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Application of the string method to compute minimum energy paths for a chain of bi‐stable elements using the finite element method and molecular dynamics
Author(s) -
Ulz Manfred
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610267
Subject(s) - maxima and minima , string (physics) , chain (unit) , finite element method , computation , energy (signal processing) , simple (philosophy) , phase transition , molecular dynamics , statistical physics , path (computing) , regular polygon , potential energy , energy landscape , scale (ratio) , computer science , physics , mathematics , algorithm , mathematical analysis , classical mechanics , geometry , theoretical physics , thermodynamics , quantum mechanics , philosophy , epistemology , programming language
Activated processes are frequently found in solid state mechanics. The energy landscape of such processes show a non‐convex behaviour, and therefore the computation of energy barriers between two stable minima is of importance. Such barriers are revealed by computing minimum energy paths. The string method is a simple and efficient algorithm to move curves over an energy landscape and to identify minimum energy paths. A hierarchical two‐scale model recently introduced to the literature (molecular dynamics coupled with the finite element method) is used in this paper to investigate the string method in a model phase transition in a copper single crystal. To do so, bi‐stable elements are constructed and the energetic behaviour of a two‐elements chain is investigated. We identify successfully the minimum energy path between two local stable minima of the chain and demonstrate thereby the performance of the string method applied to a complex multiscale model. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)