Statistical topology of perturbed two-dimensional lattices

Hannes Leipold; Emanuel A. Lazar; Kenneth A. Brakke; David J. Srolovitz

doi:10.1088/1742-5468/2016/04/043103

Statistical topology of perturbed two-dimensional lattices

Hannes Leipold, Emanuel A. Lazar, Kenneth A. Brakke, David J. Srolovitz

Research output: Contribution to journal › Article › peer-review

Abstract

The Voronoi cell of any atom in a lattice is identical. If atoms are perturbed from their lattice coordinates, then the topologies of the Voronoi cells of the atoms will change. We consider the distribution of Voronoi cell topologies in two-dimensional perturbed systems. These systems can be thought of as simple models of finite-temperature crystals. We give analytical results for the distribution of Voronoi topologies of points in two-dimensional Bravais lattices under infinitesimal perturbations and present a discussion with numerical results for finite perturbations.

Original language	English
Article number	043103
Journal	Journal of Statistical Mechanics: Theory and Experiment
Volume	2016
Issue number	4
DOIs	https://doi.org/10.1088/1742-5468/2016/04/043103
State	Published - 13 Apr 2016
Externally published	Yes

Keywords

exact results
networks
random graphs
random/ordered microstructures (theory)
stochastic processes (theory)

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1088/1742-5468/2016/04/043103

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title = "Statistical topology of perturbed two-dimensional lattices",

abstract = "The Voronoi cell of any atom in a lattice is identical. If atoms are perturbed from their lattice coordinates, then the topologies of the Voronoi cells of the atoms will change. We consider the distribution of Voronoi cell topologies in two-dimensional perturbed systems. These systems can be thought of as simple models of finite-temperature crystals. We give analytical results for the distribution of Voronoi topologies of points in two-dimensional Bravais lattices under infinitesimal perturbations and present a discussion with numerical results for finite perturbations.",

keywords = "exact results, networks, random graphs, random/ordered microstructures (theory), stochastic processes (theory)",

author = "Hannes Leipold and Lazar, {Emanuel A.} and Brakke, {Kenneth A.} and Srolovitz, {David J.}",

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T1 - Statistical topology of perturbed two-dimensional lattices

AU - Leipold, Hannes

AU - Lazar, Emanuel A.

AU - Brakke, Kenneth A.

AU - Srolovitz, David J.

PY - 2016/4/13

Y1 - 2016/4/13

N2 - The Voronoi cell of any atom in a lattice is identical. If atoms are perturbed from their lattice coordinates, then the topologies of the Voronoi cells of the atoms will change. We consider the distribution of Voronoi cell topologies in two-dimensional perturbed systems. These systems can be thought of as simple models of finite-temperature crystals. We give analytical results for the distribution of Voronoi topologies of points in two-dimensional Bravais lattices under infinitesimal perturbations and present a discussion with numerical results for finite perturbations.

AB - The Voronoi cell of any atom in a lattice is identical. If atoms are perturbed from their lattice coordinates, then the topologies of the Voronoi cells of the atoms will change. We consider the distribution of Voronoi cell topologies in two-dimensional perturbed systems. These systems can be thought of as simple models of finite-temperature crystals. We give analytical results for the distribution of Voronoi topologies of points in two-dimensional Bravais lattices under infinitesimal perturbations and present a discussion with numerical results for finite perturbations.

KW - exact results

KW - networks

KW - random graphs

KW - random/ordered microstructures (theory)

KW - stochastic processes (theory)

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U2 - 10.1088/1742-5468/2016/04/043103

DO - 10.1088/1742-5468/2016/04/043103

M3 - مقالة

SN - 1742-5468

VL - 2016

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 4

M1 - 043103

ER -

Statistical topology of perturbed two-dimensional lattices

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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