Particle Simulation with Cellular Automaton

This study will attempt to simulate particle movement during various events (asteroid impacts, explosions, collisions) using a Cellular Automaton model and examining the forces acting on the coordinate system itself, instead of each individual particle. By dividing space into a three-dimensional grid of cubes, all the particles contained in the same cube could be treated as a solid block of matter. By examining the stresses acting on the block, the motion of the particles could be found. This motion would result in a flow of particles into an adjacent block. The advantage to this method is that the forces acting on a cube already include forces from adjacent cubes, so the particle motion can be calculated without referring to forces on other, distant co-ordinates. This should make the calculation simpler, faster and more efficient. 1 The problem with simulators With traditional particle simulators, the computer must keep track of the position, velocity, and physical properties (mass, charge, etc) of every particle. Considering the number of air particles in just this room, the memory required to store this information on the machine is enormous. While performing the actual simulation, the program must find the forces acting on each particle by comparing its location with every other particle to determine if there is even a possibility of an interaction between them. Since most particles are too far apart to interfere with each other, this process involves numerous unnecessary calculations. To improve the efficiency in both memory and processing, this project will apply the Cellular Automaton model to simulate an asteroid colliding with the Earth’s surface. This project is supported by the National Science Foundation. 2 The cellular automaton model To avoid the unnecessary distance checking, the computer must know the distance between particles before accessing their memory locations. If the particles could be grouped in memory according to position, the program would only need to check certain memory locations to find all the particles that might affect the current particle. This is the goal of the Cellular Automata method: to divide space into a grid of ’cells’ and keep track of the number of particles in each cell. As a result, each cell is only affected by its adjacent cells. This technique saves considerable memory useage and processing power. In fact, the process is an excellent candidate for parallelization, making it highly adaptable to multi-processor supercomputing.