相关论文: Boundary Dynamics of Sweeping Interface

In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution…

Boundary-catalytic branching processes describe a broad class of natural phenomena where the population of diffusing particles grows due to their spontaneous binary branching (e.g., division, fission or splitting) on a catalytic boundary…

We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear…

In this survey we present the state of the art about the asymptotic behavior and stability of the modified Mullins--Sekerka flow and the surface diffusion flow of smooth sets, mainly due to E.~Acerbi, N.~Fusco, V.Julin and M.Morini. First…

Motivated by a novel method for granular segregation, we analyze the one dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate of absorption are given by explicit…

We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the…

This Communication reports a geometrical factor that is necessary in the diffusion boundary condition across surface steps. Specifically, this factor relates adatom concentration to its spatial gradient at a surface step, and it describes…

We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…

We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The…

This paper is devoted to the anomalous diffusion limit of kinetic equations with a fractional Fokker-Planck collision operator in a spatially bounded domain. We consider two boundary conditions at the kinetic scale: absorption and specular…

We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…

This study employs molecular dynamics simulations to investigate droplet dynamics when a stationary droplet on a solid surface is struck by another droplet of similar size from above. The focus is on the jumping behavior of the merged…

A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The…

This paper is devoted to the study of propagation dynamics for a large class of non-monotone evolution systems. In two directions of the spatial variable, such a system has two limiting systems admitting the spatial translation invariance.…

We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…

We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the…

The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near…

The interactions between dislocations and interface/grain boundaries, including dislocation absorption, transmission, and reflection, have garnered significant attention from the research community for their impact on the mechanical…

Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…

Propagating interfaces are ubiquitous in nature, underlying instabilities and pattern formation in biology and material science. Physical principles governing interface growth are well understood in passive settings; however, our…