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Elliptic beta integrals and solvable models of statistical mechanics
Elliptic beta integrals solvable models
2010/12/23
The univariate elliptic beta integral was discovered by the author in 2000. Recently Bazhanov and Sergeev have interpreted it as a star-triangle relation (STR). This important observation is discussed...
Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
line operators conformal sigma-models supergroups
2010/12/23
We study line operators in the two-dimensional sigma-model on PSl(n|n) using the current-current OPEs. We regularize and renormalize these line operators, and compute their fusion up to second order ...
Solitonic Models Based on Quantum Groups and the Standard Model
Solitonic Models Quantum Groups the Standard Model
2010/12/23
The idea that the elementary particles might have the symmetry of knots has had a long history. In any current formulation of this idea, however, the knot must be quantized. The present review is a su...
Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
Stokes Phenomena Non-perturbative Completion
2010/12/24
The Stokes multipliers in the matrix models are invariants in the string-theory moduli space and related to the D-instanton chemical potentials. They not only represent non-perturbative information bu...
Perturbative stability of SFT-based cosmological models
Perturbative stability SFT-based cosmological models
2010/12/24
We review the appearance of multiple scalar fields in linearized SFT based cosmological models with a single non-local scalar field. Some of these local fields are canonical real scalar fields and som...
Towards a proof of AGT conjecture by methods of matrix models
AGT conjecture matrix models
2010/12/24
A matrix model approach to proof of the AGT relation is briefly reviewed. It starts from the substitution of conformal blocks by the Dotsenko-Fateev beta-ensemble averages and Nekrasov functions by a...
Multi-Matrix Models and Tri-Sasaki Einstein Spaces
Multi-Matrix Models Tri-Sasaki Einstein Spaces
2010/12/24
Localization methods reduce the path integrals in {\cal N} >= 2 supersymmetric Chern-Simons gauge theories on S^3 to multi-matrix integrals. A recent evaluation of such a two-matrix integral for the {...
In this paper we perform the 1/N expansion of the colored three dimensional Boulatov tensor model. As in matrix models, we obtain a systematic topological expansion, with more and more complicated to...
Mass-Transport Models with Multiple-Chipping Processes
Mass-Transport Models Multiple-Chipping Processes
2010/11/22
We study mass-transport models with multiple-chipping processes. The rates of these processes are dependent on the chip size and mass of the fragmenting site. In this context, we consider k-chip moves...
Density models for streamer discharges: beyond cylindrical symmetry and homogeneous media
cylindrical symmetry homogeneous media
2010/11/16
Streamer electrical discharges are often investigated with computer simulations of density models (also called drift-diffusion-reaction models). We review these models, detailing their physical found...
Thermodynamically Consistent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities
Diffuse Interface Models Incompressible Two-Phase Flows Different Densities
2010/11/12
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and gl...
Models and measures of mixing and effective diffusion
Models and measures mixing and effective diffusion
2010/11/16
Mixing a passive scalar field by stirring can be measured in a variety of ways including tracer particle dispersion, via the flux-gradient relationship, or by suppression of scalar concentration vari...