Pascal O. Luthi

Cellular Automata And Lattice Boltzmann Techniques: An Approach To Model And Simulate Complex Systems

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.

Lattice Boltzmann computations and applications to physics

We discuss the lattice Boltzmann computing approach, its connection with cellular automata and present a new model for simulating wave propagation in complex environments. We illustrate the behavior of our model on several applications like radio wave propagation in a city, solid body motion and fracture phenomena.

Wave Propagation in Urban Microcells: a Massively Parallel Approach Using the TLM Method

We consider a new approach to modeling wave propagation in urban environments, based on the Transmission Line Matrix (TLM) method. Two-dimensional simulations are performed using a map of a city A renormalization technique is proposed to convert the results to the three-dimensional space. Our approach provides good predictions for the intensity of a wave when compared with in-situ measurements and is appropriate to very fast massively parallel computations. In order to provide a performance analysis, the algorithm has been used as a benchmark on different parallel architecture (CM200, CM5, IBM SP2 and Cray T3D).

Microscopic approach to the formation of Liesegang patterns

A microscopic approach to the formation of Liesegang patterns, based on a cellular automata model, is presented. This approach gives a consistent description of several types of patterns observed experimentally (bands, rings, and spirals). Quantitative predictions are made about the generic laws (time, spacing, and width laws) governing the formation of these patterns. Emphasis is put on the role played by the fluctuations in such nonequilibrium systems.

A cellular automaton model for neurogenesis in Drosophila

Abstract A cellular automaton (CA) is constructed for the formation of the central nervous system of the Drosophila embryo. This is an experimentally well-studied system in which complex interactions between neighbouring cells appear to drive their differentiation into different types. It appears that all the cells initially have the potential to become neuroblasts, and all strive to this end, but those which differentiate first block their as yet undifferentiated neighbours from doing so. The CA makes use of observational evidence for a lateral inhibition mechanism involving signalling products S of the ‘proneural’ or neuralizing genes. The key concept of the model is that cells are continuously producing , but the production rate is lowered by inhibitory signals received from neighbouring cells which have advanced further along the developmental pathway. Comparison with experimental data shows that it well accounts for the observed proportion of neuroectodermal cells delaminating as neuroblasts.

A Lattice Boltzmann Wave Model and its Applications

We present a lattice Boltzmann model for simulating wave propagation in complex environments. We illustrate the behavior of our model on several applications and discuss its ability to describe solid body motion and fracture phenomena.