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Condition estimates for numerical co...

North Carolina State University.

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Condition estimates for numerical continuation with applications to atomic and molecular fluids.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Condition estimates for numerical continuation with applications to atomic and molecular fluids./
Author:	Dickson, Kelly Irene.
Description:	112 p.
Notes:	Adviser: C. T. Kelley.
Contained By:	Dissertation Abstracts International69-09B.
Subject:	Chemistry, General. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3329237
ISBN:	9780549820772

Condition estimates for numerical continuation with applications to atomic and molecular fluids.
Dickson, Kelly Irene.

Condition estimates for numerical continuation with applications to atomic and molecular fluids. - 112 p.

Adviser: C. T. Kelley.

Thesis (Ph.D.)--North Carolina State University, 2008.

Numerical continuation is the process of solving nonlinear equations of the form G(u, lambda) = 0 for various parameter values, lambda. We discuss established numerical continuation techniques for solution paths of G(u, lambda) = 0 containing regular points and simple folds. Pseudo-arclength continuation is a widely used technique that no longer solves G( u, lambda) = 0 directly, but solves a newly parameterized version F(u(s), lambda(s)) = 0 where s is arclength. We present a new characterization for certain classes of points that leads to an upper bound on ||( F')-1||. This bound is needed to meaningfully quantify the convergence of Newton's method in the context of pseudo-arclength continuation.

ISBN: 9780549820772Subjects--Topical Terms:

1021807
Chemistry, General.

Condition estimates for numerical continuation with applications to atomic and molecular fluids.
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020 $a 9780549820772
035 $a (UMI)AAI3329237
035 $a AAI3329237
040 $a UMI $c UMI
100 1 $a Dickson, Kelly Irene. $3 1064488
245 1 0 $a Condition estimates for numerical continuation with applications to atomic and molecular fluids.
300 $a 112 p.
500 $a Adviser: C. T. Kelley.
500 $a Source: Dissertation Abstracts International, Volume: 69-09, Section: B, page: 5443.
502 $a Thesis (Ph.D.)--North Carolina State University, 2008.
520 $a Numerical continuation is the process of solving nonlinear equations of the form G(u, lambda) = 0 for various parameter values, lambda. We discuss established numerical continuation techniques for solution paths of G(u, lambda) = 0 containing regular points and simple folds. Pseudo-arclength continuation is a widely used technique that no longer solves G( u, lambda) = 0 directly, but solves a newly parameterized version F(u(s), lambda(s)) = 0 where s is arclength. We present a new characterization for certain classes of points that leads to an upper bound on ||( F')-1||. This bound is needed to meaningfully quantify the convergence of Newton's method in the context of pseudo-arclength continuation.
520 $a In particle fluids, it is important to accurately predict conditions under which the structure and thermodynamics of a fluid change. Of particular interest are phase transitions, for instance, when water turns from liquid to vapor as a function of temperature. Such information can often be obtained through rigorous and accurate continuation studies, yet is historically burdensome to produce computationally. To this end, we present new integral equation theory that model atomic and molecular fluids developed by the Institute of Molecular Design at the University of Houston. We show cases for which this new theory results in more accurate fluid structure and thermodynamics than previously reported in the literature. We discuss the numerical continuation problems of interest for both atomic and molecular fluids and how to implement them using this new theory and software developed at Sandia National Laboratories. Employing these theoretical and computational tools, we provide evidence for the potential to uncover new chemical and physical properties of fluids in an accurate and efficient way.
590 $a School code: 0155.
650 4 $a Chemistry, General. $3 1021807
650 4 $a Mathematics. $3 515831
690 $a 0405
690 $a 0485
710 2 0 $a North Carolina State University. $3 1018772
773 0 $t Dissertation Abstracts International $g 69-09B.
790 $a 0155
790 1 0 $a Kelley, C. T., $e advisor
791 $a Ph.D.
792 $a 2008
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3329237