A Study of Self-Organization in Small Systems with Simple Dynamics
William J. B. Oldham *
Texas Tech University, 3877 Royal Troon Drive Round Rock, Texas 78664, USA.
James Rejcek
University of Texas at Arlington, 6009 Carey Rd. Ft. worth, TX 76140, USA.
*Author to whom correspondence should be addressed.
Abstract
Self-organization in small systems of particles with simple dynamic laws has been simulated. The purpose of this work is to investigate self-organization in small systems where we could follow individual particles. The intention is to look for pattern formation as the system evolves. For the two kinds of systems studied, the motion and the final system state for various dynamic iterations are presented. In the first system design, two kinds of particles are simulated. Like particles have a repulsive force, while unlike particles have an attractive force. Initially, the particles are randomly distributed in a two dimensional square bounded region, and then allowed to dynamically interact for a number of iterations. In experiment 1 the particles have different polarity. Using the inverse square law force, modified at short distances, most cases resulted in equilibrium with the particles of opposite polarity paired up. Since this was a state of equilibrium no more movement occurred. In the second experiment, there are two groups of particles initially separated by a boundary. The particles on each side of the boundary are further divided into two groups referred to as strong or weak particles. In this experiment the resulting patterns were clusters of particles. The forces among all of the particles can be varied to study the configurations that result from the dynamics. The results of the experiments are presented in graphical format. The main conclusion is that this model can be used to study small dynamic systems.
Keywords: Self-organization, computer simulation, evolution, dynamics, non-equilibrium, particle-to-particle interaction, cluster formation.