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from visual import *
from random import random
from time import clock
N = 3
Ntotal = N*N*N
scolor = (1,1,0)
springs = []
atoms = []
m = 1.
k = 1.
L = 1.
R = 0.3*L
Rs = 0.9*R # end of spring is Rs from center of atom
def getn(N, nx, ny, nz): # find nth atom given nx, ny, nz
return (ny)*(N**2)+(nx)*N+(nz)
def makespring(natom1, natom2, radius): # make spring from nnth atom to iith atom
if natom1 > natom2:
r12 = atoms[natom2].pos-atoms[natom1].pos
dir = norm(r12)
springs.append( helix(pos=atoms[natom1].pos+Rs*dir,
axis=(L-2*Rs)*dir,
radius = radius, color=scolor, thickness = 0.04))
springs[-1].natom1 = natom1
springs[-1].natom2 = natom2
angle = springs[-1].axis.diff_angle( vector(0,1,0))
if angle < 0.1 or angle > pi-0.1:
springs[-1].up = vector(-1,0,0) # avoid pathologies if too near the y axis (default "up")
def crystal(N=3, delta=1.0, R=None, sradius=None):
if R == None:
R = 0.2*delta
if sradius == None:
sradius = R/5.
xmin = -(N-1.0)/2.
ymin = xmin
zmin = xmin
natom = 0
for ny in range(N):
y = ymin+ny*delta
hue = (ny)/(N+1.0)
c = color.hsv_to_rgb((hue,1.0,1.0))
for nx in range(N):
x = xmin+nx*delta
for nz in range(N):
z = zmin+nz*delta
atoms.append(sphere(pos=(x,y,z), radius=R, color=c))
atoms[-1].p = vector()
atoms[-1].near = range(6)
atoms[-1].wallpos = range(6)
atoms[-1].natom = natom
atoms[-1].indices = (nx,ny,nz)
natom = natom+1
for a in atoms:
natom1 = a.natom
nx, ny, nz = a.indices
if nx == 0: # left
# if this neighbor is the wall, save location:
a.near[0] = None
a.wallpos[0] = a.pos-vector(L,0,0)
else:
natom2 = getn(N,nx-1,ny,nz)
a.near[0] = natom2
makespring(natom1, natom2, sradius)
if nx == N-1: # right
a.near[1] = None
a.wallpos[1] = a.pos+vector(L,0,0)
else:
natom2 = getn(N,nx+1,ny,nz)
a.near[1] = natom2
makespring(natom1, natom2, sradius)
if ny == 0: # down
a.near[2] = None
a.wallpos[2] = a.pos-vector(0,L,0)
else:
natom2 = getn(N,nx,ny-1,nz)
a.near[2] = natom2
makespring(natom1, natom2, sradius)
if ny == N-1: # up
a.near[3] = None
a.wallpos[3] = a.pos+vector(0,L,0)
else:
natom2 = getn(N,nx,ny+1,nz)
a.near[3] = natom2
makespring(natom1, natom2, sradius)
if nz == 0: # back
a.near[4] = None
a.wallpos[4] = a.pos-vector(0,0,L)
else:
natom2 = getn(N,nx,ny,nz-1)
a.near[4] = natom2
makespring(natom1, natom2, sradius)
if nz == N-1: # front
a.near[5] = None
a.wallpos[5] = a.pos+vector(0,0,L)
else:
natom2 = getn(N,nx,ny,nz+1)
a.near[5] = natom2
makespring(natom1, natom2, sradius)
a.near = tuple(a.near)
a.wallpos = tuple( a.wallpos)
# Nearpos is a list of references to the nearest neighbors' positions,
# taking into account wall effects.
a.nearpos = []
for i in range(6):
natom = a.near[i]
if natom == None: # if this nearest neighbor is the wall
a.nearpos.append( a.wallpos[i])
else:
a.nearpos.append(atoms[natom].pos)
return atoms
sradius = R/4.
vrange = 0.2*L*sqrt(k/m)
dt = 2.*pi*sqrt(m/k)/40.
atoms = crystal(N=N, delta=L, R=R, sradius=sradius)
scene.autoscale = 0
ptotal = vector()
for a in atoms:
px = m*(-vrange/2+vrange*random())
py = m*(-vrange/2+vrange*random())
pz = m*(-vrange/2+vrange*random())
a.p = vector(px,py,pz)
ptotal = ptotal+a.p
for a in atoms:
a.p = a.p-ptotal/(N**2)
# Convert to tuples for faster indexing access. We aren't growing any more of them.
springs = tuple(springs)
atoms = tuple(atoms)
tt = clock()
Nsteps = 0
# Evaluate a couple of constants outside the loop
k_dt = k * dt
dt_m = dt / m
while 1:
rate(50)
for a in atoms:
nearpos = vector_array( a.nearpos)
r = nearpos - a.pos
# F = k*(r.norm()*(r.mag()-L))
a.p += k_dt *(r.norm()*(r.mag()-L)).sum() # using capabilities of Numeric module
for a in atoms:
a.pos += a.p * dt_m
for s in springs:
r12 = atoms[s.natom2].pos-atoms[s.natom1].pos
dir = norm(r12)
s.pos = atoms[s.natom1].pos+Rs*dir
s.axis = (r12.mag-2*Rs)*dir
if Nsteps == 100:
tt = clock()-tt
print '%0.1f' % tt, 'sec for', Nsteps, 'steps with', N, 'on a side'
Nsteps += 1
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