Geodesic
Vortex dynamics, combinatorics and statistics
Chjan C. Lim1
1 Dept. of Mathematical Sciences RPI, Troy, NY 12180, USA
ESAIM. Proceedings, Tome 1 (1996), pp. 169-180.

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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.
DOI : 10.1051/proc:1996018

Chjan C. Lim 1

1 Dept. of Mathematical Sciences RPI, Troy, NY 12180, USA 
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Chjan C. Lim. Vortex dynamics, combinatorics and statistics. ESAIM. Proceedings, Tome 1 (1996), pp. 169-180. doi : 10.1051/proc:1996018. http://geodesic.mathdoc.fr/articles/10.1051/proc:1996018/

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