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Generalised twists as elastic energy extremals on annuli, Squaternions and lifting twist loops to the spinor groups
journal contribution
posted on 2023-06-09, 08:40 authored by Mohammad Shahrokhi-Dehkordi, Ali TaheriAli TaheriLet X = {x ? Rn : a < |x| < b} be a generalized annulus and consider the Dirichlet energy functional F[u; X] = 1/2?x |?u(x)|²dx, over the space of admissible maps A?(X) = {u ? W¹,²(X, Rn) : det ?u =1 a.e. in X, u|?X = ?}, where ? is the identity map. In this paper we consider a class of maps referred to as generalized twists and examine them in connection with the Euler–Lagrange equation associated with F[·, X] on A?(X). The approach is novel and is based on lifting twist loops from SO(n) to its double cover Spin(n) and reformulating the equations accordingly. We restrict our attention to low dimensions and prove that for n = 4 the system admits infinitely many smooth solutions in the form of twists while for n = 3 this number sharply reduces to one. We discuss some qualitative features of these solutions in view of their remarkable explicit representation through the exponential map of Spin(n).
History
Publication status
- Published
File Version
- Published version
Journal
Analysis and ApplicationsISSN
0219-5305Publisher
World Scientific PublishingExternal DOI
Issue
2Volume
11Page range
124-150Department affiliated with
- Physics and Astronomy Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-11-07First Open Access (FOA) Date
2017-11-07First Compliant Deposit (FCD) Date
2017-11-06Usage metrics
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