ] - xyz[j][PZ] r = math.sqrt(dx*dx + dy*dy + dz*dz) xyz[i][FX] = xyz[i][FX] + dx/(r*r*r) xyz[i][FY] = xyz[i][FY] + dy/(r*r*r) xyz[i][FZ] = xyz[i][FZ] + dz/(r*r*r) xyz[j][FX] = xyz[j][FX] - dx/(r*r*r) xyz[j][FY] = xyz[j][FY] - dy/(r*r*r) xyz[j][FZ] = xyz[j][FZ] - dz/(r*r*r) def update(): global step step += 1 find_pair() pnum = 0 while pnum < PN: # set force that collects particles xyz[pnum][FX] = xyz[pnum][FX] + CF*(lsize/2.0 - xyz[pnum][PX]) xyz[pnum][FY] = xyz[pnum][FY] + CF*(lsize/2.0 - xyz[pnum][PY]) xyz[pnum][FZ] = xyz[pnum][FZ] + CF*(lsize/2.0 - xyz[pnum][PZ]) # if too large force is making , reset. CUT = 10000 for f in FF: if xyz[pnum][f] > abs(CUT): xyz[pnum][f] = 0 xyz[pnum][VX] = xyz[pnum][VX] + 0.5*Dt*xyz[pnum][FX] xyz[pnum][VY] = xyz[pnum][VY] + 0.5*Dt*xyz[pnum][FY] xyz[pnum][VZ] = xyz[pnum][VZ] + 0.5*Dt*xyz[pnum][FZ] xyz[pnum][FX] = 0.0 xyz[pnum][FY] = 0.0 xyz[pnum][FZ] = 0.0 pnum += 1 print "- step =", step," -" pnum = 0 while pnum < PN: #update position xyz[pnum][PX] = xyz[pnum][PX] + Dt*xyz[pnum][VX] xyz[pnum][PY] = xyz[pnum][PY] + Dt*xyz[pnum][VY] xyz[pnum][PZ] = xyz[pnum][PZ] + Dt*xyz[pnum][VZ] pnum += 1 def init_lattice(): #PN = line_num^3 delt = lsize/line_num; xv_sum = 0 yv_sum = 0 zv_sum = 0 pnum = 0 k = 0 while k < line_num: j = 0 while j < line_num: i = 0 while i < line_num: xyz[pnum][PX] = delt * i xyz[pnum][PY] = delt * j xyz[pnum][PZ] = delt * k pnum += 1 i += 1 j += 1 k += 1 pnum = 0 while pnum < PN: xyz[pnum][VX] = random.uniform(-1,1) # 1 x-velocity xyz[pnum][VY] = random.uniform(-1,1) # 2 y-velocity xyz[pnum][VZ] = random.uniform(-1,1) # 3 z-velocity xv_sum += xyz[pnum][VX] yv_sum += xyz[pnum][VY] zv_sum += xyz[pnum][VZ] pnum += 1 xv_sum = xv_sum / PN yv_sum = yv_sum / PN zv_sum = zv_sum / PN pnum = 0 while pnum < PN: xyz[pnum][VX] = xyz[pnum][VX] - xv_sum xyz[pnum][VY] = xyz[pnum][VY] - yv_sum xyz[pnum][VZ] = xyz[pnum][VZ] - zv_sum pnum += 1 def draw(): cx = cy = cz = lsize * 0.5 glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT) glClearColor(0.0, 0.0, 0.0, 1.0) glLoadIdentity() glColor3f(1.0,1.0,0.0) gluLookAt(5*math.sin(th)*math.cos(ph)+cx, 5*math.cos(th)+cy, 5*math.sin(th)*math.sin(ph)+cz,\ cx, cy, cz, -math.cos(th)*math.cos(ph),math.sin(th),-math.cos(th)*math.sin(ph) ) glBegin(GL_LINE_LOOP) glVertex3d(0,0,0) glVertex3d(0,lsize,0) glVertex3d(lsize,lsize,0) glVertex3d(lsize,0,0) glEnd() glBegin(GL_LINE_LOOP) glVertex3d(0,0,lsize) glVertex3d(0,lsize,lsize) glVertex3d(lsize,lsize,lsize) glVertex3d(lsize,0,lsize) glEnd() glBegin(GL_LINES) glVertex3d(0,0,0) glVertex3d(0,0,lsize) glEnd() glBegin(GL_LINES) glVertex3d(0,lsize,0) glVertex3d(0,lsize,lsize) glEnd() glBegin(GL_LINES) glVertex3d(lsize,0,0) glVertex3d(lsize,0,lsize) glEnd() glBegin(GL_LINES) glVertex3d(lsize,lsize,0) glVertex3d(lsize,lsize,lsize) glEnd() pnum = 0 while pnum < PN: glPointSize(3.0) glColor3f(0.3, 0.3, 1.0) glBegin(GL_POINTS) glVertex3d(xyz[pnum][PX], xyz[pnum][PY], xyz[pnum][PZ]) glEnd() #Reduce particle velocity xyz[pnum][VX] *= 0.99 xyz[pnum][VY] *= 0.99 xyz[pnum][VZ] *= 0.99 pnum = pnum + 1 update() glutSwapBuffers() 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) def motion(x, y): global ph, th, mx, my dltx = mx -x dlty = my -y #Invalid large motion if 10 < abs(dltx): dltx = 0 if 10 < abs(dlty): dlty = 0 ph = ph - 0.01*dltx th = th + 0.01*dlty glutPostRedisplay() glutSwapBuffers() mx = x my = y if __name__ == "__main__": init_lattice() glutInitWindowPosition(50, 50); glutInitWindowSize(500, 500); glutInit(sys.argv) glutInitDisplayMode(GLUT_RGBA | GLUT_DOUBLE ) glutCreateWindow("pyOpenGL TEST") glutDisplayFunc(draw) glutReshapeFunc(reshape) glutMotionFunc(motion); init() glutIdleFunc(idle) glutMainLoop() # END ---- |
Slowly down the speed while trapping the ion particles.
Particles are repulsed by the Coulomb force, and they are gathered in the center while being perturbed by the center-directed force. Molecular Dynamics Reduce the velocity of the particle every step.
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