Related papers: A Mathematical Treatment to Determine Transient Gr…
Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time. In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks.…
A qualitative behavior of grain size dependent resistance of polycrystalline films has been worked out by extending the earlier model (Volger's model) for polycrystalline films. Growth of grain size is considered to be accompanied with a…
A simple analytical model of intergranular normal stresses is proposed for a general elastic polycrystalline material with arbitrary shaped and randomly oriented grains under uniform loading. The model provides algebraic expressions for the…
We present a numerical approach for accurately evolving a dust grain-size distribution undergoing number-conserving (such as sputtering) and/or mass-conserving (such as shattering) processes. As typically observed interstellar dust…
We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in…
Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically.…
We revisit the longstanding question of the onset of sediment transport driven by a turbulent fluid flow via laboratory measurements. We use particle tracking velocimetry to quantify the fluid flow as well as the motion of individual…
The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a…
We consider Gaussian approximation in a variant of the classical Johnson--Mehl birth-growth model with random growth speed. Seeds appear randomly in $\mathbb{R}^d$ at random times and start growing instantaneously in all directions with a…
A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field…
Grain size is an important control on mantle viscosity and permeability, but is difficult or impossible to measure in situ. We construct a two-dimensional, single phase model for the steady-state mean grain size beneath a mid-ocean ridge.…
This paper proposes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant with the directed nature of the graph edges. It is proved that the…
Exchange-driven growth is a process in which pairs of clusters interact and exchange a single unit of mass. The rate of exchange is given by an interaction kernel $K(j,k)$ which depends on the masses of the two interacting clusters. In this…
We explore the effects of surface tension and mobility models in simulations of grain growth using threshold dynamics algorithms that allow performing large scale simulations, while naturally capturing the Herring angle condition at…
We study conserved one-dimensional models of particle diffusion, attachment and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) ~ m^{-k}, k>0. Heuristic scaling arguments based on…
We study models for surface growth with a wetting and a roughening transition using simple and pair mean-field approximations. The simple mean-field equations are solved exactly and they predict the roughening transition and the correct…
The classical Lifshitz-Slyozov-Wagner theory of domain coarsening predicts asymptotically self-similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field.…
The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic…
Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual…
Turbulence is the dominant source of collisional velocities for grains with a wide range of sizes in protoplanetary disks. So far, only Kolmogorov turbulence has been considered for calculating grain collisional velocities, despite the…