Self-organized Hydrodynamics in an Annular Domain: Modal Analysis and Nonlinear Effects
Mathematical Physics
2014-07-01 v1 math.MP
Abstract
The Self-Organized Hydrodynamics model of collective behavior is studied on an annular domain. A modal analysis of the linearized model around a perfectly polarized steady-state is conducted. It shows that the model has only pure imaginary modes in countable number and is hence stable. Numerical computations of the low-order modes are provided. The fully non-linear model is numerically solved and nonlinear mode-coupling is then analyzed. Finally, the efficiency of the modal decomposition to analyze the complex features of the nonlinear model is demonstrated.
Cite
@article{arxiv.1406.7852,
title = {Self-organized Hydrodynamics in an Annular Domain: Modal Analysis and Nonlinear Effects},
author = {Pierre Degond and Hui Yu},
journal= {arXiv preprint arXiv:1406.7852},
year = {2014}
}