eprintid: 9691
rev_number: 9
eprint_status: archive
userid: 1
dir: disk0/00/00/96/91
datestamp: 2009-07-30 15:29:10
lastmod: 2015-04-24 23:21:52
status_changed: 2012-08-14 15:30:22
type: preprint
metadata_visibility: show
creators_name: Lebiedz, Dirk
creators_name: Reinhardt, Volkmar
creators_name: Siehr, Jochen
title: Minimal Curvature Trajectories: Riemannian Geometry Concepts for Model Reduction in Chemical Kinetics
ispublished: pub
subjects: 510
divisions: 708000
keywords: langsame invariante Mannigfaltigkeitmodel reduction , slow invariant manifold , chemical kinetics , nonlinear optimization , Riemannian geometry
cterms_swd: Ordnungsreduktion
cterms_swd: Reaktionskinetik
cterms_swd: Nichtlineare Optimierung
cterms_swd: Riemannsche Geometrie
cterms_swd: Krümmung
abstract: In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes. The aim is to approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold. We present a novel method for computing approximations of such manifolds using trajectory-based optimization. We discuss Riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics. The optimization criteria correspond to a suitable mathematical formulation of "minimal relaxation" of chemical forces along reaction trajectories under given constraints. We present various geometrically motivated criteria and the results of their application to three test case reaction mechanisms serving as examples. We demonstrate that accurate numerical approximations of slow invariant manifolds can be obtained.
abstract_translated_lang: eng
class_scheme: pacs
class_labels: 37M99, 37N40, 92E20, 80A30
date: 2009
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00009691
ppn_swb: 164821147X
own_urn: urn:nbn:de:bsz:16-opus-96911
language: eng
bibsort: LEBIEDZDIRMINIMALCUR2009
full_text_status: public
citation:   Lebiedz, Dirk ; Reinhardt, Volkmar ; Siehr, Jochen  (2009) Minimal Curvature Trajectories: Riemannian Geometry Concepts for Model Reduction in Chemical Kinetics.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/9691/1/Lebiedz2009.pdf