| Comment on "Identification of low order manifolds: validating the algorithm of Maas and Pope" [Chaos 9, 108-123 (1999)]. | |
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MedLine Citation:
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PMID: 17199405 Owner: NLM Status: PubMed-not-MEDLINE |
Abstract/OtherAbstract:
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It is claimed by Rhodes, Morari, and Wiggins [Chaos 9, 108-123 (1999)] that the projection algorithm of Maas and Pope [Combust. Flame 88, 239-264 (1992)] identifies the slow invariant manifold of a system of ordinary differential equations with time-scale separation. A transformation to Fenichel normal form serves as a tool to prove this statement. Furthermore, Rhodes, Morari, and Wiggins [Chaos 9, 108-123 (1999)] conjectured that away from a slow manifold, the criterion of Maas and Pope will never be fulfilled. We present two examples that refute the assertions of Rhodes, Morari, and Wiggins. In the first example, the algorithm of Maas and Pope leads to a manifold that is not invariant but close to a slow invariant manifold. The claim of Rhodes, Morari, and Wiggins that the Maas and Pope projection algorithm is invariant under a coordinate transformation to Fenichel normal form is shown to be not correct in this case. In the second example, the projection algorithm of Maas and Pope leads to a manifold that lies in a region where no slow manifold exists at all. This rejects the conjecture of Rhodes, Morari, and Wiggins mentioned above. |
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Authors:
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Dietrich Flockerzi; Wolfram Heineken |
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Publication Detail:
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Type: Journal Article |
Journal Detail:
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Title: Chaos (Woodbury, N.Y.) Volume: 16 ISSN: 1054-1500 ISO Abbreviation: Chaos Publication Date: 2006 Dec |
Date Detail:
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Created Date: 2007-01-03 Completed Date: 2007-03-27 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 100971574 Medline TA: Chaos Country: United States |
Other Details:
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Languages: eng Pagination: 048101; author reply 048102 Citation Subset: - |
Affiliation:
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Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, D-39106 Magdeburg, Germany. |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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