Vortex dynamics, combinatorics and statistics

Vortex Dynamics, Combinatorics and Statistics

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 sym-plectic transformations to Jacobi-type variables which are based on a binary tree algorithm, is introduced and extended to t...

Recent Advances in 2D and 2.5D Vortex statistics and dynamics

This review paper offers both an overview of the recent developments in vortex statistics, and a detailed critical review of some of the advances as well as open problems in the area. A fruitful new direction in vortex dynamics concerns vortical systems with very large numbers of vortices in which statistical methods play a pivotal role. After a review of some of the older equilibrium statistic...

Combinatorics, Words and Symbolic Dynamics

Universal statistics of vortex lines.

We study the vortex lines that are a feature of many random or disordered three-dimensional systems. These show universal statistical properties on long length scales, and geometrical phase transitions analogous to percolation transitions but in distinct universality classes. The field theories for these problems have not previously been identified, so that while many numerical studies have bee...

Current and vortex statistics in microwave billiards.

Using the one-to-one correspondence between the Poynting vector in a microwave billiard and the probability current density in the corresponding quantum system, probability densities and currents were studied in a microwave billiard with a ferrite insert as well as in an open billiard. Distribution functions were obtained for probability densities, currents, and vorticities. In addition, the vo...