Structures emerging in systems out of equilibrium are in general of greater complexity and variety than their equilibrium counterparts. This wealth of be- haviour is both the reason for current interest in the field and the source of dif- ficulties in the analysis of non-equilibrium phenomena. We propose to study a class of model systems with simplified microdynamics (lattice gas automata) in order to investigate the meso and macroscopic behaviour of spatially extended systems under non-equilibrium constraints. Lattice gas automata exhibit features that make them well-suited to model these complex systems under both equi- librium and non-equilibrium conditions: They possess a large number of degrees of freedom, they are non-linear and, furthermore, they exhibit spontaneous fluc- tuations. Their discrete nature facilitates the computational implementation of their dynamics, making it possible to investigate large systems, and yielding ac- cess to quantities that are hard to obtain in experiments or from other theoretical approaches. As a prototypical system, we shall analyze theoretically and numeri- cally a thermal lattice gas automaton to investigate the appearance of long-range correlations in a fluid subject to a temperature gradient, away from critical points and hydrodynamic instabilities. We further investigate the properties of the dis- tribution of temperature fluctuations in such a fluid, when both a temperature gradient and turbulence are present. The results of these simulations will be com- pared to experiments and also to stochastic models, which include the effects of fluctuations in a phenomenological manner.
This proposal is intended as a continuation of current research being carried out by the applicant under a EC 'Human Capital and Mobility' fellowship within the network Nonlinear dynamics and statistical physics of spatially extended sys- tems.