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Nonlocal models with a finite range ...

Tian, Xiaochuan.

Nonlocal models with a finite range of nonlocal interactions.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Nonlocal models with a finite range of nonlocal interactions./
Author:	Tian, Xiaochuan.
Description:	1 online resource (221 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
Contained By:	Dissertation Abstracts International78-07B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369569308

Nonlocal models with a finite range of nonlocal interactions.
Tian, Xiaochuan.

Nonlocal models with a finite range of nonlocal interactions. - 1 online resource (221 pages)

Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Nonlocal phenomena are ubiquitous in nature. The nonlocal models investigated in this thesis use integration in replace of differentiation and provide alternatives to the classical partial differential equations. The nonlocal interaction kernels in the models are assumed to be as general as possible and usually involve finite range of nonlocal interactions. Such settings on one hand allow us to connect nonlocal models with the existing classical models through various asymptotic limits of the modeling parameter, and on the other hand enjoy practical significance especially for multiscale modeling and simulations.

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

Mode of access: World Wide Web

ISBN: 9781369569308Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Nonlocal models with a finite range of nonlocal interactions.
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020 $a 9781369569308
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035 $a (MiAaPQ)columbia:13753
035 $a AAI10256402
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Tian, Xiaochuan. $3 1180594
245 1 0 $a Nonlocal models with a finite range of nonlocal interactions.
264 0 $c 2017
300 $a 1 online resource (221 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: 78-07(E), Section: B.
500 $a Adviser: Qiang Du.
502 $a Thesis (Ph.D.) $c Columbia University $d 2017.
504 $a Includes bibliographical references
520 $a Nonlocal phenomena are ubiquitous in nature. The nonlocal models investigated in this thesis use integration in replace of differentiation and provide alternatives to the classical partial differential equations. The nonlocal interaction kernels in the models are assumed to be as general as possible and usually involve finite range of nonlocal interactions. Such settings on one hand allow us to connect nonlocal models with the existing classical models through various asymptotic limits of the modeling parameter, and on the other hand enjoy practical significance especially for multiscale modeling and simulations.
520 $a To make connections with classical models at the discrete level, the central theme of the numerical analysis for nonlocal models in this thesis concerns with numerical schemes that are robust under the changes of modeling parameters, with mathematical analysis provided as theoretical foundations. Together with extensive discussions of linear nonlocal diffusion and nonlocal mechanics models, we also touch upon other topics such as high order nonlocal models, nonlinear nonlocal fracture models and coupling of models characterized by different scales.
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
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Columbia University. $b Applied Mathematics. $3 1180595
773 0 $t Dissertation Abstracts International $g 78-07B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10256402 $z click for full text (PQDT)

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