def g_force(self, o): r = self.pos - o.pos if mag2(r) > 0: return -norm(self.pos - o.pos) * g * self.mass * o.mass / mag2(self.pos - o.pos) return vector()
def kinetic_energy(self): return 0.5 * self.mass * mag2(self.v())
def Simulation():
config.Atoms = [] # spheres
p = [] # momentums (vectors)
apos = [] # positions (vectors)
ampl = 0 #амплитуда движения
period = 5
k = 1.4E-23 # Boltzmann constant
R = 8.3
dt = 1E-5
time = 0
def checkCollisions(Natoms, Ratom):
hitlist = []
r2 = 2 * Ratom
for i in range(Natoms):
for j in range(i):
dr = apos[i] - apos[j]
if dr.mag < r2:
hitlist.append([i, j])
return hitlist
def speed(time, piston_mode, period, ampl, temp):
if (piston_mode == 0):
return 0
if (piston_mode == 1):
return ampl / 10 * 3 * sin(time / period * 2 * pi) * sqrt(
3 * config.mass * k * temp) / (5 * config.mass) / period * 100
if (piston_mode == 2):
if (time % period < period // 2):
return 1.5 * ampl / 10 * sqrt(3 * config.mass * k * temp) / (
5 * config.mass) / period * 100
else:
return -1.5 * ampl / 10 * sqrt(3 * config.mass * k * temp) / (
5 * config.mass) / period * 100
if (piston_mode == 3):
if (time % period < period // 5):
return 5 * ampl / 10 * sqrt(3 * config.mass * k * temp) / (
5 * config.mass) / period * 100
else:
return -5 / 4 * ampl / 10 * sqrt(
3 * config.mass * k * temp) / (5 *
config.mass) / period * 100
if (piston_mode == 4):
if (time % period < 4 * period // 5):
return 5 / 4 * ampl / 10 * sqrt(3 * config.mass * k * temp) / (
5 * config.mass) / period * 100
else:
return -5 * ampl / 10 * sqrt(3 * config.mass * k * temp) / (
5 * config.mass) / period * 100
width, height = config.w.win.GetSize()
offset = config.w.dheight
deltav = 100 # histogram bar width
disp = display(
window=config.w,
x=offset,
y=offset,
forward=vector(0, -0.05, -1),
range=1, # userspin = False,
width=width / 3,
height=height)
g1 = gdisplay(window=config.w,
x=width / 3 + 2 * offset,
y=2 * offset,
background=color.white,
xtitle='t',
ytitle='v',
foreground=color.black,
width=width / 3,
height=height / 2 - 2 * offset)
g2 = gdisplay(window=config.w,
x=width / 3 + 2 * offset,
y=height / 2 + offset,
background=color.white,
foreground=color.black,
width=width / 3,
height=height / 2 - 2 * offset)
# adding empty dots to draw axis
graph_average_speed = gcurve(gdisplay=g1, color=color.white)
graph_average_speed.plot(pos=(3000, 1500))
graph_temp = gcurve(gdisplay=g2, color=color.white)
graph_temp.plot(pos=(3000, config.Natoms * deltav / 1000))
speed_text = wx.StaticText(config.w.panel,
pos=(width / 3 + 2 * offset, offset),
label="Средняя скорость")
graph_text = wx.StaticText(config.w.panel,
pos=(width / 3 + 2 * offset, height / 2),
label="")
L = 1 # container is a cube L on a side
d = L / 2 + config.Ratom # half of cylinder's height
topborder = d
gray = color.gray(0.7) # color of edges of container
# cylinder drawing
cylindertop = cylinder(pos=(0, d - 0.001, 0), axis=(0, 0.005, 0), radius=d)
ringtop = ring(pos=(0, d, 0), axis=(0, -d, 0), radius=d, thickness=0.005)
ringbottom = ring(pos=(0, -d, 0),
axis=(0, -d, 0),
radius=d,
thickness=0.005)
body = cylinder(pos=(0, -d, 0), axis=(0, 2 * d, 0), radius=d, opacity=0.2)
# body_tmp = cylinder(pos = (0, d, 0), axis = (0, 2 * d, 0), radius = d + 0.1, color = (0, 0, 0))
# ceil = box(pos = (0, d, 0), length = 5, height = 0.005, width = 5, color = (0, 0, 0))
# floor = box(pos = (0, -d, 0), length = 100, height = 0.005, width = 100, color = (0, 0, 0))
# left = box(pos = (d + 0.005, 0, 0), axis = (0, 1, 0), length = 100, height = 0.005, width = 100, color = (0, 0, 0))
# right = box(pos = (-d - 0.005, 0, 0), axis = (0, 1, 0), length = 100, height = 0.005, width = 100, color = (0, 0, 0))
# uniform particle distribution
for i in range(config.Natoms):
