Related papers: Modeling of Oscillatory Driven Surface Evolution
A vibrational model of transport properties of dense fluids assumes that solid-like oscillations of atoms around their temporary equilibrium positions dominate the dynamical picture. The temporary equilibrium positions of atoms do not form…
We show that the oscillatory driving of crystal surfaces can induce pattern formation or smoothening. The driving force can be of quite different origin such as a pulsed laser beam, an electric field, or elasticity. Depending on driving…
A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion-beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories.…
We present a one dimensional model for the development of corrugations in roads subjected to compressive forces from a flux of cars. The cars are modeled as damped harmonic oscillators translating with constant horizontal velocity across…
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…
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…
The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…
A mathematical model is developed to analyze the growth/decay rate of surface perturbations of an ultrathin metal film on an amorphous substrate (SiO_{2}). The formulation combines the approach of Mullins [J. Appl. Phys. v30, 77, 1959] for…
A dynamical model is proposed for isotropic turbulence driven by steady forcing that yields a viscosity independent dynamics for the small-scale (inertial) regime. This reproduces the Kolmogorov spectrum for the two-point velocity…
After emerging to the solar surface, the Sun's magnetic field displays a complex and intricate evolution. The evolution of the surface field is important for several reasons. One is that the surface field, and its dynamics, sets the…
We review the surface flux transport model for the evolution of magnetic flux patterns on the Sun's surface. Our underlying motivation is to understand the model's prediction of the polar field (or axial dipole) strength at the end of the…
Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is…
We propose and study a continuum model for the dynamics of amorphizable surfaces undergoing ion-beam sputtering (IBS) at intermediate energies and oblique incidence. After considering the current limitations of more standard descriptions in…
A continuum model for growth of solids is developed, considering adatom deposition, surface diffusion, and configuration dependent incorporation rate. For amorphous solids it is related to surface energy densities. The high adatom density…
Driven surface diffusion occurs, for example, in molecular beam epitaxy when particles are deposited under an oblique angle. Elastic phase transitions happen when normal modes in crystals become soft due to the vanishing of certain elastic…
We consider a particle that is subject to a constant force and scatters inelastically on a vibrating periodically corrugated floor. At small friction and small radius of the circular scatterers the dynamics is dominated by resonances…
We extend the concept of optical flow with spatiotemporal regularisation to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. The purpose of this paper is to introduce variational motion…
Patterns on curved surfaces are ubiquitous, yet the influence of surface geometry on pattern dynamics remains elusive. We recently reported a new mechanism of pattern propagation in which a static pattern on a flat plane becomes a…
This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…