Related papers: A Kinetic Model for Grain Growth
In this paper, we present a continuum model for the dynamics of low angle grain boundaries in two dimensions based on the motion of constituent dislocations of the grain boundaries. The continuum model consists of an equation for the motion…
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…
A linear bubble model of grain growth is introduced to study the conditions under which an isolated grain can grow to a size much larger than the surrounding matrix average (abnormal growth). We first consider the case of bubbles of two…
A formula of grain growth rate, based on a nonlinear capillarity-driven relation, is derived to predict and interpret realistic growth processes in polycrystalline systems. The derived formula reveals how the growth and stagnation of grains…
Actin growth is a fundamental biophysical process and it is, at the same time, a prototypical example of diffusion-mediated surface growth. We formulate a coupled chemo-mechanical, one-dimensional growth model encompassing both material…
We study a nonlinear kinetic model of mass exchange between interacting grains. The transition rates follow the Arrhenius equation with an activation energy that depends on the grain mass. We show that the activation parameter can be…
In this paper we introduce kinetic equations for the evolution of the probability distribution of two goods among a huge population of agents. The leading idea is to describe the trading of these goods by means of some fundamental rules in…
The evolution of grain structures in materials is a complex and multiscale process that determines the material's final properties. Understanding the dynamics of grain growth is a key factor for controlling this process. We propose a…
One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum…
Nonequilibrium thermodynamics formalism is proposed to derive the flux of grainy (bubbles-containing) matter, emerging in a nucleation growth process. Some power and non-power limits, due to the applied potential as well as owing to basic…
Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is…
A novel continuum theory of incoherent interfaces with triple junctions is applied to study three-dimensional coupled grain boundary (GB) motion in polycrystalline materials. The kinetic relations for grain dynamics, relative sliding and…
We investigate the non-linear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle…
A model for ionic and electronic grain boundary transport through thin films, scales or membranes with columnar grain structure is introduced. The grain structure is idealized as a lattice of identical hexagonal cells - a honeycomb pattern.…
We consider aligning self-propelled particles in two dimensions. Their motion is given by generalized Langevin equations and includes non-additive N-particle interactions. The qualitative behavior is as for the famous Vicsek model. We…
The kinetic theory of a self-gravitating system is considered in the framework of Bhatnager-Gross-Krook model. This approach offers a unique and tractable setup for studying the central, collision-dominated region of the system, as well as…
Most metallic and ceramic materials are comprised of a space-filling collection of crystalline grains separated by grain boundaries. While this grain structure has been studied for more than a century, there few rigorous results regarding…
In this work, we discuss kinetic descriptions of flocking models, of the so-called Cucker-Smale and Motsch-Tadmor types. These models are given by Vlasov-type equations where the interactions taken into account are only given long-range…
The goal of the present paper is to explore the long-time behavior of the growth-fragmentation equation formulated in the case of equal mitosis and variability in growth rate, under fairly general assumptions on the coefficients. The first…
We introduce a deductive statistical mechanics approach for granular materials which is formally built from few realistic physical assumptions. The main finding is an universal behavior for the distribution of the density fluctuations. Such…