Stability and convergence of the string method for computing minimum energy paths∗

Brian Van Koten; Mitchell Luskin

doi:10.1137/18M1201032

Stability and convergence of the string method for computing minimum energy paths^∗

Brian Van Koten, Mitchell Luskin

School of Mathematics

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

3 Scopus citations

Abstract

We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden [J. Chem. Phys., 126 (2007), 164103] to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.

Original language	English (US)
Pages (from-to)	873-898
Number of pages	26
Journal	Multiscale Modeling and Simulation
Volume	17
Issue number	2
DOIs	https://doi.org/10.1137/18M1201032
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics

Keywords

Convergence
Minimum energy path
Stability
String method

Publisher link

10.1137/18M1201032

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Cite this

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abstract = "We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden [J. Chem. Phys., 126 (2007), 164103] to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.",

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AU - Luskin, Mitchell

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AB - We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden [J. Chem. Phys., 126 (2007), 164103] to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.

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KW - Stability

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