Related papers: A Mathematical Treatment to Determine Transient Gr…
In this paper, the effect on the ultrasonic attenuation of the grain size heterogeneity in polycrystals is analyzed. First, new analytical developments allowing the extension of the unified theory of Stanke and Kino to general grain size…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited…
The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for a Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can…
A model for diffusion-controlled spherical particle growth is presented and solved numerically, showing how, on cooling at sufficient rate from a given fraction solid, growth velocity first increases, and then decreases rapidly when solute…
We give a comprehensive rate equation description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j,…
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…
A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on…
We have studied the growth kinetics of isolated precipitates growing from a supersaturated matrix in 3-dimensions (3-D) using phase field models; we assume isotropic interfacial energy consider both constant and variable diffusivity. We…
Measurements of cell size dynamics have established the adder principle as a robust mechanism of cell size homeostasis. In this framework, cells add a nearly constant amount of size during each cell cycle, independent of their size at…
The paper develops one-parametric family of the sand-piles dealing with the grains' local losses on the fixed amount. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean height of the…
We review some recent coarse-graining and multi-scale methods, but also put forward some new ideas for addressing such issues. We find that, if one is guided by nonequilibrium statistical mechanics and thermodynamics, it is possible to…
We present a method to include the evolution of the grain size and grain opacity $\kappa_\mathrm{gr}$ in the equations describing the structure of protoplanetary atmospheres. The key assumption of this method is that a single grain size…
We present a new model of homogeneous aggregation that contains the essential physical ideas of the classical predecessors, the Becker-Doring and Lifshitz-Slyovoz models. These classical models, which give different predictions, are…
Grain growth simulation is crucial for predicting metallic material microstructure evolution during annealing and resulting final mechanical properties, but traditional partial differential equation-based methods are computationally…
In this work, we study the crystalline nuclei growth in glassy systems focusing primarily on the early stages of the process, at which the size of a growing nucleus is still comparable with the critical size. On the basis of molecular…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…