Related papers: Nonlocality in kinetic roughening
In this paper we focus on crystal surfaces led out of equilibrium by a growth or erosion process. As a consequence of that the surface may undergo morphological instabilities and develop a distinct structure: ondulations, mounds or…
The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is…
We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and…
Using the linearity property of the Mullins-Herring equation when the velocity is zero with a Gaussian noise, we obtain an analytic form for the global mean-square surface width and height-height correlation function. This can be used to…
The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces…
We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions…
Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…
This paper proposes a one-dimensional lattice model with long-range interactions which, in the continuum, keeps its nonlocal behaviour. In fact, the long-time evolution of the localized waves is governed by an asymptotic equation of the…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
Motivated by a series of experiments that revealed a temperature dependence of the dynamic scaling regime of growing surfaces, we investigate theoretically how a nonequilibrium growth process reacts to a sudden change of system parameters.…
The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysis is carried for a moving front in the quasi-static regime…
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…
We describe the surface properties of a simple lattice model of a sandpile that includes evolving structural disorder. We present a dynamical scaling hypothesis for generic sandpile automata, and additionally explore the kinetic roughening…
We discuss the possibility that, besides roughening, a vicinal surface could display preroughening (PR), and consider the possible mechanisms for its promotion. Within the framework of a terrace-step-kink model, it turns out that a PR…
Localization of plastic strain induced by softening can be objectively described by a regularized plasticity model that postulates a dependence of the current yield stress on a nonlocal softening variable defined by a differential…
Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain…
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…
The nonlocal world presents an abundance of surprises and wonders to discover. These special properties of the nonlocal world are usually the consequence of long-range interactions, which, especially in presence of geometric structures and…
We present a theoretical and numerical investigation of the effect of a time-varying external driving force on interface growth. First, we derive a relation between the roughening exponents which comes from a generalized Galilean…
The long-ranged elastic model, which is believed to describe the evolution of a self-affine rough crack-front, is analyzed to linear and non-linear orders. It is shown that the nonlinear terms, while important in changing the front…