The popular reaction–diffusion model for the negative bias temperature instability is discussed from the viewpoint of stochastic chemical kinetics. We present a microscopic formulation of the reaction–diffusion model based on the reaction–diffusion master equation and solve it using the stochastic simulation algorithm. The calculations are compared to the macroscopic version as well as establis...

We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.

We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derive...

We study the separate variable blow-up patterns associated to following second order reaction–diffusion equation: ?tu=?um+|x|?um,posed for x?RN, t?0, where m>1, dimension N?2 and ?>0. A new explicit critical exponent ?c=2(m?1)(N?1)3m+1is introduced a classification of profiles is given. The most interesting contribution paper showing that existence behavior split into different regimes by ?c al...

Crystal dissolution may include three component processes: interface reaction, diffusion and complications due to convection. We report here a theoretical and experimental study of crystal dissolution in silicate melt without convection. A reaction-diffusion equation is developed and numerically solved. The results show that during non-convective crystal dissolution in silicate melt, the interf...

The local mass of weak solutions to the discrete diffusive coagulation-fragmentation equation is proved to converge, in the fast reaction limit, to the solution of a nonlinear diffusion equation, the coagulation and fragmentation rates enjoying a detailed balance condition.

In this paper, we investigated a density-dependent reaction-diffusion equation, u(t)=(u(m))(xx)+u-u(m). This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation, which is widely used in population dynamics, combustion theory, and plasma physics. By employing a suitable transformation, this equation was mapped to the anomalous diffusion equation where th...

In this work, we consider the nonequilibrium thermodynamics of a reaction-diffusion system at a given temperature, using the Master equation. The information potential is defined as the logarithm of the stationary state. We compare the approximations, given by the Fokker–Planck equation and the Wentzel-Kramers-Brillouin method directly applied to the Master equation, and prove that they lead to...