相关论文: Nucleation and growth of lattice crystals
The behavior of a surface energy $\mathcal F(E,u)$, where $E$ is a set of finite perimeter and $u\in L^1(\partial^* E, \mathbb R_+)$ is studied. These energies have been recently considered in the context of materials science to derive a…
Aluminum alloys, the most widely utilized lightweight structural materials, predominantly depend on coherent complex-structured nano-plates to enhance their mechanical properties. Despite several decades of research, the atomic-scale…
We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…
The structure of the light proton and neutron rich nuclei is studied in a microscopic multicluster model using the stochastic variational method. This approach enables us to describe the weakly bound nature of these nuclei in a consistent…
We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the…
Control of the crystallization process is central to developing novel materials with atomic precision to meet the demands of electronic and quantum technology applications. Semiconductor nanowires grown by the vapor-liquid-solid process are…
We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…
We have generalized our ``unified'' model of evolutionary ecology by taking into account the possible movements of the organisms from one ``patch'' to another within the same eco-system. We model the spatial extension of the eco-system…
This paper describes a lattice version of the Skyrme model in 2+1 and 3+1 dimensions. The discrete model is derived from a consistent discretization of the radial continuum problem. Subsequently, the existence and stability of the skyrmion…
Mass parameters for collective variables of a dinuclear system and strongly deformed mononucleus are microscopically formulated with the linear response theory making use of the width of single particle states and the…
The growth of crystals confined in porous or cellular materials is ubiquitous in Nature and industry. Confinement affects the formation of biominerals in living organisms, of minerals in the Earth's crust and of salt crystals damaging…
We consider a Markovian growth process on a partially ordered set $\Lambda$, equivalent to last passage percolation (LPP) with independent (not necessarily identical) exponentially distributed weights on the elements of $\Lambda$. Such a…
The dynamics of a system of particles subject to a 4th order potential field modeling the space-time evolution of wedge disclinations is studied, focusing on finite systems of disclinations within a circular domain. Existence theorems for…
We study a d-dimensional lattice model of diffusing coalescing massive particles, with two parameters controlling deposition and evaporation of monomers. The unique stationary distribution for the system exhibits a phase transition in all…
The goal of this work is to analyze a model for the rate-independent evolution of sets with finite perimeter. The evolution of the admissible sets is driven by that of a given time-dependent set, which has to include the admissible sets and…
I is argued here that (at least light) nuclei may reside in a sweet spot: bound weakly enough to be insensitive to the details of the interaction, but dense enough to be insensitive to the exact values of the large two-body scattering…
We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous nonequilibrium phase transition from a condensed phase, in which a single `flock'…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter…