We show that in a reaction diffusion system on a two-dimensional substrate with advection in the confined direction, the drift (advection) induced instability occurs through a Hopf bifurcation, which can become a double Hopf bifurcation. The box size in the direction of the drift is a vital parameter. Our analysis involves reduction to a low dimensional dynamical system and constructing amplitu...

This review addresses issues of various drift–diffusion and inhomogeneous advection problems with without resetting on comblike structures. Both a Brownian diffusion search drift an the comb structures are analyzed. The analytical results verified by numerical simulations in terms coupled Langevin equations for structure. subordination approach is one main technical methods used here, we demons...

The different kinds of boundary conditions for standard and fractional diffusion and advection diffusion equations are analyzed. Near the interface between two phases there arises a transition region which state differs from the state of contacting media owing to the different material particle interaction conditions. Particular emphasis has been placed on the conditions of nonperfect diffusive...

Direct numerical simulations of turbulent Taylor-Couette flows are performed to investigate the effect a traveling wave control on torque and heat transfer. In flow, inner outer cylinders rotating immobile, respectively, temperature difference between cylinder walls is maintained as constant. The ratio 0.882, Reynolds number set 84,000. A wave-like blowing suction imposed an wall. parametric st...

An approach to integrate transport equations with fluxes being complex non-linear functions of physical parameters and their gradients, as it is predicted by theoretical models for micro-instabilities in plasma, is proposed. This approach operates without any splitting of the flux on diffusive and convective components normally involved in transport calculations. Introduction By considering tra...

We formulate the generalized master equation for a class of continuous-time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean-f...