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For 3D geometries, we consider stones (modeled as convex polyhedra) subject to weathering with planar slices of random orientation and depth successively removing material, ultimately yielding smooth and round (i.e. spherical) shapes. An…
The dynamics of the development of instability of the free surface of liquid helium, which is charged by electrons localized above it, is studied. It is shown that, if the charge completely screens the electric field above the surface and…
We numerically investigate the nearly self-similar blowup of the generalized axisymmetric Navier--Stokes equations. First, we rigorously derive the axisymmetric Navier--Stokes equations with swirl in both odd and even dimensions, marking…
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…
We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…
The surface of a thin liquid film with nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. We present the results of experiments on one of the simplest variable curvature surfaces: a stepped…
We present models of surfaces of crystals in an environment where molecular beam epitaxy (MBE) and related methods of crystal growth like atomic layer epitaxy (ALE) can be performed. Besides detailed models of reconstructed (001) surfaces…
The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on…
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…
Extensive dynamical simulations of Restricted Solid on Solid models in $D=2+1$ dimensions have been done using parallel multisurface algorithms implemented on graphics cards. Numerical evidence is presented that these models exhibit KPZ…
In the standard treatment of heterogeneous nucleation on a surface, the energy of the surface is assumed to be homogeneous. Often its value is obtained from some macroscopic measurement. We ask the question what happens if we consider the…
Energies of graphene nanocones with 1 to 5 pentagonal disclinations are studied on an atomically detailed level. The numerical results are interpreted in terms of three different contributions to the cone energy: the core disclination…
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…
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.…
Growth of nanoclusters and nanopillars is considered in a model of surface deposition of building blocks (atoms) diffusionally transported from solution to the forming surface structure. Processes of surface restructuring are also accounted…
The structural relaxation of amorphous materials is described as arising from the superposition of elementary processes with varying activation energies. We show that it is possible to obtain the kinetic parameters of these processes from…
The growth of a crystal is usually determined by its surface. Many factors influence the growth dynamics. Energy barriers associated with the presence of steps most often decide about the emerging pattern. The height and type of…
The basic physics of nucleation in solid \hl{single-crystal} nanoparticles is revealed by a phase-field theory that includes surface energy, chemical reactions and coherency strain. In contrast to binary fluids, which form arbitrary contact…
A fluid in equilibrium in a finite volume $V$ with particle number $N$ at a density $\rho = N/V$ exceeding the onset density $\rho_f $ of freezing may exhibit phase coexistence between a crystalline nucleus and surrounding fluid. Using a…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…