Related papers: Interface disappearance in fast reaction limit
Invasion phenomena for heterogeneous reaction-diffusion equations are contemporary and challenging questions in applied mathematics. In this paper we are interested in the question of spreading for a reaction-diffusion equation when the…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
I consider a bistable reaction-diffusion system on the interface of deep fluid interacting with Marangoni flow. The method of matched asymptotic expansions is used to resolve the singularity at a sharp interface between the alternative…
We investigate the thermodynamic limit of Dicke superradiance. We find an expression for the system's density matrix that we can prove is exact in the limit of large atom numbers N. This is in contrast to previously known solutions whose…
We consider the asymptotic limit of a diffuse interface model for tumor-growth when a parameter $\varepsilon$ proportional to the thickness of the diffuse interface goes to zero. An approximate solution which shows explicitly the behavior…
A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition at the face $x=0$ is studied with the aim of finding explicit…
We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite time. Upon collision, some of the colliding particles are…
We present a thermodynamic theory of plane coherent solid-solid interfaces in multicomponent systems subject to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated separately using…
With the adiabatic assumption in the cooling process, we discussed a new mechanism on Upsilon(1S) suppression that is due to the fast heating process at the early stage of the fireball instead of its finite decay width in finite temperature…
We introduce a new kinetic interface model suitable for simulating adsorption-reaction processes which take place preferentially at surface defects such as steps and vacancies. As the average interface velocity is taken to zero, the self-…
Phase field models are powerful tools to tackle free boundary problems. For phase transformations involving diffusion, the evolution of the non conserved phase field is coupled to the evolution of the conserved diffusion field. Introducing…
This article considers nonlocal heat flows into a singular target space. The problem is the parabolic analogue of a stationary problem that arises as the limit of a singularly perturbed elliptic system. It also provides a gradient flow…
Although ubiquitous in nature and industrial processes, transport processes at the interface during evaporation and condensation are still poorly understood. Experiments have shown temperature discontinuities at the interface during…
We propose a three-component reaction-diffusion system yielding an asymptotic logarithmic time-dependence for a moving interface. This is naturally related to a Stefan-problem for which both one-sided Dirichlet-type and von Neumann-type…
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media locally with different constant conductivities, where initially one medium has temperature 0 and the other has temperature…
We consider an analytically solvable model of two interacting electrons that allows for the calculation of the exact exchange-correlation kernel of time-dependent density functional theory. This kernel, as well as the corresponding density…
The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…
We study irreversible A-B reaction kinetics at a fixed interface separating two immiscible bulk phases, A and B. We consider general dynamical exponent $z$, where $x_t\sim t^{1/z}$ is the rms diffusion distance after time $t$. At short…
It is shown that a macroscopic superposition state of radiation, strongly interacting with an ensemble of two-level atoms, is removed generating a coherent state describing a classical radiation field, when the thermodynamic limit is taken…
Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End functionalized homopolymers of different species interact at the interface instantaneously and irreversibly…