Answer the questions about HPP lattice gas automata,
In this model, the lattice is square, and particles can move to any of the four sites whose cells share a common edge. Particles cannot move diagonally.
If two particles collide head-on, for example a particle moving to the left meets a particle moving to the right, the outcome will be two particles leaving the site at right angles to the direction they came in.
So here are the questions:
1 Write a rule for a collision with a hard wall, at which the particle 'bounces back
2 Start with periodic boundary conditions and a concentrated density of cells around the middle of the lattice. Does the gas spread to a homogeneous distribution
3 Modify the periodic boundary conditions into hard walls. Measure the pressure on one wall (i.e. the number of particles colliding with the wall during a time increment divided by the length of the wall) and make a plot of how
pressure varies with the initial density of particles (i.e. number of particles
divided by the area of the lattice).
4 Add a wall separating the left hand side from the right hand side. Include
a small opening in the wall. Show the evolution of pressure on the wall on
the right hand side and the wall on the left hand side.
5 Do you observe the phenomenon of "relaxation"? Does the system evolve
to a state that is uniform in a certain sense? Discuss this in light of the
microscopic reversibility of the system and the 2nd law of thermodynamics.