qq = 2 * pi * random.random()
x = sqrt(random.random()) * L * cos(qq) / 2
y = L * random.random() - L / 2
z = sqrt(random.random()) * L * sin(qq) / 2
if i == 0:
# particle with a trace
config.Atoms.append(
sphere(pos=vector(x, y, z),
radius=config.Ratom,
color=color.cyan,
make_trail=False,
retain=100,
trail_radius=0.3 * config.Ratom))
else:
config.Atoms.append(
sphere(pos=vector(x, y, z), radius=config.Ratom, color=gray))
apos.append(vector(x, y, z))
# waiting to start, adjusting everything according to changing variables
"""WAITING TO START"""
last_Natoms = config.Natoms
last_Ratom = config.Ratom
while config.start == 0:
if config.menu_switch == 0:
disp.delete()
g1.display.delete()
g2.display.delete()
graph_text.Destroy()
speed_text.Destroy()
return
if config.Natoms > last_Natoms:
for i in range(config.Natoms - last_Natoms):
qq = 2 * pi * random.random()
x = sqrt(random.random()) * L * cos(qq) / 2
y = L * random.random() - L / 2
z = sqrt(random.random()) * L * sin(qq) / 2
if last_Natoms == 0:
# particle with a trace
config.Atoms.append(
sphere(pos=vector(x, y, z),
radius=config.Ratom,
color=color.cyan,
make_trail=False,
retain=100,
trail_radius=0.3 * config.Ratom))
else:
config.Atoms.append(
sphere(pos=vector(x, y, z),
radius=config.Ratom,
color=gray))
apos.append(vector(x, y, z))
last_Natoms = config.Natoms
elif config.Natoms < last_Natoms:
for i in range(last_Natoms - config.Natoms):
config.Atoms.pop().visible = False
apos.pop()
last_Natoms = config.Natoms
if last_Ratom != config.Ratom:
for i in range(last_Natoms):
config.Atoms[i].radius = config.Ratom
last_Ratom = config.Ratom
if config.model == 0:
if config.piston_mode >= 1:
graph_text.SetLabel("Температура")
else:
graph_text.SetLabel("Распределение скоростей частиц")
sleep(0.1)
# freezed all variables, ready to start
last_T = config.T
last_ampl = config.ampl
last_period = config.period
last_piston_mode = config.piston_mode
last_model = config.model
pavg = sqrt(3 * config.mass * k *
last_T) # average kinetic energy p**2/(2config.mass) = (3/2)kT
for i in range(last_Natoms):
theta = pi * random.random()
phi = 2 * pi * random.random()
px = pavg * sin(theta) * cos(phi)
py = pavg * sin(theta) * sin(phi)
pz = pavg * cos(theta)
p.append(vector(px, py, pz))
if last_model == 1:
disp.delete()
unavail = wx.StaticText(
config.w.panel,
style=wx.ALIGN_CENTRE_HORIZONTAL,
label="Отображение модели недоступно в режиме статистики",
pos=(offset, height / 2 - offset))
unavail.Wrap(width / 3)
last_period = last_period / 10
last_piston_mode += 1
graph_text.SetLabel("Температура")
""" DRAW GRAPHS """
g1.display.delete()
g2.display.delete()
if last_piston_mode == 0:
g1 = gdisplay(window=config.w,
x=width / 3 + 2 * offset,
y=2 * offset,
background=color.white,
xtitle='t',
ytitle='v',
foreground=color.black,
width=width / 3,
height=height / 2 - 2 * offset,
ymin=0.7 * pavg / config.mass,
ymax=1.3 * pavg / config.mass)
g2 = gdisplay(window=config.w,
x=width / 3 + 2 * offset,
y=height / 2 + offset,
background=color.white,
foreground=color.black,
xtitle='v',
ytitle='Frequency',
width=width / 3,
height=height / 2 - 2 * offset,
xmax=3000 / 300 * last_T,
ymax=last_Natoms * deltav / 1000)
else:
g1 = gdisplay(window=config.w,
x=width / 3 + 2 * offset,
y=2 * offset,
background=color.white,
xtitle='t',
ytitle='v',
foreground=color.black,
width=width / 3,
height=height / 2 - 2 * offset)
g2 = gdisplay(window=config.w,
x=width / 3 + 2 * offset,
y=height / 2 + offset,
background=color.white,
xtitle='t',
ytitle='T',
foreground=color.black,
width=width / 3,
height=height / 2 - 2 * offset)
graph_average_speed = gcurve(gdisplay=g1, color=color.black)
if last_piston_mode:
graph_temp = gcurve(gdisplay=g2, color=color.black)
else:
