Related papers: Interface disappearance in fast reaction limit
It is known that when the diffuse interface thickness $\epsilon$ vanishes, the sharp interface limit of the stochastic reaction-diffusion equation is formally a stochastic geometric flow. To capture and simulate such geometric flow, it is…
In this work, we construct a transformation between the solutions to the following reaction-convection-diffusion equation $$ \partial_t u=(u^m)_{xx}+a(x)(u^m)_x+b(x)u^m, $$ posed for $x\in\real$, $t\geq0$ and $m>1$, where $a$, $b$ are two…
In this paper, we establish a general convergence theorem for solutions of multivariate stochastic differential equations with countably many singular terms expressed as integrals with respect to local times. The processes under…
We consider the slow nonlinear diffusion equation subject to a constant absorption rate and construct local self-similar solutions for reversing (and anti-reversing) interfaces, where an initially advancing (receding) interface gives way to…
The fast reaction limit for a nonlinear bulk-surface reaction-diffusion system is investigated. This system describes a reversible reaction with arbitrary stoichiometric coefficients, where one chemical is present in a bounded vessel…
We consider a transmission problem in which the interior domain has infinitely ramified structures. Transmission between the interior and exterior domains occurs only at the fractal component of the interface between the interior and…
The efficiency and cooling power of a two-terminal thermoelectric refrigerator are analyzed near the limit of vanishing dissipation (ideal system), where the optimal efficiency is the Carnot one, but the cooling power then unfortunately…
We derive explicit solution representations for linear, dissipative, second-order Initial-Boundary Value Problems (IBVPs) with coefficients that are spatially varying, with linear, constant-coefficient, two-point boundary conditions. We…
In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small "escape window" in the otherwise impermeable boundary, once it arrives to this window and over-passes an…
We derive an expression for the 4-point conductance of a general quantum junction in terms of the density response function. Our formulation allows us to show that the 4-point conductance of an interacting electronic system possessing…
In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled…
In this paper we consider a one-dimensional reaction-diffusion model with piecewise continuous reaction term that describes propagation of autoignition fronts in reactive co-flow jets in a certain parametric regime. The model is reduced to…
We study the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity and derive a free boundary problem with hysteresis to describe the macroscopic evolution in the parabolic scaling limit. The first part of…
The arrow of time problem remains one of the most intriguing questions of modern physics. We investigate one particular example of this problem: the irreversibility of heat transfer through an interface between two materials. This special…
We explore the physics of thermal impedance matching at the interface between two dissimilar materials by controlling the properties of a single atomic mass or bond. The maximum thermal current is transmitted between the materials when we…
In this study we try to answer the qustion : What happens when explicit constraints are introduced such that the low energy, long wavelength modes of a system are unavailable ? This question has assumed some importance in recent years due…
We discuss a numerical method for convection-diffusion-reaction problems with a free boundary in 1D. The method is based on the numerical modelling of the interface evolution, the transformation to a fixed domain problem and the…
We consider a monostable time-delayed reaction-diffusion equation arising from population dynamics models. We let a small parameter tend to zero and investigate the behavior of the solutions. We construct accurate lower barriers --- by…
In systems described by the scattering theory, there is an upper bound, lower than Carnot, on the efficiency of steady-state heat to work conversion at a given output power. We show that interacting systems can overcome such bound and…
Conformal field theories can exchange energy through a boundary interface. Imposing conformal boundary conditions for static interfaces implies energy conservation at the interface. Recently, the reflective and transmitive properties of…