Cellular Automata and Lattice Boltzmann Techniques: An Approach to Model and Simulate Complex Systems

Abstract

We discuss the cellular automata approach and its extensions, the lattice Boltzmann and multiparticle methods. The potential of these techniques is demonstrated in the case of modeling complex systems. In particular, we consider applications taken from various fields of physics, such as reaction-diffusion systems, pattern formation phenomena, fluid flows, fracture processes and road traffic models.

Coarse-grained numerical bifurcation analysis of lattice Boltzmann models

“…Since the macroscopic mean flow of the reactants in a reaction-diffusion system is zero, the more general expression for the equilibrium distribution in [14,16,17] …”

“…If the step size is sufficiently small, the dominant eigenvalues of the numerical time integrator will be very good approximations to the eigenvalues µ l of the exact time integrator and can be used to judge the stability of the computed fixed points. One can then still use (16) to compute approximations to the eigenvalues λ l . A LBM defines a map.…”

Estimation of a semi-physical GLBE model using dual EnKF learning algorithm coupled with a sensor network design strategy: Application to air field monitoring

“…In this suitable formulation [2,1], the speed of sound c s and the weighting factors w α depend on the lattice geometry. For the D2Q9 model, the speed of sound is defined as c 2 s = c 2 /3 and the weighting factors are given by: Figure 2 gives an overview of the stream and collide steps for a fluid cell during one time step.…”

“…Our approach consisted in a state-space filtering problem with the objective of learning the system parameters of a conventional computational fluid dynamic (CFD) model. The a priori knowledge of the physical 2 laws that govern the studied system was introduced by a Navier-Stokes model discretized by the lattice Boltzmann approach for fluid flow simulation [1], [2], [3], [4], [5]. This deterministic model which operated in the forward direction, was able to reproduce the macroscopic behavior of a fluid accurately by a microscopic simulation of particle dynamics.…”

Dynamics Analysis Method of Cellular Automata for Complex Networking Storage System

“…A node on the boundary generates a data object according to the Poisson stream with arrival rate of p and sends it to a destination node selected randomly from the nodes on the boundary. Fig.1 The model of storage network architecture with Von Neumann neighborhood [7] (2) Inner nodes (routers) only forward data objects received from neighbor nodes. There is a buffer with the size of L in each inner node, which stores the remainder data objects that need to wait for forwarding the next time.…”