Self-organization on Riemannian manifolds
| Autor: | Razvan C. Fetecau, Beril Zhang |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Self-organization Control and Optimization Applied Mathematics Hyperbolic space 010102 general mathematics Mathematical analysis FOS: Physical sciences Dynamical Systems (math.DS) 01 natural sciences Nonlinear Sciences - Adaptation and Self-Organizing Systems 010101 applied mathematics Set (abstract data type) Mathematics - Analysis of PDEs Interaction potential Mechanics of Materials FOS: Mathematics Geometry and Topology Mathematics - Dynamical Systems 0101 mathematics Convection–diffusion equation Constant (mathematics) Adaptation and Self-Organizing Systems (nlin.AO) Analysis of PDEs (math.AP) Rotation group SO |
| Zdroj: | Journal of Geometric Mechanics. 11:397-426 |
| ISSN: | 1941-4897 |
| DOI: | 10.3934/jgm.2019020 |
| Popis: | We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on the density, modelled via an interaction potential. We set up the model on general Riemannian manifolds and provide a framework for constructing interaction potentials which lead to equilibria that are constant on their supports. We consider such potentials for two specific cases (the two-dimensional sphere and the two-dimensional hyperbolic space) and investigate analytically and numerically the long-time behaviour and equilibrium solutions of the aggregation model on these manifolds. Equilibria obtained numerically with other interaction potentials are also presented. 30 pages, 8 figures |
| Databáze: | OpenAIRE |
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