Сellular automata simulation
A Cellular Automaton (CA) is nowadays an object of ever growing interest as a mathematical model for spatial dynamics simulation. Due to the CA ability to simulate nonlinear and discontinuous processes, it is expected to become a complement to partial differential equations. Particularly, the CA may be helpful when there is no other mathematical model of a phenomenon under simulation.
By this time, many modifications and extensions of mathematical CA-models were developed. All of them are descendants of a classical von-Neumann's CA, but may use any type of alphabet, any kind of updating transition functions, and asynchronous mode of operation. Such extended CA are capable of simulating a number of processes in physics, chemistry, biology and sociology. The most known are CA-models of reaction-diffusion processes, wave propagation, phase transition, self-organization etc.. More complicated CA called the Gas--Lattice models are used in hydrodynamics, some of dealing with a real alphabet.
In chemistry and microelectronics, asynchronous probabilistic CA with multi-adjustable cells (in chemistry being referred to as Monte Carlo methods), are intensively used for studying a surface reaction on catalysts and processes of the epitaxial growth of crystals. The processes are simulated by mimicking real movements and interactions of atoms and molecules. This type of processes have no mathematical description in terms of PDE, because continuous functions cannot capture the behavior of discrete micro- and nano- particles.
Although the diversity of processes being simulated resulted in enlarging of CA-models capacity, the imperative properties of CA still remain. They are as follows:
- CA consists of many identical simple processing units (cells);
- Interactions between cells are constrained by a small (relative to the total amount of cells) neighborhood.
CA modeling is a young domain of Computer Science, where the investigations proceed in two intersecting forms:
- theoretical study of CA-models as dynamical systems,
- development of methods and tools for computer simulation using CA-models.
Our scientific group is involved in the development of computer CA simulation methods algorithms and their implementation on modern types of computer architectures. The following topics in the field of CA-simulation are currently under investigation.
- Lattice -Gas CA-models and its extentions for simulating gas streams
- Lattice-Gas CA-models for simulation waves propagating in heterogeneous media
- Asynchronous probabilistic CA-models for surface chemical reaction simulation
- Stable pattern-formation CA-models
- CA-models for self-organization in biosystems (Lake Baykal organisms population)