def __init__(self, reference, tangent):
self.t = visual.norm(tangent)
# make reference vector orthogonal to tangent
proj_r_to_t = reference.dot(tangent) / tangent.dot(tangent) * tangent
self.r = visual.norm(reference - proj_r_to_t)
# make bitangent vector orthogonal to the others
self.s = visual.norm(self.t.cross(self.r))
def GetElementWorldLocation(self, ElementKey):
"""Returns the location of the specified element in world coordinates."""
assert ElementKey in self._elementDict
self._elementDict.get(ElementKey).SetVisible(isVisible)
localPos = self.GetElement(ElementKey).pos
xAxis = visual.norm(self._myFrame.axis)
zAxis = visual.norm(visual.cross(self._myFrame.axis, self._myFrame.up))
yAxis = visual.norm(visual.cross(z_axis, x_axis))
worldPos = self._myFrame.pos + (localPos.x * xAxis) + (localPos.y * yAxis) + (localPos.z * zAxis)
return worldPos
def GetElementWorldLocation(self, ElementKey):
"""Returns the location of the specified element in world coordinates."""
assert ElementKey in self._elementDict
self._elementDict.get(ElementKey).SetVisible(isVisible)
localPos = self.GetElement(ElementKey).pos
xAxis = visual.norm(self._myFrame.axis)
zAxis = visual.norm(visual.cross(self._myFrame.axis, self._myFrame.up))
yAxis = visual.norm(visual.cross(z_axis, x_axis))
worldPos = self._myFrame.pos + (localPos.x * xAxis) + (
localPos.y * yAxis) + (localPos.z * zAxis)
return worldPos
def _set_plane_vectors(self):
cx, cy, cz = self.center.getPosition()
x, y, z = self.motors[0].getPosition()
self.v1 = norm(vector(x-cx, y-cy, z-cz))
x, y, z = self.motors[2].getPosition()
self.v2 = norm(vector(x-cx, y-cy, z-cz))
# Calculate pitch and roll
self.pitch = 90 - degrees(self.v1.diff_angle(vector(0, 1, 0)))
self.roll = degrees(self.v2.diff_angle(vector(0, 1, 0))) - 90
# calculate yaw, (this works if the quad is close to a horizontal position)
if self.v1.z <= 0:
self.yaw = degrees(self.v1.diff_angle(vector(1, 0, 0)))
else:
self.yaw = 360 - degrees(self.v1.diff_angle(vector(1, 0, 0)))
def c_acel(self, xm, obj):
acel = v.vector(0, 0, 0)
for i in obj:
if i.id != self.id:
acel += (i.mass * (v.norm(i.pos - xm) * G) /
(v.mag(i.pos - xm)**2))
return acel
def build(self, Verticies, Faces, Colors=None, Normals=None, IsSoft=False):
"""Build a displayable tri-mesh object. This is an overload of ode.TriMeshData.build()."""
# Fill out our TriMeshData object properties by calling the parent
ode.TriMeshData.build(self, Verticies, Faces)
self._verticies = []
self._colors = []
self._normals = []
# Expand the mesh to make it suitable for use with Visual
for face in Faces:
for index, vertex in enumerate(face):
self._verticies.append(Verticies[vertex])
if Colors is not None:
self._colors.append(Colors[vertex])
else:
# Assign a default
self._colors.append(visual.color.white)
if Normals is not None:
self._normals.append(Normals[vertex])
else:
# Compute the normals using cross products
normal = visual.norm(visual.cross(Verticies[face[index]], Verticies[face[(index + 1) % 3]]))
self._normals.append(normal)
if IsSoft:
# Need to go back and average normals -- implement later
pass
def build(self, Verticies, Faces, Colors=None, Normals=None, IsSoft=False):
"""Build a displayable tri-mesh object. This is an overload of ode.TriMeshData.build()."""
# Fill out our TriMeshData object properties by calling the parent
ode.TriMeshData.build(self, Verticies, Faces)
self._verticies = []
self._colors = []
self._normals = []
# Expand the mesh to make it suitable for use with Visual
for face in Faces:
for index, vertex in enumerate(face):
self._verticies.append(Verticies[vertex])
if Colors is not None:
self._colors.append(Colors[vertex])
else:
# Assign a default
self._colors.append(visual.color.white)
if Normals is not None:
self._normals.append(Normals[vertex])
else:
# Compute the normals using cross products
normal = visual.norm(
visual.cross(Verticies[face[index]],
Verticies[face[(index + 1) % 3]]))
self._normals.append(normal)
if IsSoft:
# Need to go back and average normals -- implement later
pass
def handleCollision(self, other):
difference = other.p - self.p
if mag(difference) < self.radius + other.radius:
vrelative = other.v - self.v
normal = norm(difference)
vrn = dot(vrelative, normal)
if vrn < 0:
#Collision Detected!
