Tonia Ricciardi

Vortices in the Maxwell-Chern-Simons Theory

Our aim is to prove rigorously that the Chern-Simons model of Hong, Kim, and Pac [13] and Jackiw and Weinberg [14] (the CS model) and the Abelian Higgs model of Ginzburg and Landau (the AH model, see [15]) are unified by the Maxwell-Chern-Simons theory introduced by Lee, Lee, and Min in [16] (MCS model). In [16] the authors give a formal argument that shows how to recover both the CS and AH models out of their theory by taking special limits for the values of the physical parameters involved. To make this argument rigorous, we consider the existence and multiplicity of periodic vortex solutions for the MCS model and analyze their asymptotic behavior as the physical parameters approach these limiting values. We show that, indeed, the given vortices approach (in a strong sense) vortices for the CS and AH models, respectively. For this purpose, we are led to analyze a system of two elliptic PDEs with exponential nonlinearities on a flat torus. c 2000 John Wiley & Sons, Inc.

Asymptotics for Maxwell-Chern-Simons multivortices

Chern–Simons gauge theories are of interest in several areas of physics, including high-Tc superconductivity, as they can describe particles which are both electrically and magnetically “charged”. On the other hand, the introduction of the Chern–Simons term into the Lagrangian results in serious di5culties for a rigorous treatment of the corresponding equations of motion. Therefore a considerable e7ort has been devoted in recent years to the study of models with a self-dual structure. Such a structure allows us to obtain time-independent, energy-minimizer solutions to the full second-order equations of motion by solving appropriate *rst-order equations, also known as the “Bogomol’nyi equations” [11]. These particular solutions are called multivortices. For an overview of self-dual Chern–Simons theories see the monograph of Dunne [8]. In [9,10], Hong et al. and Jackiw and Weinberg introduced a Chern–Simons model, where the Maxwell term is neglected in order to achieve self-duality. We call this model the CS model. The CS multivortices have proved to be particularly interesting from the mathematical viewpoint, and have been extensively analyzed (see references

Concentrating solutions for a Liouville type equation with variable intensities in 2D-turbulence.

We construct sign-changing concentrating solutions for a mean field equation describing turbulent Euler flows with variable vortex intensities and arbitrary orientation. We study the effect of variable intensities and orientation on the bubbling profile and on the location of the vortex points.

Blow-up behavior for a degenerate elliptic \sinh -Poisson equation with variable intensities

In this paper, we provide a complete blow-up picture for solution sequences to an elliptic sinh-Poisson equation with variable intensities arising in the context of the statistical mechanics description of two-dimensional turbulence, as initiated by Onsager. The vortex intensities are described in terms of a probability measure

Asymptotics for selfdual vortices on the torus and on the plane : A gluing technique

\mathcal P

On the Blow-Up of Solutions to Liouville-Type Equations

P defined on the interval

Sign-changing two-peak solutions for an elliptic free boundary problem related to confined plasmas

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