相关论文: Boundary Dynamics of Sweeping Interface

Dislocation-interface interactions dictate the mechanical properties of polycrystalline materials through dislocation absorption, emission and reflection and interface sliding. We derive a mesoscale interface boundary condition to describe…

A new approach is developed to derive an analytical form for mobility corrections in phase-field models for pure material solidification. Similar to the thin interface limit approach (Karma and Rappel, 1996) it seeks to remove systematic…

We prove the convergence of an implicit time discretization for the one-phase Mullins-Sekerka equation, possibly with additional non-local repulsion, proposed in [F. Otto, Arch. Rational Mech. Anal. 141 (1998) 63--103]. Our simple argument…

The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime are examined. The challenging non-rectilinear mixed-boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion…

The dynamics of drop(s) has been simulated by the finite volume/moving mesh interface tracking method (MMIT) with adaptive mesh refining and coarsening. In MMIT, the interface is of zero thickness and moves in a Lagrangian fashion. A number…

We study numerically the depinning transition of driven elastic interfaces in a random-periodic medium with localized periodic-correlation peaks in the direction of motion. The analysis of the moving interface geometry reveals the existence…

We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different…

Probing the fluid dynamics of thin films is an excellent tool to study the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid due to the fact that the dewetting process, an internal…

The thermally activated creep motion of an elastic interface weakly driven on a disordered landscape is one of the best examples of glassy universal dynamics. Its understanding has evolved over the last 30 years thanks to a fruitful…

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…

Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…

Droplet(s) breakup and coalescence have been simulated by the finite volume/moving mesh interface tracking method (MMIT) with adaptive mesh refining and coarsening. In this method, the interface is zero-thickness and moves in a Lagrangian…

In an effort to study the stability of contact lines in fluids, we consider the dynamics of a drop of incompressible viscous Stokes fluid evolving above a one-dimensional flat surface under the influence of gravity. This is a free boundary…

A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…

From the Navier-Stokes-Korteweg (NSK) equations, the exact relations between the fundamental surface physical quantities for two-phase viscous flow with diffuse interface are derived, including density gradient, shear stress, vorticity,…

We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet…

The Smoluchowski diffusion equation describes diffusion in the presence of external forces. Studying the mechanical response of soft materials to linear forces, such as shear, results in a boundary value problem involving an…

We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves…

We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution…

We present a full classification of the short-time behaviour of the interfaces and local solutions to the nonlinear parabolic $p$-Laplacian type reaction-diffusion equation of non-Newtonian elastic filtration \[…