Related papers: The physics of boundary conditions in reaction-dif…
Subdiffusion with reaction $A+B\rightarrow B$ is considered in a system which consists of two homogeneous media joined together; the $A$ particles are mobile whereas $B$ are static. Subdiffusion and reaction parameters, which are assumed to…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
We combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions. We analyze the behavior of facets at the parts of the boundary where these conditions are imposed. We devote…
A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to…
We construct models where initial and boundary conditions can be found from the fundamental rules of physics, without the need to assume them, they will be derived from the action principle. Those constraints are established from physical…
We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes.…
Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary…
We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We…
A general derivation is proposed for several boundary conditions arisen in the lattice Boltzmann simulations of various physical problems. Pair-wise moment conservations are proposed to enforce the boundary conditions with given macroscopic…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…
This work was motivated by a lacking general consensus in the exact form of the boundary conditions (BCs) required on the solid surfaces for the continuum modeling of RF plasmas. Various kinds of number and energy density BCs on solid…
In this paper, we investigate the effects of stochastic resetting on diffusion in $\R^d\backslash \calU$, where $\calU$ is a bounded obstacle with a partially absorbing surface $\partial \calU$. We begin by considering a Robin boundary…
We have studied anomalous diffusion of a particle in a random medium in which the passage of the particle may modify the state of the visited sites. The simplicity of the dynamics allows analytic solution. Interesting propagation and…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
We study the appearance of a boundary condition along an interface between two regions, one with constant diffusivity $1$ and the other with diffusivity $\eps>0$, when $\eps\to0$. In particular, we take Fick's diffusion law in a context of…
Diffusion-induced Ramsey narrowing that appears when atoms can leave the interaction region and repeatedly return without lost of coherence is investigated using strong collisions approximation. The effective diffusion equation is obtained…
Reaction-diffusion-advection media on semi-infinite domains are important in chemical, biological and ecological applications, yet remain a challenge for pattern formation theory. To demonstrate the rich emergence of nonlinear traveling…