Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation search. In this paper we study the conditions of the existence and stability properties of the equilibrium solutions in a reaction-diffusion model in which predator mortality is neither a constant nor an unbounded functio...

In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the equilibrium distributions equal those of the Maxwell-Boltzmann distribution. These constraints can...

In an opposed-jet diffusion flame experiment, under certain conditions, after the extinction of the diffusion flame, an edge flame can be obtained. This ring-shaped edge flame was first reported in 1959 by Potter and Butler but received little attention. It was reported again recently in a numerical and an experimental work and is responsible for an interesting transition between two distinct b...