相关论文: Sharp-interface limits of Cahn-Hilliard models and…

At the molecular scale there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to…

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal and lateral stiffnesses rise linearly with the applied load, and the load rises exponentially…

We analyze the continuum limit of a thresholding algorithm for motion by mean curvature of one dimensional interfaces in various space-time discrete regimes. The algorithm can be viewed as a time-splitting scheme for the Allen-Cahn equation…

We compute properties of the interface of the 3-dimensional Ising model for a wide range of temperatures, covering the whole region from the low temperature domain through the roughening transition to the bulk critical point. The interface…

We further study the interfaces arising in a situation of inhomogeneity. More precisely, we identify a characteristic length for the gradient percolation model, that enables us to tighten previous estimates established for it. This allows…

Using stability arguments, this Brief Report suggests that a term that enhances the surface tension in the presence of large height fluctuations should be included in the Kardar-Parisi-Zhang equation. A one-loop renormalization group…

Imbibition phenomena have been widely used experimentally and theoretically to study the kinetic roughening of interfaces. We critically discuss the existing experiments and some associated theoretical approaches on the scaling properties…

The fundamental problem of friction in the presence of macroscopic adhesion, as in soft bodies, is receiving interest from many experimentalists. Since the first fracture mechanics `purely brittle' model of Savkoor and Briggs, models have…

This paper introduces for the first time the concepts of non-coherent interfaces and microstructure-driven interface forces in the framework of micromorphic elasticity. It is shown that such concepts are of paramount importance when…

The Functionalized Cahn-Hilliard equation has been proposed as a model for the interfacial energy of phase-separated mixtures of amphiphilic molecules. We study the existence of a nonnegative weak solutions of a gradient flow of the…

The dynamics of a one-dimensional crystalline interface model with long-range interactions is investigated. In the absence of randomness, the linear response mobility decreases to zero when the temperature approaches the roughening…

The purpose of this paper is to investigate the Cahn-Hillard approximation for entire minimal hypersurfaces in the hyperbolic space. Combining comparison principles with minimization and blow-up arguments, we prove existence results for…

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…

Within mean-field theory we determine the universal scaling function for the effective force acting on a single colloid located near the interface between two coexisting liquid phases of a binary liquid mixture close to its critical…

Effective interface conditions for a periodically voided thin layer separating two homogeneous bulk regions are derived for the elastic wave equation by taking the simultaneous limit of vanishing layer periodicity and layer thickness. The…

We study the dynamics and equilibrium profile shapes of contact lines for wetting in the case of a spatially inhomogeneous solid wall with stripe defects. Using a phase-field model with conserved dynamics, we first numerically determine the…

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…

When a viscous fluid partially fills a Hele--Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman--Taylor instability. We consider the evolution of a fluid region of finite extent, bounded…

We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a mean curvature flow with Dirichlet or dynamic boundary…

The mathematical analysis of diffuse-interface models for multiphase flows has attracted significant attention due to their ability to capture complex interfacial dynamics, including curvature effects, within a unified, energetically…