difference = norm(difference)
#Compute magnitude of Impulse
Imag = -(1 + restitution) * vrn / (1.0 / self.mass +
1.0 / other.mass)
I = Imag * normal # convert to a vector
#Apply impulse to both affected balls
self.v -= I / self.mass
other.v += I / other.mass
def __setattr__(self, attr, val):
old_val = 1.0
if attr == 'size':
old_val = getattr(self, attr, 1.0)
# Make sure the axis property of frames is normalized.
"""
if attr == 'axis' and len(val) == 3:
norm = sqrt(val[0] ** 2 + val[1] ** 2 + val[2] ** 2)
val = (val[0]/norm, val[1]/norm, val[2]/norm)
super(MyFrame, self).__setattr__(attr, val)
"""
if attr in ['color', 'opacity', 'material']:
super(MyFrame, self).__setattr__(attr, val)
for obj in self.objects:
setattr(obj, attr, val)
elif attr == 'size':
super(MyFrame, self).__setattr__('is_initialized', True)
super(MyFrame, self).__setattr__(attr, val)
# If an extrusion, no need to resize: we already resize before (only extrusions have an 'e' field)
if getattr(self, 'e', False):
pass
else:
for obj in self.objects:
for p in size_loc_prop[obj.type]:
setattr(obj, p, getattr(obj, p)*val/old_val)
# Also adjust the distance of the frame from the origin to fit the scaling. Do this only the second time
# this factor is changed (so that when reading from file we won't do this twice).
"""
if getattr(self, 'is_initialized', False):
self.x *= val/old_val
self.y *= val/old_val
self.z *= val/old_val
"""
elif attr == 'up': # Make sure 'up' and 'axis' are perpendicular
val = v.vector(val)
val = v.norm(val - v.norm(self.axis) * val.dot(v.norm(self.axis)))
super(MyFrame, self).__setattr__(attr, val)
else:
super(MyFrame, self).__setattr__(attr, val)
def sampleCurve(curve, sampleCount):
points = []
tangents = []
parameterValues = []
step = 1.0 / (sampleCount - 1)
t = 0
last_point = curve(t)
points.append(last_point)
parameterValues.append(0)
for i in range(1, sampleCount):
t += step
current_point = curve(t)
points.append(current_point)
tangents.append(visual.norm(current_point - last_point))
parameterValues.append(t)
last_point = current_point
# use a point outside the [0; 1] interval to compute the tanget
# note: the curve might not be always defined outside this interval!
t += step
tangents.append(visual.norm(curve(t) - last_point))
return (points, tangents, parameterValues)
def rotation_matrix(omega):
theta = mag(omega)
if theta == 0:
return np.matrix(np.identity(3))
axis = norm(omega)
a = cos(theta / 2)
b, c, d = -axis * sin(theta / 2)
aa, bb, cc, dd = a * a, b * b, c * c, d * d
bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d
return np.matrix([[aa+bb-cc-dd, 2*(bc+ad), 2*(bd-ac)],
[2*(bc-ad), aa+cc-bb-dd, 2*(cd+ab)],
[2*(bd+ac), 2*(cd-ab), aa+dd-bb-cc]])
def makespring(natom1, natom2, radius):
""" make spring from nnth atom to iith atom"""
if natom1 > natom2:
r12 = ATOM[natom2].pos-ATOM[natom1].pos
direct = vp.norm(r12)
SPRINGS.append(vp.helix(pos=ATOM[natom1].pos+RS*direct,
axis=(L-2*RS)*direct,
radius=radius,
color=SCOLOR, thickness=0.04)) #, shininess=0.9))
SPRINGS[-1].atom1 = ATOM[natom1]
SPRINGS[-1].atom2 = ATOM[natom2]
angle = SPRINGS[-1].axis.diff_angle(vp.vector(0, 1, 0))
# avoid pathologies if too near the y axis (default "up")
if angle < 0.1 or angle > PI-0.1:
SPRINGS[-1].up = vp.vector(-1, 0, 0)
def proj(a,b):
'''Projects the vector a along the direction of b.'''
