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Parameterized locally invariant mani...

Sawant, Aarti.

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Parameterized locally invariant manifolds: A tool for multiscale modeling.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Parameterized locally invariant manifolds: A tool for multiscale modeling./
Author:	Sawant, Aarti.
Description:	113 p.
Notes:	Source: Dissertation Abstracts International, Volume: 66-10, Section: B, page: 5486.
Contained By:	Dissertation Abstracts International66-10B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3191612
ISBN:	9780542363252

Parameterized locally invariant manifolds: A tool for multiscale modeling.
Sawant, Aarti.

Parameterized locally invariant manifolds: A tool for multiscale modeling. - 113 p.

Source: Dissertation Abstracts International, Volume: 66-10, Section: B, page: 5486.

Thesis (Ph.D.)--Carnegie Mellon University, 2005.

In this thesis two methods for coarse graining in nonlinear ODE systems are demonstrated through analysis of model problems. The basic ideas of a method for model reduction and a method for non-asymptotic time-averaging are presented, using the idea of the Parameterized locally invariant manifolds. New approximation techniques for carrying out this methodology are developed. The work is divided in four categories based on the type of coarse-graining used: reduction of degrees of freedom, spatial averaging, time averaging and a combination of space and time averaging.

ISBN: 9780542363252Subjects--Topical Terms:

1018410
Applied Mechanics.

Parameterized locally invariant manifolds: A tool for multiscale modeling.
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020 $a 9780542363252
035 $a (UnM)AAI3191612
035 $a AAI3191612
040 $a UnM $c UnM
100 1 $a Sawant, Aarti. $3 1915816
245 1 0 $a Parameterized locally invariant manifolds: A tool for multiscale modeling.
300 $a 113 p.
500 $a Source: Dissertation Abstracts International, Volume: 66-10, Section: B, page: 5486.
500 $a Adviser: Amit Acharya.
502 $a Thesis (Ph.D.)--Carnegie Mellon University, 2005.
520 $a In this thesis two methods for coarse graining in nonlinear ODE systems are demonstrated through analysis of model problems. The basic ideas of a method for model reduction and a method for non-asymptotic time-averaging are presented, using the idea of the Parameterized locally invariant manifolds. New approximation techniques for carrying out this methodology are developed. The work is divided in four categories based on the type of coarse-graining used: reduction of degrees of freedom, spatial averaging, time averaging and a combination of space and time averaging.
520 $a Model problems showing complex dynamics are selected and various features of the PLIM method are elaborated. The quality and efficiency of the different coarse-graining approaches are evaluated. From the computational standpoint, it is shown that the method has the potential of serving as a subgrid modeling tool for problems in engineering.
520 $a The developed ideas are evaluated on the following model problems: Lorenz System, a 4D Hamiltonian System due to Hald, 1D Elastodynamics in a strongly heterogeneous medium, kinetics of a phase transforming material with wiggly energy due to Abeyaratne, Chu and James, 2D gradient system with wiggly energy due to Menon, and macroscopic stress-strain behavior of an atomic chain based on the Frenkel-Kontorova model.
590 $a School code: 0041.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Engineering, Materials Science. $3 1017759
690 $a 0346
690 $a 0794
710 2 0 $a Carnegie Mellon University. $3 1018096
773 0 $t Dissertation Abstracts International $g 66-10B.
790 1 0 $a Acharya, Amit, $e advisor
790 $a 0041
791 $a Ph.D.
792 $a 2005
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3191612