國立虎尾科技大學 |

Continuum Limit and Synchronization Conditions for Coupled Oscillators on Lattices.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Continuum Limit and Synchronization Conditions for Coupled Oscillators on Lattices./
Author:	Wu, Tianqi.
Description:	1 online resource (56 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 80-10, Section: B.
Contained By:	Dissertations Abstracts International80-10B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781392004623

Continuum Limit and Synchronization Conditions for Coupled Oscillators on Lattices.
Wu, Tianqi.

Continuum Limit and Synchronization Conditions for Coupled Oscillators on Lattices. - 1 online resource (56 pages)

Source: Dissertations Abstracts International, Volume: 80-10, Section: B.

Thesis (Ph.D.)--New York University, 2019.

Includes bibliographical references

Kuramoto oscillators coupled through a graph provide one of the most influential models for the study of collective synchronizations. We propose the first sufficient synchronization conditions for lattice models. This sufficient condition is optimal as an L∞ synchronization condition. We also propose a novel continuum limit of the Kuramoto oscillators on lattices, by viewing the lattice as a discretization of the space. In the continuous model we have an analogous synchronization condition. To prove the continuous (discrete) synchronization conditions, we show the existence of solutions to some (discrete) elliptic PDE of divergence form. The two main ingredients in the proof are variational methods and gradient estimates for (discrete) elliptic PDE's.

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

Mode of access: World Wide Web

ISBN: 9781392004623Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Continuous synchronizationIndex Terms--Genre/Form:

554714
Electronic books.

Continuum Limit and Synchronization Conditions for Coupled Oscillators on Lattices.
LDR:02146ntm a22003737 4500 001 1144191
005 20240531083754.5
006 m o d
007 cr mn ---uuuuu
008 250605s2019 xx obm 000 0 eng d
020 $a 9781392004623
035 $a (MiAaPQ)AAI13421111
035 $a (MiAaPQ)nyu:13458
035 $a AAI13421111
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Wu, Tianqi. $3 1469135
245 1 0 $a Continuum Limit and Synchronization Conditions for Coupled Oscillators on Lattices.
264 0 $c 2019
300 $a 1 online resource (56 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: Dissertations Abstracts International, Volume: 80-10, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Young, Lai-Sang.
502 $a Thesis (Ph.D.)--New York University, 2019.
504 $a Includes bibliographical references
520 $a Kuramoto oscillators coupled through a graph provide one of the most influential models for the study of collective synchronizations. We propose the first sufficient synchronization conditions for lattice models. This sufficient condition is optimal as an L∞ synchronization condition. We also propose a novel continuum limit of the Kuramoto oscillators on lattices, by viewing the lattice as a discretization of the space. In the continuous model we have an analogous synchronization condition. To prove the continuous (discrete) synchronization conditions, we show the existence of solutions to some (discrete) elliptic PDE of divergence form. The two main ingredients in the proof are variational methods and gradient estimates for (discrete) elliptic PDE's.
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
653 $a Continuous synchronization
653 $a Discretization of the space
653 $a Kuramoto oscillators
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 New York University. $b Mathematics. $3 1180487
773 0 $t Dissertations Abstracts International $g 80-10B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13421111 $z click for full text (PQDT)