Related papers: Effective behavior of an interface propagating thr…
We investigate the localization transition for a simple model of interface which interacts with an inhomonegeous defect plane. The interface is modeled by the graph of a function $\phi: \mathbb Z^2 \to \mathbb Z$,and the disorder is given…
We consider an Ising model on a square grid with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution…
The evolution of the interface between two ideal dielectric liquids in a strong vertical electric field is studied. It is found that a particular flow regime, for which the velocity potential and the electric field potential are linearly…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems…
We investigate the behaviour of solutions of a fractional semilinear partial differential equation that models the evolution of an interface in a random medium. We show a pinning result and apply it to the related homogenizing process.
We study unique continuation over an interface using a stabilized unfitted finite element method tailored to the conditional stability of the problem. The interface is approximated using an isoparametric transformation of the background…
The dynamics of driven interfaces through disordered media is a common framework for a myriad of diverse systems starting from mode-I fracture, vortex lines in superconductors, magnetic domain walls to invading fluid in a porous medium to…
We study the tilt dependence of the pinning-depinning transition for an interface described by the anisotropic quenched Kardar-Parisi-Zhang equation in 2+1 dimensions, where the two signs of the nonlinear terms are different from each…
We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure-field. We model the…
In this paper, we study the slow patterns of multilayer dislocation dynamics modeled by a multiscale parabolic equation in the half-plane coupled with a dynamic boundary condition on the interface. We focus on the influence of bulk dynamics…
In this paper we describe the asymptotic behavior of rigid spin lattice energies by exhibiting a continuous interfacial limit energy as scaling to zero the lattice spacing. The limit is not trivial below a percolation threshold: it can be…
Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous…
We propose an equation that describes the shape of the driven contact line in dynamics in the presence of an arbitrary (possibly random) distribution of the surface defects. It is shown that the triple contact line depinning differs from…
Phenomenological theories of interfacial interactions have targeted terrestrial applications since long time and their exploitation has inspired our research programme to build up a macroscopic theory of gas-surface interactions targeting…
The motion of a thin elastic plate interacting with a viscous fluid is investigated. A periodic force acting on the plate is considered, which in a setting without damping could lead to a resonant response. The interaction with the viscous…
The dynamics of a single crack moving through a heterogeneous medium is studied in the quasi-static approximation. Equations of motion for the crack front are formulated and the resulting scaling behaviour analyzed. In a model scalar system…
We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is…
In this paper we investigate the dynamical behavior of an interface or polymer, in interaction with a distant attractive substrate. The interface is modeled by the graph of a nearest neighbor path with non-negative integer coordinates, and…
Several methods for handling sloping fluid-solid interfaces with the elastic parabolic equation are tested. A single-scattering approach that is modified for the fluid-solid case is accurate for some problems but breaks down when the…