Related papers: Decay of one dimensional surface modulations
We consider the dynamical properties of a simple model of vibrational surface modes. We obtain the exact spectrum of surface excitations and discuss their dynamical features. In addition to the usually discussed localized and oscillatory…
We consider two-phase fluid deformable surfaces as model systems for biomembranes. Such surfaces are modeled by incompressible surface Navier-Stokes-Cahn-Hilliard-like equations with bending forces. We derive this model using the…
Dense granular flows exhibit both surface deformation and secondary flows due to the presence of normal stress differences. Yet, a complete mathematical modelling of these two features is still lacking. This paper focuses on a steady…
The dynamics of solid-liquid interfaces controlled by solute precipitation and/or dissolution due to the chemical reaction at the interface were computed in two dimensions using a phase field models. Sharp-interface asymptotic analysis…
We perform computer simulations of a Cahn-Hilliard model of phase separation which has dynamical asymmetry between the two coexisting phases. The dynamical asymmetry is incorporated by considering a mobility function which is order…
We introduce a new notion of viscosity solutions for the level set formulation of the motion by crystalline mean curvature in three dimensions. The solutions satisfy the comparison principle, stability with respect to an approximation by…
We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging…
Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a flat metric with several cone-type…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
This paper investigates faceting mechanisms induced by electromigration in the regime where atomic steps are transparent. For this purpose we study several vicinal orientations by means of in-situ (optical diffraction, electronic…
A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model (Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. {\bf 104},…
In this article, we study the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2 + \alpha)-little-H\"older regular…
Accurate and economical modeling of near-surface transport processes is a standing challenge for various engineering and atmospheric boundary-layer flows. In this paper, we address this challenge by utilizing a stochastic one-dimensional…
Nambu-Goto model is investigated by using the canonical Monte Carlo simulation technique on dynamically triangulated surfaces of spherical topology. We find that the model has four distinct phases; crumpled, branched-polymer, linear, and…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that…
We consider the coagulation-decoagulation model on an one-dimensional lattice of length $L$ with open boundary conditions. Based on the empty interval approach the time evolution is described by a system of $\frac{L(L+1)}{2}$ differential…
We present the results of a large-scale simulation of a Dynamically Triangulated Random Surface with extrinsic curvature embedded in three-dimensional flat space. We measure a variety of local observables and use a finite size scaling…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
We propose a simple discrete model to study the nonequilibrium fluctuations of two locally coupled 1+1 dimensional systems (interfaces). Measuring numerically the tilt-dependent velocity we construct a set of stochastic continuum equations…