Modeling wave mechanics using lattice gas automata

摘要

The study of wave mechanics in electromagnetism has traditionally been approached from a differential equation description of the physics. An alternative are Lattice Gas Automata, which arc discrete dynamical systems and are based on a microscopic model of the physics being simulated. A lattice gas automaton (LGA) is an extremely large regular lattice of simple interconnected cells where each cell of the lattice implements the same rule. The use of LGAs has received the most attention in the modeling of fluid dynamics, and are capable of yielding the same behavior as that described by the Navier-Stokes (NS) equation, which govern the fluid's dynamics. The use of LGAs for modeling linear wave mechanics is fairly straightforward as it is a limiting case of the more general NS equation. In this paper we discuss how lattice gas automata are used to model linear wave behavior, with specific emphasis on the added requirements for application to electromagnetism. Several obstacles, such as the ability to model material inhomogeneities and dissipation, have to be considered. More importantly, the standard LGA rules offer only scalar based descriptions. We present a method of implementing vector LGA's, thus giving a basis for modeling Maxwell's equations.