A continuous approach to discrete ordering on S^2

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

We consider the classical problem to find optimal distributions of interacting particles on a sphere by solving an evolution problem for a particle density. The higher order surface partial differential equation is an approximation of a surface dynamic density functional theory. We motivate the approach phenomenologically and sketch a derivation of the model starting from an interatomic potential. Different numerical approaches are discussed to solve the evolution problem: (a) an implicit approach to describe the surface using a phase-field description, (b) a parametric finite element approach, and (c) a spectral method based on nonequispaced fast Fourier transforms on the sphere. Results for computed minimal energy configurations are discussed for various particle numbers and are compared with known rigorous asymptotic results. Furthermore extensions to other more complex and evolving surfaces are mentioned.

Details

OriginalspracheEnglisch
Seiten (von - bis)314-334
FachzeitschriftMultiscale Modeling and Simulation
Jahrgang9
Ausgabenummer1
PublikationsstatusVeröffentlicht - 17 Feb. 2011
Peer-Review-StatusJa

Externe IDs

Scopus 79955920215

Schlagworte

Forschungsprofillinien der TU Dresden

DFG-Fachsystematik nach Fachkollegium

Fächergruppen, Lehr- und Forschungsbereiche, Fachgebiete nach Destatis

Schlagwörter

  • ordering on curved surfaces, Thomson problem, dynamic density functional theory, phase-field crystal, PDE on surfaces

Bibliotheksschlagworte