return vector(dot(a, norm(b)) * norm(b))
T_step = step_interval
s = sphere(make_trail=True, pos=[ride_radius + ride_radius2, 0, 0], radius=0.1)
s.trail_object.color = color.yellow
a_tangential = arrow(pos=[1, 0, 0], axis=[0, 1, 0], color=color.red)
a_inward = arrow(pos=[1, 0, 0], axis=[-1, 0, 0], color=color.blue)
for theta in arange(0, 100 * pi, T_step):
rate(60)
r = vector(ride_radius*cos(theta) + ride_radius2*cos(p*theta), \
ride_radius*sin(theta) + ride_radius2*sin(p*theta), 0)
velocity = vector(-ride_radius*sin(theta)-ride_radius2*p*sin(p*theta), \
ride_radius*cos(theta)+ride_radius2*p*cos(p*theta),0)
vel = str(velocity).strip('[]')
acceleration = vector(-ride_radius*cos(theta) - ride_radius2*p**2*cos(p*theta), \
-ride_radius*sin(theta) - ride_radius2*p**2*sin(p*theta), 0)
tangential_acceleration = (dot(velocity, acceleration) /
mag(velocity)) * norm(velocity)
tang_accel = str(tangential_acceleration).strip('[]')
inward_acceleration = acceleration - tangential_acceleration
in_accel = str(inward_acceleration).strip('[]')
s.pos = r
a_tangential.pos = r
a_inward.pos = r
a_tangential.axis = tangential_acceleration
a_inward.axis = inward_acceleration
data.append([theta, vel, tang_accel, in_accel])
for row in data:
ws.append(row)
ws.append(["Major Radius: ", r1])
ws.append(["Minor Radius: ", r2])
nl = 1 # nl = 100
CF = vp.frame(frame=ROTOR_FRAME, pos=(0, 0, THK / 2. + C1 / 2.0))
for i in range(nl):
# Extrude rotor core profile to get the full core body
GE3 = vp.extrusion(pos=[(0, 0, i * DLT), (0, 0, i * DLT + THK)],
shape=G3,
color=(0.7, 0.7, 0.705),
twist=0.0,
frame=CF)
# Do the core wire windings
# Here is a trick to build a saw-teeth profile, to represent many single windings
N = 20 # coils
VRIGHT = vp.vector(.3, 1.3)
R = vp.mag(VRIGHT) / (2 * N)
VRIGHT = vp.norm(VRIGHT)
# S is the cross sectional profile of "winding block"
S = vp.Polygon([(-.1, -.65), (0, -.65), (.3, .65), (-.1, .65)])
for n in range(N):
RIGHT = vp.vector(0, -.65) + (R + n * 2 * R) * VRIGHT
# Add saw-teeth on the block to represent wires
S += vp.shapes.circle(pos=(RIGHT.x, RIGHT.y), radius=R, np=4)
# Define the winding path as a rounded rectangle
P = vp.shapes.rectangle(width=.5, height=THK)
P += vp.shapes.circle(pos=(0, -THK / 2), radius=.25, np=10)
P += vp.shapes.circle(pos=(0, +THK / 2), radius=.25, np=10)
WRFS = []
for i in range(NS):
# We need a separate frame for individiual winding section
WRF = vp.frame(frame=CF, pos=(0, 2, THK / 2.))
if FIXLENGTH:
FIXLENGTH = not FIXLENGTH
S_LENGTH.color = (0.6, 0.6, 1.0)
FIXTHETA = not FIXTHETA
if FIXTHETA:
S_THETA.color = (0.0, 1.0, 0.0)
else:
S_THETA.color = (0.6, 1.0, 0.6)
if DRAG:
vp.rate(100)
NEWOBS = vp.scene.mouse.project(normal=vp.vector(1, 0, 0), d=0)
if NEWOBS and (NEWOBS != OBS):
OBS = NEWOBS
if not FIXLENGTH and not FIXTHETA:
BVECTOR = OBS
if BVECTOR.mag > 20:
BVECTOR = BVECTOR*(20/BVECTOR.mag)
B.axis = BVECTOR
elif FIXLENGTH:
LENGTH = 3.9
BVECTOR = LENGTH*vp.norm(OBS)
B.axis = BVECTOR
elif FIXTHETA:
LENGTH = vp.mag(OBS)
BVECTOR = LENGTH*vp.norm(vp.vector(0, 0.3, 1))
B.axis = BVECTOR
CVECTOR = vp.cross(AVECTOR, B.axis)
C.axis = CVECTOR
F.pos = vp.transpose((vp.sin(T)-2, vp.cos(T)+2, 0*T))
# disk
for T in vp.arange(0, 2*PI, 0.1):
A.append(pos=(vp.cos(T), 0, vp.sin(T)))
A.append(pos=(vp.cos(T), 0.2, vp.sin(T)))
# box
for i in range(8):
P = vp.vector((i/4)%2 - 2.5, (i/2)%2 - 0.5, (i)%2 - 0.5)
