Related papers: Pointed vortex loops in ideal 2D fluids
We prove a definitive theorem on the asymptotic stability of point vortex solutions to the full Euler equation in 2 dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported perturbation of a point vortex…
Recent studies of pseudo-plane ideal flow (PIF) reveal a ubiquitous presence of vortex alignment in both homogeneous and stratified fluids, and in both inertial and rotating reference frames as well. The exact solutions of a steady-state…
We discuss a simple and experimentally available realization of fracton physics. We note that superfluid vortices form a Hamiltonian system that conserves total dipole moment and trace of the quadrupole moment of vorticity; thereby…
Vortex lattices are constructed in terms of linear combinations of solutions for Scr\"{o}dinger equation with a constant potential. The vortex lattices are mapped on the spaces with two-dimensional rotationally symmetric potentials by using…
In this work we identify a previously unexplored type of topological defect in spiral spin liquids -- the momentum vortex -- and reveal its dominant role in shaping the low energy physics of such systems. Spiral spin liquids are a class of…
Quantum vortices in superfluids have been an important research area for many decades. Naturally, research on this topic has focused on two and three-dimensional superfluids, in which vortex cores form points and lines, respectively. Very…
We rigorously construct continuous curves of rotating vortex patch solutions to the two-dimensional Euler equations. The curves are large in that, as the parameter tends to infinity, the minimum along the interface of the angular fluid…
The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and…
The complete point symmetry group of the barotropic vorticity equation on the sphere is determined. The method we use relies on the invariance of megaideals of the maximal Lie invariance algebra of a system of differential equations under…
Creation of stable intrinsically anisotropic self-bound states with embedded vorticity is a challenging issue. Previously, no such states in Bose-Einstein condensates (BECs) or other physical settings were known. Dipolar BEC suggests a…
A new method for the creation of 3D solitary topological modes, corresponding to vortical droplets of a two-component dilute superfluid, is presented. We use the recently introduced system of nonlinearly coupled Gross-Pitaevskii equations,…
We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in…
We present global 2-D inviscid disk simulations with an embedded planet, emphasizing the non-linear dynamics in its co-orbital region. We find that the potential vorticity of the flow in this region is not conserved due to the presence of…
The equilibrium behavior of vortices in the classical two-dimensional (2D) XY model with uncorrelated random phase shifts is investigated. The model describes Josephson-Junction arrays with positional disorder, and has ramifications in a…
This paper deals with the existence of $N$ vortex patches located at the vertex of a regular polygon with $N$ sides that rotate around the center of the polygon at a constant angular velocity. That is done for Euler and (SQG)$_\beta$…
In this work we study the dynamical behavior of two interacting vortex pairs, each one of them consisting of two point vortices with opposite circulation in the 2d plane. The vortices are considered as effective particles and their…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
Vortex rings are remarkably stable structures occurring in numerous systems: for example in turbulent gases, where they are at the origin of weather phenomena [1]; in fluids with implications for biology [2]; in electromagnetic discharges…
The goal of this paper is to give a detailed analytical description of the global dynamics of N points interacting through the singular logarithmic potential and subject to the following symmetry constraint: at each instant they form an…
The behaviour of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain…