相关论文: On two continuous models for the dynamics of sandp…

We model formation and evolution of transverse dune fields. In the model, only the cross section of the dune is simulated. The only physical variable of relevance is the dune height, from which the dune width and velocity are determined, as…

The Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. The dynamics of the sandpiles occur when the grains topple over a graph. In this study, we allow the graph to evolve…

Here we give further evidences to support our scaling relation described in our previous paper [cond-mat/0006459, Phys. Rev. Lett. Vol.85, pp.1238 (2000)].

In this paper we study $\infty$-Laplacian type diffusion equations in weighted graphs obtained as limit as $p\to \infty$ to two types of $p$-Laplacian evolution equations in such graphs. We propose these diffusion equations, that are…

A discussion of epitaxial growth is presented for those situations (OMVPE, CBE, ALE, MOMBE, GSMBE, etc.) when the kinetics of surface processes associated with molecular precursors may be rate limiting. Emphasis is placed on the…

We report experimental and numerical results on the growth of a super stable heap (SSH). Such a regime appears for flows in a thin channel and for high flow rate : the flow occurs atop a nearly static heap whose angle is stabilized by the…

This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…

The paper presents results from kinetic Monte Carlo simulations of kinetic surface roughening using an important and experimentally relevant model of epitaxial growth -- the solid-on-solid model with Arrhenius dynamics. A restriction on…

We study a variational model for the quasistatic growth of cracks with fractional di- mension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic…

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 the effect of a constant electrical field applied on vicinal surfaces such as the Si$(111)$ surface. An electrical field parallel to the steps induces a meandering instability with a nonzero phase shift. Using the…

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around…

A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover,…

See the updated version arXiv:nlin/0111028.

We define a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so…

In this article we apply the technique proposed in Deng-Hou-Yu (Comm. PDE, 2005) to study the level set dynamics of the 2D quasi-geostrophic equation. Under certain assumptions on the local geometric regularity of the level sets of…

Stably stratified fluids subject to sustained forcing are known to develop step-like density "staircases", where nearly homogeneous layers alternate with thin interfaces of strong stratification. However, long-time numerical investigations…

This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…

We obtain an analytical solution of a one-dimensional sandpile problem in a thick flow regime, when it can be formulated in terms of linear equations. It is shown that a space periodicity takes place during the sandpile evolution even for a…

Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a…