class System:
def __init__(self,
cell=None,
nballs=10,
step=0,
gc=None,
input=None,
logfile=sys.stdout,
velfile=None,
velint=0,
kT=None,
hist=False):
self.cell = cell
if input is not None:
self.load(input)
else:
self.balls = lattice(nballs, cell)
if kT is not None:
# ra.seed(1)
self.thermalize(kT)
self.balls.interact(cell)
self.step = step
self.gc = gc
self.logfile = logfile
self.velfile = velfile
self.velinterval = velint
self.kT = kT
self.hist = hist
self.histx = Hist(-5, +5, 0.05)
self.histy = Hist(-5, +5, 0.05)
def thermalize(self, kT):
self.balls.randomize(kT)
# Remove total translation
velsum = np.sum(self.balls.vel, axis=0)
velsum /= self.balls.N
self.balls.vel -= velsum
def OneStep(self, dt):
# Progress Momenta (half)
self.balls.accel(dt / 2.0)
# Progress Position
self.balls.forward(dt)
self.balls.resetforce()
# Force
self.pot, virsum = self.balls.interact(self.cell)
# Progress Momenta (half)
self.balls.accel(dt / 2.0)
# temperature scaling
# if self.kT is not None:
if False:
kin = self.balls.kinetic()
dof = self.balls.N * self.cell.shape[0]
factor = (self.kT * dof / 2.0) / kin
factor = 1.0 - (1.0 - factor) * 0.001
self.balls.rescale(factor)
# Data output
if self.logfile is not None:
dof = self.balls.dim * self.balls.N
kin = self.balls.kinetic()
kT = 2.0 * kin / dof
z = 1.0 - virsum / (dof * kT)
self.logfile.write(
"%s %s %s %s %s %s\n" %
(self.step, kT, z, kin + self.pot, kin, self.pot))
if self.velfile is not None and self.step % self.velinterval == 0:
for i in range(0, N):
self.velfile.write("%s\n" %
sqrt(2.0 * self.balls[i].kinetic()))
# histogram
for v in self.balls.vel:
self.histx.accum(v[0], 1.0)
if len(v.shape) > 1:
self.histy.accum(v[1], 1.0)
self.step += 1
def draw(self):
if self.gc is not None:
dim = self.cell.shape[0]
if 2 < dim:
avgvel = 1.0
if self.kT is not None:
avgvel = sqrt(dim * self.kT)
self.balls.draw(self.cell, self.gc, avgvel)
else:
self.balls.draw(self.cell, self.gc, 0.0)
if dim > 1:
canvasx = self.cell[0] * self.gc.zoom
canvasy = self.cell[1] * self.gc.zoom
if self.hist:
self.histx.draw(0, canvasy, canvasx, canvasy / 2)
self.histx.draw(canvasx,
canvasy,
canvasx / 2,
canvasy,
vertical=True)
else:
canvasx = self.cell[0] * self.gc.zoom
canvasy = self.gc.zoom
if self.hist:
self.histx.draw(0, canvasy, canvasx, canvasy / 2)
# self.histx.draw(canvasx,canvasy,canvasx/2,canvasy,vertical=True)
def load(self, file):
self.balls = []
s = file.readline()
self.cell = unserialize(s)
s = file.readline()
x = unserialize(s)
x = int(x[0])
for i in range(0, x):
self.balls.append(Particle(file=file))
s = file.readline()
# serialize
def __str__(self):
s = serialize(self.cell)
s += "%s\n" % len(self.balls)
for i in range(0, len(self.balls)):
s += "%s\n" % self.balls[i]
return s
def save(self, file):
file.write("%s\n" % self)
class System:
def __init__(self,
cell=None,
nballs=10,
step=0,
gc=None,
input=None,
