We study the Turing instability to stationary spatial patterns in reaction-transport systems with inertia. After a brief discussion of hyperbolic reaction-diffusion equations and reaction-Cattaneo equations we focus on reaction randomwalks, which are themost natural generalization of reactiondiffusion equations. We analyze the effect of inertia in the transport on spatial instabilities of the h...

Analytical models require significant simplification of the real-world system, especially in the case of solute transport in subsurface groundwater. This article presents an analytical study of one-dimensional non-reactive solute transport in a homogeneous finite porous medium. The governing advection-dispersion equation, which includes retardation factor, is included for solute transport. The ...

In recent years, the Lattice Boltzmann (LB) method has become a powerful numerical tool for simulating complex fluid flows and modeling physics and chemistry in fluids. Derived from the continuum Boltzmann equation used in statistical mechanics, the LB method has the advantage of describing non-equilibrium dynamics, especially in fluid-flow applications involving interfacial dynamics and comple...

in this paper, a modeling tool for risk assessment analysis of the movement of hydrocarbon contaminants in the vadose zone and mass flux of contamination release into the groundwater table was developed. also, advection-diffusion-reaction equations in combination with a three-phase equilibrium state between trapped air, soil humidity, and solid particles of unsaturated soil matrix were numerica...