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The Wave Kinetic Theory of Three Wave and Four Wave Models.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	The Wave Kinetic Theory of Three Wave and Four Wave Models./
Author:	Ma, Xiao.
Description:	1 online resource (233 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
Contained By:	Dissertations Abstracts International84-12B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798379718060

The Wave Kinetic Theory of Three Wave and Four Wave Models.
Ma, Xiao.

The Wave Kinetic Theory of Three Wave and Four Wave Models. - 1 online resource (233 pages)

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

Thesis (Ph.D.)--Princeton University, 2023.

Includes bibliographical references

In this thesis, we introduce new techniques for studying the random series expansion of dispersive PDEs. We take a quadratic KdV type and a cubic Klein-Gordon type equation as examples to demonstrate the different techniques in three wave and four wave models. For three wave models, we introduce a counting argument to handle the degeneracy problems of the resonance surface and the loss of derivative problem. For four wave models, we introduce a novel renormalization argument and prove a renormalized Wick theorem. We provide a heuristic argument that this renormalization is able to remove all bad terms from the L2 mass term, combining with an almost cancellation identity of the regular pairing and the Deng-Hani's Feynman diagram analysis.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798379718060Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Feynman diagramIndex Terms--Genre/Form:

554714
Electronic books.

The Wave Kinetic Theory of Three Wave and Four Wave Models.
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245 1 4 $a The Wave Kinetic Theory of Three Wave and Four Wave Models.
264 0 $c 2023
300 $a 1 online resource (233 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
500 $a Advisor: Ionescu, Alexandru.
502 $a Thesis (Ph.D.)--Princeton University, 2023.
504 $a Includes bibliographical references
520 $a In this thesis, we introduce new techniques for studying the random series expansion of dispersive PDEs. We take a quadratic KdV type and a cubic Klein-Gordon type equation as examples to demonstrate the different techniques in three wave and four wave models. For three wave models, we introduce a counting argument to handle the degeneracy problems of the resonance surface and the loss of derivative problem. For four wave models, we introduce a novel renormalization argument and prove a renormalized Wick theorem. We provide a heuristic argument that this renormalization is able to remove all bad terms from the L2 mass term, combining with an almost cancellation identity of the regular pairing and the Deng-Hani's Feynman diagram analysis.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Statistical physics. $3 528048
650 4 $a Applied mathematics. $3 1069907
653 $a Feynman diagram
653 $a Wave turbulence
653 $a Four wave models
653 $a Wave kinetic theory
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0217
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Princeton University. $b Mathematics. $3 1180706
773 0 $t Dissertations Abstracts International $g 84-12B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30487908 $z click for full text (PQDT)