Lumping analysis for the prediction of long-time dynamics: From monomolecular reaction systems to inherent structure dynamics of glassy materials

Lempesis, N; Tsalikis, DG; Boulougouris, GC; Theodorou, DN

dc.contributor.author	Lempesis, N	en
dc.contributor.author	Tsalikis, DG	en
dc.contributor.author	Boulougouris, GC	en
dc.contributor.author	Theodorou, DN	en
dc.date.accessioned	2014-03-01T02:02:24Z
dc.date.available	2014-03-01T02:02:24Z
dc.date.issued	2011	en
dc.identifier.issn	00219606	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29316
dc.subject.other	Computational costs	en
dc.subject.other	Discrete dynamical systems	en
dc.subject.other	First-order kinetic reaction	en
dc.subject.other	Glassy materials	en
dc.subject.other	Global optimum	en
dc.subject.other	High-dimensional	en
dc.subject.other	Inherent structures	en
dc.subject.other	Lennard-Jones mixtures	en
dc.subject.other	Limiting equilibrium	en
dc.subject.other	Local minimums	en
dc.subject.other	Long-time dynamics	en
dc.subject.other	Lumped system	en
dc.subject.other	Master equations	en
dc.subject.other	Molecular dynamics trajectories	en
dc.subject.other	Monomolecular reactions	en
dc.subject.other	Monte Carlo Simulation	en
dc.subject.other	Original systems	en
dc.subject.other	Plot analysis	en
dc.subject.other	Reduction process	en
dc.subject.other	Singular values	en
dc.subject.other	Slow dynamics	en
dc.subject.other	Algorithms	en
dc.subject.other	Computer simulation	en
dc.subject.other	Dynamical systems	en
dc.subject.other	Molecular dynamics	en
dc.subject.other	Monte Carlo methods	en
dc.subject.other	Probability distributions	en
dc.subject.other	Rate constants	en
dc.subject.other	Reaction kinetics	en
dc.subject.other	Dynamics	en
dc.title	Lumping analysis for the prediction of long-time dynamics: From monomolecular reaction systems to inherent structure dynamics of glassy materials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1063/1.3663207	en
heal.identifier.secondary	http://dx.doi.org/10.1063/1.3663207	en
heal.identifier.secondary	204507	en
heal.publicationDate	2011	en
heal.abstract	In this work we develop, test, and implement a methodology that is able to perform, in an automated manner, lumping of a high-dimensional, discrete dynamical system onto a lower-dimensional space. Our aim is to develop an algorithm which, without any assumption about the nature of the systems slow dynamics, is able to reproduce accurately the long-time dynamics with minimal loss of information. Both the original and the lumped systems conform to master equations, related via the lumping analysis introduced by Wei and Kuo Ind. Eng. Chem. Fundam. 8, 114 (1969), and have the same limiting equilibrium probability distribution. The proposed method can be used in a variety of processes that can be modeled via a first order kinetic reaction scheme. Lumping affords great savings in the computational cost and reveals the characteristic times governing the slow dynamics of the system. Our goal is to approach the best lumping scheme with respect to three criteria, in order for the lumped system to be able to fully describe the long-time dynamics of the original system. The criteria used are: (a) the lumping error arising from the reduction process; (b) a measure of the magnitude of singular values associated with long-time evolution of the lumped system; and (c) the size of the lumped system. The search for the optimum lumping proceeds via Monte Carlo simulation based on the Wang-Landau scheme, which enables us to overcome entrapment in local minima in the above criteria and therefore increases the probability of encountering the global optimum. The developed algorithm is implemented to reproduce the long-time dynamics of a glassy binary Lennard-Jones mixture based on the idea of inherent structures, where the rate constants for transitions between inherent structures have been evaluated via hazard plot analysis of a properly designed ensemble of molecular dynamics trajectories. © 2011 American Institute of Physics.	en
heal.journalName	Journal of Chemical Physics	en
dc.identifier.doi	10.1063/1.3663207	en
dc.identifier.volume	135	en
dc.identifier.issue	20	en