Related papers: A solvable model of interface depinning in random …
A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is…
The present paper is devoted to the study of transition fronts of nonlocal Fisher-KPP equations in time heterogeneous media. We first construct transition fronts with prescribed interface location functions, which are natural…
Abstract. The present work considers a change in the momentum under the transfer of a solution through the interface. It is shown that pressure related to the partial volumes of components arises in a solution under diffusion. As a result,…
By using a limit analysis for the motion equations of viscous fluid endowed with internal capillarity, we are able to propose a dynamical expression for the surface tension of moving liquid-vapour interfaces without any phenomenological…
The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation admits space monotone transition fronts with…
We investigate the evolution of a single unbounded interface between ordered phases in two-dimensional Ising ferromagnets that are endowed with single-spin-flip zero-temperature Glauber dynamics. We examine specifically the cases where the…
Long linear polymers in a depinned interfaces environment have been studied for a long time, for instance in \cite{Caravenna2009depinning} when the temperature is constant. In this paper, we study an extension of this model by making the…
We investigate the interaction between an infinite cylinder and a free fluid-fluid interface governed only by its surface tension. We study the deformation of an initially flat interface when it is deformed by the presence of a cylindrical…
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The…
The explicit form of the interface equation of motion derived assuming a minimal surface is extended to general bicontinuous interfaces that appear in the diffusion limited stage of the phase separation process of binary mixtures. The…
We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…
We consider asymptotic problems concerning the motion of interface separating the regions of large and small values of the solution of a reaction-diffusion equation in the media consisting of domains with different characteristics…
We extend the theory of topological localised interface modes to systems with damping. The spectral problem is formulated as a root-finding problem for the interface impedance function and Rouch\'e's theorem is used to track the zeros when…
We consider a model for the evolution of an interface in a heterogeneous environment governed by a parabolic equation. The heterogeneity is introduced as obstacles exerting a localized dry friction. Our main result establishes the emergence…
Finite-thickness interphases between different constituents in heterogeneous materials are often replaced by a zero-thickness interface model. Commonly accepted interface models intuitively assume that the interface layer is situated…
The Ising model of statistical physics has served as a keystone example of phase transitions, thermodynamic limits, scaling laws, and many other phenomena and mathematical methods. We introduce and explore an Ising game, a variant of the…
Consider the scattering of time-harmonic point sources by an infinite locally rough interface with bounded obstacles embedded in the lower half-space. The model problem is first reduced to an equivalent integral equation formulation defined…
We consider the case of a deformable material interface between two immiscible moving media, both of them being magnetiable. The time dependence of the metric at the interface introduces a non linear term, proportional to the mean…
In this note we prove that appropriately scaled threshold dynamics-type algorithms corresponding to the fractional Laplacian of order $\alpha \in (0,2)$ converge to moving fronts. When $\alpha \geqq 1$ the resulting interface moves by…
Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking/capturing of dynamic interfaces between different materials on larger scales.…