Related papers: Decay of one dimensional surface modulations
We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height…
We propose a novel phase-field model for solute precipitation and dissolution in liquid solutions. Unlike in previous studies with similar scope, in our model the two non-linear coupled governing equations of the problem, which deliver the…
We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of…
In this paper we investigate the numerical approximation of a variant of the mean curvature flow. We consider the evolution of hypersurfaces with normal speed given by $H^k$, $k \ge 1$, where $H$ denotes the mean curvature. We use a level…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
We study the phase structure of a surface model by using the canonical Monte Carlo simulation technique on triangulated, fixed connectivity, and spherical surfaces with many fine holes. The size of a hole is assumed to be of the order of…
Recently Jeong and Kim [Phys. Rev. E {\bf 66}, 051605 (2002)] investigated the scaling properties of equilibrium self-flattening surfaces subject to a restricted curvature constraint. In one dimension (1D), they found numerically that the…
We study the evolution of step bunches on vicinal surfaces using a thermodynamically consistent step-flow model that (i) circumvents the quasistatic approximation that prevails in the literature by accounting for the dynamics of adatom…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
An infinite hierarchy of layering transitions exists for model polymers in solution under poor solvent or low temperatures and near an attractive surface. A flat histogram stochastic growth algorithm known as FlatPERM has been used on a…
We investigate the nonlinear evolution of the Bales-Zangwill instability, responsible for the meandering of atomic steps on a growing vicinal surface. We develop an asymptotic method to derive, in the continuous limit, an evolution equation…
Relaxation of initially out-of-equilibrium rough interfaces in presence of thermal noise is investigated using Langevin formalism. During thermal equilibration towards the well-known roughening regime, three scaling regimes observed over…
We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…
The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer…
Using renormalized field theory, we examine the dynamics of a growing surface, driven by an obliquely incident particle beam. Its projection on the reference (substrate) plane selects a ``parallel'' direction, so that the evolution equation…
In this fluid dynamics video, we present an overview of the most important results recently obtained in our group using an optical profilometric technique that allows for single-shot global measurement of free-surface deformations. This…
Exactly solvable two-dimensional polygon models, counted by perimeter and area, are described by $q$-algebraic functional equations. We provide techniques to extract the scaling behaviour of these models up to arbitrary order and apply them…
We studied scaling in kinetic roughening and phase ordering during growth of binary systems using 1+1 dimensional single-step solid-on-solid model with two components interacting via Ising-like interaction with the strength K. We found that…
In the continuum theory the time evolution of surfaces eroded by ion bombardment is modelled by stochastic partial differential equations (SPDEs). These determine the scaling regimes and universality classes of the evolving surfaces.…
The kinetics of an initially undercooled solid-liquid melt is studied by means of a generalized Phase Field model, which describes the dynamics of an ordering non-conserved field phi (e.g. solid-liquid order parameter) coupled to a…