theory_speed = gcurve(gdisplay=g2, color=color.black)
dv = 10
for v in range(0, int(3000 / 300 * last_T), dv):
theory_speed.plot(pos=(v, (deltav / dv) * last_Natoms * 4 * pi *
((config.mass /
(2 * pi * k * last_T))**1.5) *
exp(-0.5 * config.mass * (v**2) /
(k * last_T)) * (v**2) * dv))
hist_speed = ghistogram(gdisplay=g2,
bins=arange(0, int(3000 / 300 * last_T), 100),
color=color.red,
accumulate=True,
average=True)
speed_data = [] # histogram data
for i in range(last_Natoms):
speed_data.append(pavg / config.mass)
# speed_data.append(0)
""" MAIN CYCLE """
while config.start:
while config.pause:
sleep(0.1)
rate(100)
sp = speed(time, last_piston_mode, last_period, last_ampl, 300)
cylindertop.pos.y -= sp * dt
time += 1
for i in range(last_Natoms):
config.Atoms[i].pos = apos[i] = apos[i] + (p[i] / config.mass) * dt
if last_piston_mode == 0:
speed_data[i] = mag(p[i]) / config.mass
total_momentum = 0
v_sum = 0
for i in range(last_Natoms):
total_momentum += mag2(p[i])
v_sum += sqrt(mag2(p[i])) / config.mass
graph_average_speed.plot(pos=(time, v_sum / last_Natoms))
if last_piston_mode:
graph_temp.plot(pos=(time, total_momentum / (3 * k * config.mass) /
last_Natoms))
else:
hist_speed.plot(data=speed_data)
hitlist = checkCollisions(last_Natoms, last_Ratom)
for ij in hitlist:
i = ij[0]
j = ij[1]
ptot = p[i] + p[j]
posi = apos[i]
posj = apos[j]
vi = p[i] / config.mass
vj = p[j] / config.mass
vrel = vj - vi
a = vrel.mag2
if a == 0: # exactly same velocities
continue
rrel = posi - posj
if rrel.mag > config.Ratom: # one atom went all the way through another
continue
# theta is the angle between vrel and rrel:
dx = dot(rrel, norm(vrel)) # rrel.mag*cos(theta)
dy = cross(rrel, norm(vrel)).mag # rrel.mag*sin(theta)
# alpha is the angle of the triangle composed of rrel, path of atom j, and a line
# from the center of atom i to the center of atom j where atome j hits atom i:
alpha = asin(dy / (2 * config.Ratom))
d = (2 * config.Ratom) * cos(
alpha
) - dx # distance traveled into the atom from first contact
deltat = d / vrel.mag # time spent moving from first contact to position inside atom
posi = posi - vi * deltat # back up to contact configuration
posj = posj - vj * deltat
mtot = 2 * config.mass
pcmi = p[
i] - ptot * config.mass / mtot # transform momenta to cm frame
pcmj = p[j] - ptot * config.mass / mtot
rrel = norm(rrel)
pcmi = pcmi - 2 * pcmi.dot(rrel) * rrel # bounce in cm frame
pcmj = pcmj - 2 * pcmj.dot(rrel) * rrel
p[i] = pcmi + ptot * config.mass / mtot # transform momenta back to lab frame
p[j] = pcmj + ptot * config.mass / mtot
apos[i] = posi + (
p[i] / config.mass) * deltat # move forward deltat in time
apos[j] = posj + (p[j] / config.mass) * deltat
# collisions with walls
for i in range(last_Natoms):
# проекция радиус-вектора на плоскость
loc = vector(apos[i])
loc.y = 0
# вылет за боковую стенку (цилиндр радиуса L / 2 + config.Ratom)
if (mag(loc) > L / 2 + 0.01 - last_Ratom +
sqrt(p[i].x**2 + p[i].z**2) / config.mass * dt):
# проекция импульса на плоскость
proj_p = vector(p[i])
proj_p.y = 0
loc = norm(loc)
# скалярное произведение нормированного радиус-вектора на импульс (все в проекции на плоскость)
dotlp = dot(loc, proj_p)
if dotlp > 0:
p[i] -= 2 * dotlp * loc
# dotlp < 0 - атом улетает от стенки
# dotlp = 0 - атом летит вдоль стенки
loc = apos[i]
# вылет за торцы
if loc.y + p[i].y / config.mass * dt < -L / 2 - 0.01 + last_Ratom:
p[i].y = abs(p[i].y)
if loc.y + p[
i].y / config.mass * dt > cylindertop.pos.y - last_Ratom:
v_otn = p[i].y / config.mass + sp
if v_otn > 0:
p[i].y = (-v_otn - sp) * config.mass
# type here
if last_model == 0:
disp.delete()
else:
unavail.Destroy()
g1.display.delete()
g2.display.delete()
graph_text.Destroy()
speed_text.Destroy()