Kinetic Theory Model - physics

Question

Edit: I've now fixed the problem I asked about. The spheres were leaving the box in the corners, where the if statements (in the while loop shown below) got confused. In the bits of code that reverse the individual components of velocity on contact with walls, some elif statements were used. When elif is used (as far as I can tell) if the sphere exceeds more than one position limit at a time, the program only reverses the velocity component for one of them. This is rectified when replacing elif with simply if. I'm not sure if I quite understand the reason behind this, so hopefully someone cleverer than I will comment such information, but for now, if anyone has the same problem, I hope my limited input helps!
Some context first:
I'm trying to build a model of the kinetic theory of gases in VPython, as a revision exercise for my (Physics) degree. This involves me building a hollow box and putting a bunch of spheres in it, randomly positioned throughout the box. I then need to assign each of the spheres its own random velocity and then use a loop to adjust the position of each sphere with reference to its velocity vector and a time step.
The spheres should also undergo elastic collisions with each wall and all other spheres.
When a sphere meets a wall in the x-direction, its x-velocity component is reversed and similarly in the y and z directions.
When a sphere meets another sphere, they swap velocities.
Currently, my code works so far as creating the right number of spheres and distributing them randomly and giving each sphere its own random velocity. The spheres also move as they should, except for collisions. The spheres should all stay inside the box as they should bounce off all the walls. They appear to be bouncing off each other, however, occasionally a sphere or two will go straight through the box.
I am extremely new to programming and I don't quite understand what's going on here or why it's happening but I'd be very grateful if someone could help me.
Below is the code I have so far (I've tried to comment what I'm doing at each step):
##########################################################
# This code is meant to create an empty box and then create
# a certain number of spheres (num_spheres) that will sit inside
# the box. Each sphere will then be assigned a random velocity vector.
# A loop will then adjust the position of each sphere to make them
# move. The spheres will undergo elastic collisions with the box walls
# and also with the other spheres in the box.
##########################################################
from visual import *
import random as random
import numpy as np
num_spheres = 15
fps = 24 #fps of while loop (later)
dt = 1.0/fps #time step
l = 40 #length of box
w = 2 #width of box
radius = 0.5 #radius of spheres
##########################################################
# Creating an empty box with sides length/height l, width w
wallR = box(pos = (l/2.0,0,0), size=(w,l,l), color=color.white, opacity=0.25)
wallL = box(pos = (-l/2.0,0,0), size=(w,l,l), color=color.white, opacity=0.25)
wallU = box(pos = (0,l/2.0,0), size=(l,w,l), color=color.white, opacity=0.25)
wallD = box(pos = (0,-l/2.0,0), size=(l,w,l), color=color.white, opacity=0.25)
wallF = box(pos = (0,0,l/2.0), size=(l,l,w), color=color.white, opacity=0.25)
wallB = box(pos = (0,0,-l/2.0), size=(l,l,w), color=color.white, opacity=0.25)
#defining a function that creates a list of 'num_spheres' randomly positioned spheres
def create_spheres(num):
global l, radius
particles = [] # Create an empty list
for i in range(0,num): # Loop i from 0 to num-1
v = np.random.rand(3)
particles.append(sphere(pos= (3.0/4.0*l) * (v - 0.5), #pos such that spheres are inside box
radius = radius, color=color.red, index=i))
# each sphere is given an index for ease of referral later
return particles
#defining a global variable = the array of velocities for the spheres
velarray = []
#defining a function that gives each sphere a random velocity
def velocity_spheres(sphere_list):
global velarray
for sphere in spheres:
#making the sign of each velocity component random
rand = random.randint(0,1)
if rand == 1:
sign = 1
else:
sign = -1
mu = 10 #defining an average for normal distribution
sigma = 0.1 #defining standard deviation of normal distribution
# 3 random numbers form the velocity vector
vel = vector(sign*random.normalvariate(mu, sigma),sign*random.normalvariate(mu, sigma),
sign*random.normalvariate(mu, sigma))
velarray.append(vel)
spheres = create_spheres(num_spheres) #creating some spheres
velocity_spheres(spheres) # invoking the velocity function
while True:
rate(fps)
for sphere in spheres:
sphere.pos += velarray[sphere.index]*dt
#incrementing sphere position by reference to its own velocity vector
if abs(sphere.pos.x) > (l/2.0)-w-radius:
(velarray[sphere.index])[0] = -(velarray[sphere.index])[0]
#reversing x-velocity on contact with a side wall
elif abs(sphere.pos.y) > (l/2.0)-w-radius:
(velarray[sphere.index])[1] = -(velarray[sphere.index])[1]
#reversing y-velocity on contact with a side wall
elif abs(sphere.pos.z) > (l/2.0)-w-radius:
(velarray[sphere.index])[2] = -(velarray[sphere.index])[2]
#reversing z-velocity on contact with a side wall
for sphere2 in spheres: #checking other spheres
if sphere2 != sphere:
#making sure we aren't checking the sphere against itself
if abs(sphere2.pos-sphere.pos) < (sphere.radius+sphere2.radius):
#if the other spheres are touching the sphere we are looking at
v1 = velarray[sphere.index]
#noting the velocity of the first sphere before the collision
velarray[sphere.index] = velarray[sphere2.index]
#giving the first sphere the velocity of the second before the collision
velarray[sphere2.index] = v1
#giving the second sphere the velocity of the first before the collision
Thanks again for any help!

Answer 1

The elif statements within the while loop in the code given in the original question are/were the cause of the problem. The conditional statement, elif, is only applicable if the original, if, condition is not satisfied. The circumstance wherein a sphere meets the corner of the box satisfies at least two of the conditions for reversing velocity components. This means that, while one would expect (at least) two velocity components to be reversed, only one is. That is, the direction specified by the if statement is reversed, whereas the component(s) mentioned in the elif statement(s) are not, as the first condition has been satisfied and, hence, the elif statements are ignored.
If each elif is changed to be a separate if statement, the code works as intended.