• Corpus ID: 235377335

# The Local Equilibrium State of a Crystal Surface Jump Process in the Rough Scaling Regime

@inproceedings{Katsevich2021TheLE,
title={The Local Equilibrium State of a Crystal Surface Jump Process in the Rough Scaling Regime},
author={Anya Katsevich},
year={2021}
}
We investigate the local equilibrium (LE) distribution of a crystal surface jump process as it approaches its hydrodynamic (continuum) limit in a nonstandard, “rough” scaling regime introduced by Marzuola and Weare. The rough scaling leads to a local equilibrium state whose structure is novel, to the best of our knowledge. The distinguishing characteristic of the new LE state is that the ensemble average of single lattice site observables do not vary smoothly across lattice sites. This raises…
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## References

SHOWING 1-10 OF 28 REFERENCES

### From local equilibrium to numerical PDE: Metropolis crystal surface dynamics in the rough scaling limit

This paper builds off of recent work in which we studied the local equilibrium (LE) distribution of a microscopic crystal surface jump process with Arrhenius transition rates, under the so-called

### Analysis of a fourth-order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates

• Mathematics
Pure and Applied Analysis
• 2021
We analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and long time dynamics

### Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects

• Mathematics
Nonlinearity
• 2020
We study a 4th order degenerate parabolic PDE model in one-dimension with a 2nd order correction modeling the evolution of a crystal surface under the influence of both thermal fluctuations and

### Hydrodynamic Limit for Lattice Gas Reversible under Bernoulli Measures

• Mathematics
• 1996
The hydrodynamic limit for the class of lattice gases that are reversible under the Bernoulli measures is studied by estimating the relative entropy of the microscopic state of actual system with

### Global existence and decay to equilibrium for some crystal surface models

• Mathematics
Discrete & Continuous Dynamical Systems - A
• 2019
In this paper we study the large time behavior of the solutions to the following nonlinear fourth-order equations $$\partial_t u=\Delta e^{-\Delta u},$$ $$\partial_t u=-u^2\Delta^2(u^3).$$ These

### Adatom mobility for the solid-on-solid model

• Physics
• 1995
The relaxation of a crystal surface through surface diffusion is studied within the solid-on-solid model. Two types of (conserved) dynamics are considered. ForArrhenius dynamics we show that the

### Relaxation of a family of broken-bond crystal-surface models.

• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2013
The continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solid-on-solid and discrete Gaussian models is studied, to derive several partial differential equation limits identified in previous studies.

### Existence Theorems for a Multidimensional Crystal Surface Model

• Mathematics
SIAM J. Math. Anal.
• 2016
Investigations reveal that the exponent in the equation can have a singular part in the sense of the Lebesgue decomposition theorem, and the exponential nonlinearity somehow “cancels” it out.

### Hydrodynamic Scaling Limit of Continuum Solid-On-Solid Model

A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the

### Motion by Mean Curvature from the Ginzburg-Landau Interface Model

• Mathematics
• 1997
Abstract: We consider the scalar field φt with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy . The potential V is