The small-scale structure of the ow produced by vortex methods is discussed, and contrasted with the small-scale structure produced by grid methods. Particular attention is paid to the proliferation of vortex hairpins in three dimensions; its origin is analyzed, a statistical description is given, and methods for harmlessly deleting unneeded hairpins are suggested. These methods involve renorma...

The model under consideration is a two-dimensional two-component plasma, stable against collapse for the dimensionless coupling constant β < 2. The combination of a technique of renormalized Mayer expansion with the mapping onto the sine-Gordon theory provides the full thermodynamics of the plasma in the whole stability range of β. The explicit forms of the density-fugacity relationship and of ...

This paper presents a study of the grand canonical Bose-Einstein (BE) statistics for finite number particles in an arbitrary quantum system. The thermodynamical quantities that identify BE condensation---namely, fraction ground state and specific heat---are calculated here exactly terms temperature fugacity. These calculations are complemented by numerical calculation fugacity particles, withou...

We obtain a closed form of generating functions of RNA substructure using hermitian matrix model with the Chebyshev polynomial of the second kind, which turns out to be the hypergeometric function. To match the experimental findings of the statistical behavior, we regard the substructure as a grand canonical ensemble and find its fugacity value. We also suggest a hierarchical picture based on t...

Using a combination of Boltzmann's equation and virial expansion, we study the effect of three-body losses and interactions on the momentum distribution of a homogeneous unitary Bose gas in the dilute limit where quantum correlations are negligible. The comparison of our results to the recent measurement made at JILA on a unitary gas of ^{85}Rb allows us to determine an experimental fugacity z=...

We consider a statistical mechanical model describing flux lines in type II superconductors by embedding the flux lines on a lattice wound on torus. The lines are nonintersecting and each loop of lines is associated with a fugacity z = -1. It is shown that the exact solution of this model leads to a second-order transition between the Meissner and the superconducting states as well as a first-o...