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Issue ESAIM: PROC
Volume 1, 1996
Vortex flows an related numerical methods II
Page(s) 169 - 180
DOI 10.1051/proc:1996018

ESAIM: Proc., 1996, Vol. 1, pp. 169-180
DOI: 10.1051/proc:1996018

Vortex dynamics, combinatorics and statistics

Chjan C. Lim

Dept. of Mathematical Sciences RPI, Troy, NY 12180, USA


Abstract
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


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