Related papers: Effective behavior of an interface propagating thr…
The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the…
This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential…
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…
The dynamics of an interface between the normal and superconducting phases under nonstationary external conditions is studied within the framework of the time-dependent Ginzburg-Landau equations of superconductivity, modified to include…
Phase field models frequently provide insight to phase transitions, and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via…
A periodically-uneven (in one horizontal direction) stress-free boundary covering a linear, isotropic, homogeneous, lossless solid half space is submitted to a vertically-propagating shear-horizontal plane, body wave. The rigorous theory of…
Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force…
This paper considers a family of second-order parabolic equations in divergence form with rapidly oscillating and time-dependent periodic coefficients and an interface between two periodic structures. Following a framework initiated by…
The theory of the depinning transition of elastic manifolds in random media provides a framework for the statistical dynamics of dislocation systems at yield. We consider the case of a single flexible dislocation gliding through a random…
We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic…
Moving-habitat models track the density of a population whose suitable habitat shifts as a consequence of climate change. Whereas most previous studies in this area consider 1-dimensional space, we derive and study a spatially 2-dimensional…
We study the pinning-depinning phase transition of interfaces in the quenched Kardar-Parisi-Zhang model as the external driving force $F$ goes towards zero. For a fixed value of the driving force we induce depinning by increasing the…
Viscoelasticity and rate-dependent adhesion of soft matter lead to difficulties in modeling the 'relatively simple' problem of a rigid sphere in contact with a viscoelastic half-space. For this reason, approximations in describing surface…
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…
We study the microscopic structure and the stationary propagation velocity of (1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or…
An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity interface problems on unfitted meshes with respect to the interface and domain boundary. The…
We study the local scaling properties of driven interfaces in disordered media modeled by the Edwards-Wilkinson equation with quenched noise. We find that, due to the super-rough character of the interface close to the depinning transition,…
In this work we consider the elasticity problem for two domains separated by a heterogeneous layer. The layer has an $\varepsilon-$periodic structure, $\varepsilon\ll1$, including a multiple micro-contact between the structural components.…
We investigate a model for the dynamics of a solid object, which moves over a randomly vibrating solid surface and is subject to a constant external force. The dry friction between the two solids is modeled phenomenologically as being…
We introduce a new regularized interface method for proving existence of weak solutions to nonlinear moving boundary problems with low-regularity interfaces. We study a fluid-poroelastic structure interaction (FPSI) problem coupling the…