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Computing Optimal Interfacial Structure of Modulated Phases

Part of: Statistical mechanics, structure of matter Equilibrium statistical mechanics

Published online by Cambridge University Press:  05 December 2016

Jie Xu ,
Chu Wang ,
An-Chang Shi  and
Pingwen Zhang
Jie Xu*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
Chu Wang*
Affiliation:
Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
An-Chang Shi*
Affiliation:
Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S4M1, Canada
Pingwen Zhang*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
*
*Corresponding author. Email addresses:rxj_2004@126.com (J. Xu), chuw@math.princeton.edu (C. Wang), shi@mcmaster.ca (A.-C. Shi), pzhang@pku.edu.cn (P. Zhang)
*Corresponding author. Email addresses:rxj_2004@126.com (J. Xu), chuw@math.princeton.edu (C. Wang), shi@mcmaster.ca (A.-C. Shi), pzhang@pku.edu.cn (P. Zhang)
*Corresponding author. Email addresses:rxj_2004@126.com (J. Xu), chuw@math.princeton.edu (C. Wang), shi@mcmaster.ca (A.-C. Shi), pzhang@pku.edu.cn (P. Zhang)
*Corresponding author. Email addresses:rxj_2004@126.com (J. Xu), chuw@math.princeton.edu (C. Wang), shi@mcmaster.ca (A.-C. Shi), pzhang@pku.edu.cn (P. Zhang)
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Abstract

We propose a general framework of computing interfacial structures between two modulated phases. Specifically we propose to use a computational box consisting of two half spaces, each occupied by a modulated phase with given position and orientation. The boundary conditions and basis functions are chosen to be commensurate with the bulk phases. We observe that the ordered nature of modulated structures stabilizes the interface, which enables us to obtain optimal interfacial structures by searching local minima of the free energy landscape. The framework is applied to the Landau-Brazovskii model to investigate interfaces between modulated phases with different relative positions and orientations. Several types of novel complex interfacial structures emerge from the calculations.

Keywords

Interfacemodulated phasemetastable statecompatibilityLandau-Brazovskii model

MSC classification

Secondary: 82B24: Interface problems; diffusion-limited aggregation 82-08: Computational methods
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 1 , January 2017 , pp. 1 - 15
Copyright
Copyright © Global-Science Press 2016 

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