Microscopic patterns in the 2D phase-field-crystal model

被引：2

作者：

Martine-La Boissoniere, Gabriel ^{[1
]}

Choksi, Rustum ^{[1
]}

Lessard, Jean-Philippe ^{[1
]}

机构：

[1] McGill Univ, Dept Math & Stat, Montreal, PQ, Canada

来源：

NONLINEARITY | 2022年 / 35卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

phase field crystal; rigorously supported numerics; radial polynomial; grain boundary; polycrystalline materials; PARTIAL-DIFFERENTIAL-EQUATIONS; COMPUTER-ASSISTED PROOFS; RIGOROUS NUMERICS; DYNAMICS; CONTINUATION;

D O I：

10.1088/1361-6544/ac4d91

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using the recently developed theory of rigorously validated numerics, we address the phase-field-crystal model at the microscopic (atomistic) level. We show the existence of critical points and local minimizers associated with 'classical' candidates, grain boundaries, and localized patterns. We further address the dynamical relationships between the observed patterns for fixed parameters and across parameter space, then formulate several conjectures on the dynamical connections (or orbits) between steady states.

引用

页码：1500 / 1520

页数：21

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