A Lattice Gas Automaton Capable of Modeling Three-Dimensional Electromagnetic Fields

A lattice gas automaton (LGA) capable of modeling Maxwell's equations in three dimensions is described. The automaton is a three-dimensional interconnection of two-dimensional LGA cells, with appropriate operations at the junctions between cells to include the properties of polarization. A homogeneous mathematical description of the heterogeneous three-dimensional automaton is provided in terms of the underlying binary variables. The dynamics of the automaton conserve the scalar components of the electric and magnetic fields. The implementation of the automaton on the CAM-8 cellular automata machine is described. The LGA has been validated through calculation of resonant frequencies within various cavities. The numerical results indicate the success of the automaton in analyzing three-dimensional EM field problems. We have not proven analytically that this model reproduces Maxwell's equations in the macroscopic limit, as this is a topic of future study.

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