logfile=sys.stdout,
velfile=None,
kT=None,
hist=False):
if hist:
self.colorscheme = AbsoluteVelocity(max=5 / 2)
self.histx = Hist(-5, +5, 0.05, self.colorscheme)
self.histy = Hist(-5, +5, 0.05, self.colorscheme)
self.hist = True
else:
self.colorscheme = None
self.hist = False
if input is not None:
self.load(input)
else:
self.lattice(cell, nballs)
if kT is not None:
ra.seed(1)
self.thermalize(kT)
self.last1 = self.last2 = None
# initialize force
self.step = step
self.gc = gc
self.logfile = logfile
self.velfile = velfile
self.kT = kT
self.hist = hist
def lattice(self, cell, nballs):
self.balls = []
self.cell = cell
dim = len(cell)
if dim == 1:
self.lattice1d(nballs)
self.walls = [Wall(coeff=[1.0, 0.0]), Wall(coeff=[1.0, cell[0]])]
self.area = 2.0 * 1.0
self.volume = cell[0]
elif dim == 2:
self.lattice2d(nballs)
# d次元の壁はd+1個の係数で指示する。
# 最後の要素以外は単位ベクトルでなければいけない。
self.walls = [
Wall(coeff=[1.0, 0.0, 0.0]),
Wall(coeff=[1.0, 0.0, cell[0]]),
Wall(coeff=[0.0, 1.0, 0.0]),
Wall(coeff=[0.0, 1.0, cell[1]])
]
self.area = 2.0 * (cell[0] + cell[1])
self.volume = cell[0] * cell[1]
elif dim == 3:
self.lattice3d(nballs)
self.walls = [
Wall(coeff=[1.0, 0.0, 0.0, 0.0]),
Wall(coeff=[1.0, 0.0, 0.0, cell[0]]),
Wall(coeff=[0.0, 1.0, 0.0, 0.0]),
Wall(coeff=[0.0, 1.0, 0.0, cell[1]]),
Wall(coeff=[0.0, 0.0, 1.0, 0.0]),
Wall(coeff=[0.0, 0.0, 1.0, cell[1]])
]
self.area = 2.0 * (cell[0] * cell[1] + cell[1] * cell[2] +
cell[0] * cell[2])
self.volume = cell[0] * cell[1] * cell[2]
def thermalize(self, kT):
dim = len(self.cell)
N = len(self.balls)
# 1粒子だけにエネルギーを与える。
self.balls[0].randomize(sqrt(dim * kT * float(N)))
def rescale(self, factor):
for b in self.balls:
b.rescale(factor)
def lattice1d(self, nballs):
n = nballs
x = 0.1
while 0 < n:
self.balls += [HardDisk([x], [0.0])]
n -= 1
x += 1.12
def lattice2d(self, nballs):
n = nballs
x = 0.1
y = 0.1
while 0 < n:
self.balls += [
HardDisk([x, y], [0.0, 0.0], colorscheme=self.colorscheme)
]
n -= 1
x += 1.12
if self.cell[0] < x:
x -= self.cell[0] - (1.12 / 2.0)
y += 1.12 * sqrt(3.0) / 2.0
def lattice3d(self, nballs):
n = nballs
x = 0.1
y = 0.1
z = 0.1
while 0 < n:
self.balls += [HardDisk([x, y, z], [0.0, 0.0, 0.0])]
n -= 1
x += 1.12
if self.cell[0] < x:
x -= self.cell[0] - (1.12 / 2.0)
y += 1.12 * sqrt(3.0) / 2.0
if self.cell[0] < y:
y = 0.1
z += 1.12 * sqrt(3.0) / 2.0
def OneCollision(self, deltat):
dtmin = deltat
object1 = 0
object2 = 0
# 粒子のいずれかが壁にぶつかるまでの最短時間を調べる。
for b in self.balls:
for w in self.walls:
if b != self.last1 or w != self.last2:
dt = b.collideWall(w)
if 0 < dt < dtmin:
dtmin = dt
object1 = b
object2 = w
# 粒子同士が衝突するまでの最短時間を調べる。
N = len(self.balls)
for i in range(0, N):
for j in range(i + 1, N):
if self.balls[i] != self.last1 or self.balls[j] != self.last2:
dt = self.balls[i].collide(self.balls[j])
if 0 < dt < dtmin:
dtmin = dt
object1 = self.balls[i]
object2 = self.balls[j]
