Bastien Chopard

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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,(More)
The inherent complexity of biomedical systems is well recognized; they are multiscale, multiscience systems, bridging a wide range of temporal and spatial scales. While the importance of multiscale modelling in this context is increasingly recognized, there is little underpinning literature on the methodology and generic description of the process. The(More)
Cellular automata (CA) and lattice Boltzmann LB approaches are computational methods that ooer exibility, eeciency and outstanding amenability to parallelism when modeling complex phenomena. In this paper, the CA and LB approach are combined in the same model, in order to describe a system where point-particles are transported in a uid ow. This model is(More)
Grid refinement has been addressed by different authors in the lattice Boltzmann method community. The information communication and reconstruction on grid transitions is of crucial importance from the accuracy and numerical stability point of view. While a decimation is performed when going from the fine to the coarse grid, a reconstruction must performed(More)
We review a methodology to design, implement and execute multi-scale and multi-science numerical simulations. We identify important ingredients of multi-scale modelling and give a precise definition of them. Our framework assumes that a multi-scale model can be formulated in terms of a collection of coupled single-scale submodels. With concepts such as the(More)
Complex Automata were recently proposed as a paradigm to model multi-scale complex systems. The concept is formalized and the scale separation map is further investigated in relation with its capability to specify the components of Complex Automata. Five classes of scale separation are identified, each potentially giving rise to a specific multiscale(More)
Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice(More)
We present a simple cellular automata model of traffic in urban environments in which road junctions are implemented as rotaries. We study its generic properties and compare the numerical simulations with analytical results. We show that the dynamics is well described in terms of the queues that form at the crossings. We apply our model to the case of the(More)