B.append(pos=P)
# random sphere
L = []
for i in range(1000):
L.append(vp.vector(2, 0) + vp.norm(vp.vector(
uniform(-1, 1), uniform(-1, 1), uniform(-1, 1))))
C.pos = L
# lat/long sphere
L = []
for T in vp.arange(0, 2*PI, 0.2):
for s in vp.arange(0, PI, 0.1):
L.append((vp.cos(T)*vp.sin(s)+2, vp.sin(T)*vp.sin(s)+2, vp.cos(s)))
D.pos = L
# modify the disk
P = A
P.color = (P.color[0]*2, P.color[1]*2, P.color[2]*2)
while 1:
vp.rate(10)
if vp.scene.mouse.clicked:
from visual import vector, mag, norm
from visual import sphere, rate, color, display
from math import cos, sin, pi
from numpy import arange
d = display()
m_earth = 100.0
m_sun = 10000000.0
g = 0.000001
r = vector(70.0, 0, 0)
v = vector(0, 2.0, 0)
s_earth = sphere(pos=[r.x, r.y, r.z], radius=1, color=color.white)
s_sun = sphere(pos=[0, 0, 0], radius=2, color=color.yellow)
d.autoscale = False
while True:
rate(30)
a = -1 * norm(r) * ((g * m_earth * m_sun) / (mag(r)**2))
v = v + a
r = r + v
s_earth.pos = [r.x, r.y, r.z]
# disk
for T in vp.arange(0, 2 * PI, 0.1):
A.append(pos=(vp.cos(T), 0, vp.sin(T)))
A.append(pos=(vp.cos(T), 0.2, vp.sin(T)))
# box
for i in range(8):
P = vp.vector((i / 4) % 2 - 2.5, (i / 2) % 2 - 0.5, (i) % 2 - 0.5)
B.append(pos=P)
# random sphere
L = []
for i in range(1000):
L.append(
vp.vector(2, 0) +
vp.norm(vp.vector(uniform(-1, 1), uniform(-1, 1), uniform(-1, 1))))
C.pos = L
# lat/long sphere
L = []
for T in vp.arange(0, 2 * PI, 0.2):
for s in vp.arange(0, PI, 0.1):
L.append(
(vp.cos(T) * vp.sin(s) + 2, vp.sin(T) * vp.sin(s) + 2, vp.cos(s)))
D.pos = L
# modify the disk
P = A
P.color = (P.color[0] * 2, P.color[1] * 2, P.color[2] * 2)
while 1:
vp.rate(10)
DLT = 0.05
THK = 5.04
nl = 1 # nl = 100
CF = vp.frame(frame=ROTOR_FRAME, pos=(0, 0, THK / 2.0 + C1 / 2.0))
for i in range(nl):
# Extrude rotor core profile to get the full core body
GE3 = vp.extrusion(
pos=[(0, 0, i * DLT), (0, 0, i * DLT + THK)], shape=G3, color=(0.7, 0.7, 0.705), twist=0.0, frame=CF
)
# Do the core wire windings
# Here is a trick to build a saw-teeth profile, to represent many single windings
N = 20 # coils
VRIGHT = vp.vector(0.3, 1.3)
R = vp.mag(VRIGHT) / (2 * N)
VRIGHT = vp.norm(VRIGHT)
# S is the cross sectional profile of "winding block"
S = vp.Polygon([(-0.1, -0.65), (0, -0.65), (0.3, 0.65), (-0.1, 0.65)])
for n in range(N):
RIGHT = vp.vector(0, -0.65) + (R + n * 2 * R) * VRIGHT
# Add saw-teeth on the block to represent wires
S += vp.shapes.circle(pos=(RIGHT.x, RIGHT.y), radius=R, np=4)
# Define the winding path as a rounded rectangle
P = vp.shapes.rectangle(width=0.5, height=THK)
P += vp.shapes.circle(pos=(0, -THK / 2), radius=0.25, np=10)
P += vp.shapes.circle(pos=(0, +THK / 2), radius=0.25, np=10)
WRFS = []
for i in range(NS):
# We need a separate frame for individiual winding section
WRF = vp.frame(frame=CF, pos=(0, 2, THK / 2.0))
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()
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 proj(a, b):
'''Projects the vector a along the direction of b.'''
return vector(dot(a, norm(b)) * norm(b))
def runge_lenz(self, o): # print(cross(self.momentum, cross(self.pos, self.momentum)) - pow(self.mass, 2.0) * o.mass * g * norm(self.pos - o.pos)) return cross(self.momentum, self.l()) - pow(self.mass, 2.0) * o.mass * g * norm(self.pos - o.pos)
def arr(a, b):
'''The unit vector starting at a.pos and ending at b.pos'''
return norm(a.pos - b.pos)
