Non-Gibbsian stationary states occur in dissipative non-equilibrium systems. They are closely connected with the lack of detailed balance and the absence of a fluctuation-dissipation theorem. These states exhibit spatial correlations that are long ranged under generic conditions , even in systems with short range interactions, provided the system has slow modes and some degree of spatial anisot...

Cellular automata are good candidates for modelling and simulating complex dynamical systems, whose evolution depends on the local interactions of their constituent parts. Many macroscopic phenomena have such features, but their complexity involves sometime the interaction of heterogeneous processes, whose composition is not immediate in a cellular automaton frame. Furthermore the managing of f...

Traditional automata accept or reject their input, and are therefore Boolean. Lattice automata generalize the traditional setting and map words to values taken from a lattice. In particular, in a fully-ordered lattice, the elements are 0, 1, . . . , n − 1, ordered by the standard ≤ order. Lattice automata, and in particular lattice automata defined with respect to fully-ordered lattices, have i...

This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory.

The probability of first return to the initial interval x and the diffusion tensor D~a are calculated exactly for a ballistic Lorentz gas on a Bethe lattice or Cayley tree. It consists of a moving particle and a fixed array of scatterers, located at the nodes, and the lengths of the intervals between scatterers are determined by a geometric distribution. The same values for x and D=a apply also...

We find a simple linear relation between the thermodynamic entropy and the largest Lyapunov exponent (LLE) of an discrete hydrodynamical system, a deterministic, two-dimensional lattice gas automaton (LGCA). This relation can be extended to irreversible processes considering the Boltzmann’s H function and the expansion factor of the LLE. The definition of LLE for cellular automata is based on t...

Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of q...

Abst ract. We st udy lat tice gas automata. of fluid dynamics in the incompressible flow limit . It is shown t hat t he viscosity effect on the transition layer from the steady uniform velocity in one strea.m to the steady uniform velocity in another , adja cent strea m produces t he correct profile. We further study t he intr insic damping or smoothing action of viscous diffusion and show that...