Since lattice matrices are useful tools in various domains like automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control and so on, the study of the properties of lattice matrices is valuable. A lattice matrix A is called monotone if A is transitive or A is monotone increasing. In this paper, the convergence of...

Presented is a quantum lattice gas for Navier-Stokes fluid dynamics simulation. The quantum lattice-gas transport equation at the microscopic scale is presented as a generalization of the classical lattice-gas transport equation. A special type of quantum computer network is proposed that is suitable for implementing the quantum lattice gas. The quantum computer network undergoes a partial coll...

We investigate subshifts with a general algebraic structure and cellular automata on them, with an emphasis on (order-theoretic) lattices. Our main results concern the characterization of Boolean algebraic subshifts, conditions for algebraic subshifts to be recoded into cellwise algebras and the limit dynamics of homomorphic cellular automata on lattice subshifts.

Since the introduction of cellular automata in the late 1940’s they have been used to address various types of problems in computer science and other multidisciplinary fields. Their generative capabilities have been used for simulating and modelling various natural, physical and chemical phenomena. Besides these applications, the lattice grid of cellular automata has been providing a by-product...

We investigate subshifts with a general algebraic structure and cellular automata on them, with an emphasis on (order-theoretic) lattices. Our main results concern the characterization of Boolean algebraic subshifts, conditions for algebraic subshifts to be recoded into cellwise algebras and the limit dynamics of homomorphic cellular automata on lattice subshifts.

Geographic simulation is concerned with automata-based methodologies for simulating discrete, dynamic, and action-oriented spatial systems, combining cellular automata and multi-agent systems in a spatial context. In this paper, we propose a paradigm for integrating GIS and geosimulation into what we term Geographic Automata Systems (GAS), the latter fusing the two into full-blown, symbiotic sy...

The (meta)logic underlying classical theory of computation is Boolean (twovalued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a logic of quantum mechanics about 70 years ago. It is currently understood as a logic whose truth values are taken from an orthomodular lattice. The major difference between Boolean logic and quantum logic is that the latter does not enjoy distribut...

To describe the hydrodynamic phenomena prevailing in large industrial scale fluidised beds continuum models are required. The flow in these systems depends strongly on particle-particle interaction and gas-particle interaction. For this reason proper closure relations for these two interactions are vital for reliable predictions on the basis of continuum models. Gas-particle interaction can be ...