Related papers: A new class of models for surface relaxation with …
We study the continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solid-on-solid and discrete Gaussian models. With computational experiments and theoretical arguments we are able to…
We present simulations of the relaxation towards equilibrium of one dimensional steps and sinusoidal grooves imprinted on a surface below its roughening transition. We use a generalization of the hypercube stacking model of Forrest and…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
We study analytically the equilibrium and near-equilibrium properties of a model of surfaces relaxing via linear surface diffusion and subject to a lattice potential. We employ the variational mean field formalism introduced by Saito for…
The relaxation process of one dimensional surface modulations is re-examined. Surface evolution is described in terms of a standard step flow model. Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz…
The earthquake-like model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach…
In this article, we propose a mathematical model which explains the formation of strong bonds during the relaxation process of a soft solid on a hard surface. As a result, the soft solid relaxes to a non zero residual stress level. The…
Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial…
Models of adhesion of extended particles on linear and planar substrates are of interest in interpreting surface deposition in colloid, polymer, and certain biological systems. An introduction is presented to recent theoretical advances in…
This survey article is about discrete constant mean curvature surfaces defined by an approach related to integrable systems techniques. We introduce the notion of discrete constant mean curvature surfaces by first introducing properties of…
Our goal is to identify the type and number of static equilibrium points of solids arising from fine, equidistant $n$-discretrizations of smooth, convex surfaces. We assume uniform gravity and a frictionless, horizontal, planar support. We…
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…
An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…
We introduce a theoretical model for the compaction of granular materials by discrete vibrations which is expected to hold when the intensity of vibration is low. The dynamical unit is taken to be clusters of granules that belong to the…
In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant $n$-discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on…
The surface pattern formation on a gelation surface is analyzed using an effective surface roughness. The spontaneous surface deformation on DiMethylAcrylAmide (DMAA) gelation surface is controlled by temperature, initiator concentration,…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…