Cellular Automata as a Mesoscopic Approach to Model and Simulate Complex Systems

Abstract

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 simple applications taken from various scientific domains. We discuss our distributed particle simulation of flow, based on a parallel lattice Boltzmann Method. Efficient parallel execution is possible, provided that (dynamic) load balancing techniques are applied. Next, we present a number of case studies of flow in complex geometry, i.e. flow in porous media and in static mixer reactors. The Cellular Automata ApproachA natural way to describe a physical, chemical or biological system is to propose a model of what we think is happening. During this process we try to keep only the ingredients we believe to be essential whilst still capturing the behavior we are interested in. Using an appropriate mathematical machinery, such a model can be expressed in terms a set of equations whose solution gives the desired answers on the system. The description in terms of equations is very powerful and corresponds to a rather high level of abstraction. For a long time, this methodology has been the only tractable way for scientists to address a problem.Another approach, which has been made possible by the advent of fast computers, is to stay at the level of the model and its basic components. The idea is that all the information is already contained in the model and that a computer simulation will be able to answer any possible question on the system by just running the model for some time. Thus, there is no need to use a complicated mathematical tool to obtain a high level of description. We just need to express the model in a way which is suitable to an effective computer implementation. Cellular automata constitute a paradigm in which simple models of complex phenomena can be easily formulated. In particular, cellular automata models illustrate the fact that a complex behavior emerges out of many simply interacting components through a collective effect.The degree of reality of the model depends on the level of description we expect. When we are interested in the global or macroscopic properties of a system the microscopic details of a system are often irrelevant. On the other hand, symmetries and conservation laws are usually the essential ingredients of such mesoscopic

Oppilatio+ - A data and cognitive science based approach to analyze pedestrian flows in networks

“…In contrast, mesoscopic approaches model pedestrians as singular and discrete simulation objects. A common approach to describe mesoscopic models are cellular automata [15], which reduce the scenario to a regular grid and simulate the movement of pedestrians cell-wise [16]. Models on the mesoscopic scale require more computational effort, but their spatial resolution is higher -only limited by the size of their unit cells [17].…”