# 粒子をdtminだけ進める。
for b in self.balls:
b.forward(dtmin)
impulse = 0.0
# 衝突相手が粒子なら
if isinstance(object2, HardDisk):
(v1, t1, v2, t2) = object1.reflect(object2)
if self.velfile is not None:
self.velfile.write("%s %s\n" % (v1, t1))
self.velfile.write("%s %s\n" % (v2, t2))
self.last1 = object1
self.last2 = object2
# 壁に衝突する場合は、壁への力積から圧力が出せる。
elif isinstance(object1, HardDisk):
impulse = object1.reflectWall(object2)
self.last1 = object1
self.last2 = object2
# 最後に衝突した物体と、消費した時間を返す。
return (dtmin, impulse)
def OneStep(self, dt):
bunbo = dt * self.area
sumpulse = 0.0
ncollision = 0
while 0.0 < dt:
# 次の衝突またはdtまで粒子を進める。
(progress, impulse) = self.OneCollision(dt)
dt -= progress
sumpulse += impulse
if impulse == 0.0:
ncollision += 1
if self.hist:
for b in self.balls:
self.histx.accum(b.vel[0], progress)
if len(b.vel) > 1:
self.histy.accum(b.vel[1], progress)
# Data output
if self.logfile is not None:
dim = len(self.cell)
N = len(self.balls)
kin = 0.0
for b in self.balls:
kin += b.kinetic()
kT = 2.0 * kin / (dim * N)
#z = 1.0 + virsum / (dim * N * kT )
pressure = sumpulse / bunbo
self.logfile.write("%s %s %s %s %s\n" %
(self.step, kT, pressure * self.volume /
(N * kT), kin, ncollision))
# histogram
if self.hist:
for b in self.balls:
self.histx.accum(b.vel[0], 1.0)
if len(b.vel) > 1:
self.histy.accum(b.vel[1], 1.0)
self.step += 1
def draw(self):
if self.gc is not None:
dim = len(self.cell)
if 2 < dim:
avgvel = 0.0
if self.kT > 0.0:
avgvel = sqrt(dim * self.kT)
tmp = list(self.balls)
tmp.sort(key=lambda x: -x.pos[2])
for b in tmp:
b.draw(self.cell, self.gc, avgvel)
else:
for b in self.balls:
b.draw(self.cell, self.gc, 0.0)
if dim > 1:
canvasx = self.cell[0] * self.gc.zoom
canvasy = self.cell[1] * self.gc.zoom
if self.hist:
self.histx.draw(0, canvasy, canvasx, canvasy / 2)
self.histx.draw(canvasx,
canvasy,
canvasx / 2,
canvasy,
vertical=True)
else:
canvasx = self.cell[0] * self.gc.zoom
canvasy = self.gc.zoom
if self.hist:
self.histx.draw(0, canvasy, canvasx, canvasy / 2)
# self.histx.draw(canvasx,canvasy,canvasx/2,canvasy,vertical=True)
def load(self, file):
s = file.readline()
self.cell = unserialize(s)
self.balls = []
s = file.readline()
x = unserialize(s)
x = int(x[0])
for i in range(0, x):
self.balls.append(HardDisk(file=file))
self.walls = []
s = file.readline()
x = unserialize(s)
x = int(x[0])
for i in range(0, x):
self.walls.append(Wall(file=file))
s = file.readline()
x = unserialize(s)
self.area = float(x[0])
s = file.readline()
x = unserialize(s)
self.volume = float(x[0])
s = file.readline()
# serialize
def __str__(self):
s = serialize(self.cell)
s += "%s\n" % len(self.balls)
for i in range(0, len(self.balls)):
s += "%s\n" % self.balls[i]
s += "%s\n" % len(self.walls)
for i in range(0, len(self.walls)):
s += "%s\n" % self.walls[i]
s += "%s\n" % self.area
s += "%s\n" % self.volume
return s
def save(self, file):
file.write("%s\n" % self)