Gross-Pitaevskii vortex motion with critically scaled inhomogeneities

Matthias Kurzke; Jeremy L. Marzuola; Daniel Spirn

doi:10.1137/15M1049014

Gross-Pitaevskii vortex motion with critically scaled inhomogeneities

Matthias Kurzke, Jeremy L. Marzuola, Daniel Spirn

School of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i∂_tu = Δu + 1/ϵ² (ρ² ϵ (x) - |u|²). For a unique scaling regime |ρϵ(x) - 1| = O(log ϵ^-1), it is shown that vortices can interact both with the background perturbation and with each other. Results for associated parabolic and elliptic problems are discussed.

Original language	English (US)
Pages (from-to)	471-500
Number of pages	30
Journal	SIAM Journal on Mathematical Analysis
Volume	49
Issue number	1
DOIs	https://doi.org/10.1137/15M1049014
State	Published - 2017

Bibliographical note

Funding Information:
The work of the second author was supported in part by NSF applied math grant DMS-1312874 and NSF CAREER grant DMS-1352353. The work of the third author was supported in part by NSF CAREER grant DMS-0955687 and NSF grant DMS-1516565.

Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.

Keywords

Critical scaling
Gross-Pitaevskii
Vortices

Publisher link

10.1137/15M1049014

http://eprints.nottingham.ac.uk/40895/1/M104901.pdf

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abstract = "We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i∂tu = Δu + 1/ϵ2 (ρ2 ϵ (x) - |u|2). For a unique scaling regime |ρϵ(x) - 1| = O(log ϵ-1), it is shown that vortices can interact both with the background perturbation and with each other. Results for associated parabolic and elliptic problems are discussed.",

keywords = "Critical scaling, Gross-Pitaevskii, Vortices",

author = "Matthias Kurzke and Marzuola, {Jeremy L.} and Daniel Spirn",

note = "Funding Information: The work of the second author was supported in part by NSF applied math grant DMS-1312874 and NSF CAREER grant DMS-1352353. The work of the third author was supported in part by NSF CAREER grant DMS-0955687 and NSF grant DMS-1516565. Publisher Copyright: {\textcopyright} 2017 Society for Industrial and Applied Mathematics.",

year = "2017",

doi = "10.1137/15M1049014",

language = "English (US)",

volume = "49",

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journal = "SIAM Journal on Mathematical Analysis",

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TY - JOUR

T1 - Gross-Pitaevskii vortex motion with critically scaled inhomogeneities

AU - Kurzke, Matthias

AU - Marzuola, Jeremy L.

AU - Spirn, Daniel

N1 - Funding Information: The work of the second author was supported in part by NSF applied math grant DMS-1312874 and NSF CAREER grant DMS-1352353. The work of the third author was supported in part by NSF CAREER grant DMS-0955687 and NSF grant DMS-1516565. Publisher Copyright: © 2017 Society for Industrial and Applied Mathematics.

PY - 2017

Y1 - 2017

N2 - We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i∂tu = Δu + 1/ϵ2 (ρ2 ϵ (x) - |u|2). For a unique scaling regime |ρϵ(x) - 1| = O(log ϵ-1), it is shown that vortices can interact both with the background perturbation and with each other. Results for associated parabolic and elliptic problems are discussed.

AB - We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i∂tu = Δu + 1/ϵ2 (ρ2 ϵ (x) - |u|2). For a unique scaling regime |ρϵ(x) - 1| = O(log ϵ-1), it is shown that vortices can interact both with the background perturbation and with each other. Results for associated parabolic and elliptic problems are discussed.

KW - Critical scaling

KW - Gross-Pitaevskii

KW - Vortices

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U2 - 10.1137/15M1049014

DO - 10.1137/15M1049014

M3 - Article

AN - SCOPUS:85014504186

SN - 0036-1410

VL - 49

SP - 471

EP - 500

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

Gross-Pitaevskii vortex motion with critically scaled inhomogeneities

Abstract

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