| Issue |
ESAIM: Proc.
Volume 1, 1996
Vortex flows an related numerical methods II
|
|
|---|---|---|
| Page(s) | 169 - 180 | |
| DOI | https://doi.org/10.1051/proc:1996018 | |
| Published online | 15 August 2002 | |
Vortex dynamics, combinatorics and statistics
Dept. of Mathematical Sciences RPI, Troy, NY 12180, USA
This report represents an overview of the interconnections between the dynamics of large vortex systems, combinatorics, n-body problems and statistical mechanics. The combinatorial perturbation method for the 2D vortex problem is discussed; the essential combinatorial symplectic transformations to Jacobi-type variables which are based on a binary tree algorithm, is introduced and extended to the 3D vortex problem. Combinatorial and graph-theoretic results which are motivated by the computational needs of the vortex problem, are mentioned. They include new results on sign-nonsingular patterns and noneven digraphs. A simplified singular limit of the 3D Hamiltonian for vortex dynamics is derived and its basic properties discussed. The 2- and 3-body problems in this simple model is studied.
© EDP Sciences, ESAIM, 1996
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.