Related papers: Symmetric Relative Equilibria in the Four-Vortex P…
This article studies the vortex-wave system for the Surface Quasi-Geostrophic equation with parameter 0 < s < 1. We obtained local existence of classical solutions in H^4 under the standard ''plateau hypothesis'', H^2-stability of the…
Using a sum rule approach we calculate the frequency shifts of the quadrupole oscillations of a harmonically trapped Bose gas due to the presence of a quantized vortex. Analytic results are obtained for positive scattering lengths and large…
A main question in astrophysics and cosmology has been the severe stability of the astrophysical objects, whether a particular equilibrium configuration is stable. In this article, we study the relativistic self-gravitating, hydrostatic…
The paper proposes 4-dimensional equations for the proper characteristics of a rigid reference frame \[ {{{W}'}^{\gamma }}=\Lambda ^{0}_{\;\;i}\frac{d\Lambda ^{\gamma i}}{d{t}}\,\,,\] \[ {{{\Omega }'}^{\gamma }}=-\frac{1}{2}\,{{e}^{\alpha…
We study holographic three-dimensional fluids with vorticity in local equilibrium and discuss their relevance to analogue gravity systems. The Fefferman-Graham expansion leads to the fluid's description in terms of a comoving and rotating…
In this paper we consider an Abelian Gauge Theory in R^4 equipped with the Minkowski metric. This theory leads to a system of equations, the Klein-Gordon-Maxwell equations, which provide models for the interaction between the…
This paper deals with the variational analysis of topological singularities in two dimensions. We consider two canonical zero-temperature models: the core radius approach and the Ginzburg-Landau energy. Denoting by $\varepsilon$ the length…
Positive semidefiniteness, recursiveness, and the variety condition of a moment matrix are necessary and sufficient conditions to solve the quadratic and quartic moment problems. Also, positive semidefiniteness, combined with another…
In this paper, we consider the elliptic relative equilibria of the restricted $4$-body problems, where the three primaries form an Euler collinear configuration and the four bodies span $\mathbf{R}^2$. We obtain the symplectic reduction to…
The restricted three-vortex problem is investigated with one of the point vortices fixed in the plane. The motion of the free vortex having zero circulation is explored from a rotating frame of reference within which the free vortex with…
The inhomogeneous abelian Higgs model with a magnetic impurity in the BPS limit is studied for both relativistic and nonrelativistic regimes. Though the symmetry of spatial translation is broken by inhomogeneity, extension to an…
The notion of type of a differential 2-form in four variables is introduced and for 2-forms of type < 4, local normal models are given. If the type of a 2-form $\Omega$ is 4, then the equivalence under diffeomorphisms of $\Omega$ is reduced…
The dynamics of a constrained three-vortex problem, a free point vortex pair in the velocity field of a fixed point vortex, is investigated. The underlying dynamical system is simplified using a coordinate transformation and categorized…
Discrete analogs of extrema of curvature and generalizations of the four-vertex theorem to the case of polygons and polyhedra are suggested and developed. For smooth curves and polygonal lines in the plane, a formula relating the number of…
We investigate the rotation of a vortex around a circular obstacle in dry active matter in the presence of M half-circles distributed around the obstacle. To quantify this effect, we define the parameter {\Pi}M , which is the ratio between…
We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter $\varepsilon$. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous.…
In this article we consider $SU(2)$ Chern-Simons/Higgs theory coupled to gravity in three-dimensions. It is shown that for a cylindrically symmetric vortex both the Einstein equations and the field equations can be reduced to a set of…
We study the Boussinesq approximation for rapidly rotating stably-stratified fluids in a three dimensional infinite layer with either stress-free or periodic boundary conditions in the vertical direction. For initial conditions satisfying a…
In this paper we have resolved the apparent paradox of different mechanical equations for force and torque governing the motion of a charged particle in different inertial frames. The same paradox arises in all usual ``explanations'' of the…
A point particle approximation to the classical dynamics of well separated vortices of the abelian Higgs model is developed. A static vortex is asymptotically identical to a solution of the linearized field theory (a Klein-Gordon/Proca…