A systems-based approach to multiscale computation: Equation-free detection of coarse-grained bifurcations

Siettos, CI; Rico-Martinez, R; Kevrekidis, IG

dc.contributor.author	Siettos, CI	en
dc.contributor.author	Rico-Martinez, R	en
dc.contributor.author	Kevrekidis, IG	en
dc.date.accessioned	2014-03-01T01:23:31Z
dc.date.available	2014-03-01T01:23:31Z
dc.date.issued	2006	en
dc.identifier.issn	0098-1354	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16997
dc.subject	Bifurcation	en
dc.subject	Equation-free	en
dc.subject	Multiscale	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Engineering, Chemical	en
dc.subject.other	Algorithms	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Catalysis	en
dc.subject.other	Computation theory	en
dc.subject.other	Computer simulation	en
dc.subject.other	Mathematical models	en
dc.subject.other	Reaction kinetics	en
dc.subject.other	Bifurcation algorithms	en
dc.subject.other	Coarse grained bifurcations	en
dc.subject.other	Computational experiments	en
dc.subject.other	Equation free detection	en
dc.subject.other	Large scale systems	en
dc.subject.other	Algorithms	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Catalysis	en
dc.subject.other	Computation theory	en
dc.subject.other	Computer simulation	en
dc.subject.other	Large scale systems	en
dc.subject.other	Mathematical models	en
dc.subject.other	Reaction kinetics	en
dc.title	A systems-based approach to multiscale computation: Equation-free detection of coarse-grained bifurcations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.compchemeng.2006.05.019	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.compchemeng.2006.05.019	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	We discuss certain basic features of the equation-free (EF) approach to modeling and computation for complex/multiscale systems. We focus on links between the equation-free approach and tools from systems and control theory (design of experiments, data analysis, estimation, identification and feedback). As our illustrative example, we choose a specific numerical task (the detection of stability boundaries in parameter space) for stochastic models of two simplified heterogeneous catalytic reaction mechanisms. In the equation-free framework the stochastic simulator is treated as an experiment (albeit a computational one). Short bursts of fine scale simulation (short computational experiments) are designed, executed, and their outputs processed and fed back to the process, in integrated protocols aimed at performing the particular coarse-grained task (the detection of a macroscopic instability). Two distinct approaches are presented; one is a direct translation of our previous protocol for adaptive detection of instabilities in laboratory experiments [Rico-Martinez, R., Krisher, K., Flatgen, G., Anderson, J. S., & Kevrekidis, I. G. (2003). Adaptive detection of instabilities: An experimental feasibility study. Physica D, 176, 1-18]; the second approach is motivated from numerical bifurcation algorithms for critical point detection. A comparison of the two approaches brings forth a key feature of equation-free computation: computational experiments can be easily initialized at will, in contrast to laboratory ones. (c) 2006 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Computers and Chemical Engineering	en
dc.identifier.doi	10.1016/j.compchemeng.2006.05.019	en
dc.identifier.isi	ISI:000240794000019	en
dc.identifier.volume	30	en
dc.identifier.issue	10-12	en
dc.identifier.spage	1632	en
dc.identifier.epage	1642	en