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Development and Analysis of Computat...

ProQuest Information and Learning Co.

Development and Analysis of Computationally Efficient Methods for Analyzing Surface Effects.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Development and Analysis of Computationally Efficient Methods for Analyzing Surface Effects./
Author:	Binder, Andrew J.
Description:	1 online resource (84 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369680089

Development and Analysis of Computationally Efficient Methods for Analyzing Surface Effects.
Binder, Andrew J.

Development and Analysis of Computationally Efficient Methods for Analyzing Surface Effects. - 1 online resource (84 pages)

Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.

Thesis (Ph.D.)--University of Minnesota, 2017.

Includes bibliographical references

Experiments have shown that materials at the nanoscale exhibit new material prop- erties compared to their macro-counterparts as a result of surface effects. We rigorously examine an atomistic model that exhibits surface effects and estimate the rate of decay of this influence. Despite the highly localized nature of surface effects, the regular Cauchy-Born method is shown to be incapable of capturing the surface physics in these systems. Two methods that seek to accurately model the influence of surfaces in a molecular statics problem are examined.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369680089Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Development and Analysis of Computationally Efficient Methods for Analyzing Surface Effects.
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035 $a AAI10256577
040 $a MiAaPQ $b eng $c MiAaPQ
100 1 $a Binder, Andrew J. $3 1187167
245 1 0 $a Development and Analysis of Computationally Efficient Methods for Analyzing Surface Effects.
264 0 $c 2017
300 $a 1 online resource (84 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
500 $a Advisers: Mitchell Luskin; Daniel Spirn.
502 $a Thesis (Ph.D.)--University of Minnesota, 2017.
504 $a Includes bibliographical references
520 $a Experiments have shown that materials at the nanoscale exhibit new material prop- erties compared to their macro-counterparts as a result of surface effects. We rigorously examine an atomistic model that exhibits surface effects and estimate the rate of decay of this influence. Despite the highly localized nature of surface effects, the regular Cauchy-Born method is shown to be incapable of capturing the surface physics in these systems. Two methods that seek to accurately model the influence of surfaces in a molecular statics problem are examined.
520 $a First, the surface Cauchy-Born method is examined. An asymptotic analysis is performed to investigate the behavior of this method, and it is shown that the method does represent an improvement over the regular Cauchy-Born method. However, it does not fully capture the surface behavior. Next, a novel predictor-corrector method is introduced to better capture these effects. Using the regular Cauchy-Born solution as a predictor for material behavior, the solution is corrected over a small boundary layer at the surface of a 1D material. The decomposition of the approximation into a bulk and surface component is justified in the analysis, and the convergence of the approximation to the atomistic solution is shown. The analysis for both methods is then verified numerically.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Materials science. $3 557839
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0794
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Minnesota. $b Mathematics. $3 1180493
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10256577 $z click for full text (PQDT)

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