Related papers: Nonlocality in kinetic roughening
The essential features of many interfaces driven out of equilibrium are described by the same equation---the Kardar-Parisi-Zhang (KPZ) equation. How do living interfaces, such as the cell membrane, fit into this picture? In an endeavour to…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
Turbulent flows above a solid surface are characterised by a hydrodynamic roughness that represents, for the far velocity field, the typical length scale at which momentum mixing occurs close to the surface. Here, we are theoretically…
We study surface and bulk properties of porous films produced by a model in which particles incide perpendicularly to a substrate, interact with deposited neighbors in its trajectory, and aggregate laterally with probability of order $a$ at…
We deal with a nonlocal interaction equation describing the evolution of a particle density under the effect of a general symmetric pairwise interaction potential, not necessarily in convolution form. We describe the case of a convex (or…
A class of nonequilibrium models with short-range interactions and sequential updates is presented. The models describe one dimensional growth processes which display a roughening transition between a smooth and a rough phase. This…
We study the simple, linear, Edwards-Wilkinson equation that describes surface growth governed by height diffusion in the presence of spatiotemporally power-law decaying correlated noise. We analytically show that the surface becomes…
We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete…
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…
The meander instability of a vicinal surface growing under step flow conditions is studied within a solid-on-solid model. In the absence of edge diffusion the selected meander wavelength agrees quantitatively with the continuum linear…
The short time behavior of a disturbed system is influenced by off-shell motion and best characterized by the reduced density matrix possessing high energetic tails. We present analytically the formation of correlations due to collisions in…
The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact…
The dynamics of thin films on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the…
In this paper we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamcs. The different propagation regimes ranging from the hyperbolic to the dispersive,…
We consider a kinetic relaxation model and an associated macroscopic scalar nonlinear hyperbolic equation on a network. Coupling conditions for the macroscopic equations are derived from the kinetic coupling conditions via an asymptotic…
The static and dynamic roughenings of a growing crystalline facet is studied where the growth mechanism is controlled by a restricted-curvature (RC) geometry. A continuum equation, in analogy with the Kardar-Parisi-Zhang (KPZ) equation is…
In this work, we present a systematic approach to investigate the existence, multiplicity, and local gradient regularity of solutions for nonlocal quasilinear equations with local gradient degeneracy. Our method involves an interactive…
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous…
The dynamical mechanism at the origin of the non-local rheology of dense granular flows is investigated trough discrete element simulations. We show that the influence of a shear band on the mechanical behavior of a distant zone is…
Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of natural and technological processes, including embryonic development and 3D printing. In this paper…