Related papers: Long time confinement of multiple concentrated vor…
Multiply quantized vortices in trapped Bose-Einstein condensates are studied using the Bogoliubov theory. Suitable combinations of a localized pinning potential and external rotation of the system are found to energetically stabilize, both…
We show that, in a two-dimensional (2d) ideal fluid (also applies to a column of quasi-2d non-neutral plasma in an axial magnetic field), large elliptical vortices in a finite disk are stable. The stability is established by comparison…
We investigate the existence and especially the linear stability of single and multiple-charge quantized vortex states of nonlinear Schroedinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions.…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
The evolution of a pair of point vortices in whole space, subject to the inviscid Euler equations for incompressible fluid flow, is solved exactly for rotationally symmetric initial conditions. This exact solution shows that the vortex…
We investigate analytically the thermodynamical stability of vortices in the ground state of rotating 2-dimensional Bose-Einstein condensates confined in asymptotically homogeneous trapping potentials in the Thomas-Fermi regime. Our…
We study the stability and dynamics of vortices in two-species condensates using a two mode model. The recent experimental results obtained at JILA (M. R. Matthews, {\em et al.}, Phys. Rev. Lett. 83 (1999) 2498) and theoretical predictions…
We study the stability and dynamics of vortices in two-species condensates as prepared in the recent JILA experiment (M. R. Andrews {\em et al.}, Phys. Rev. Lett. 83 (1999) 2498). We find that of the two available configurations, in which…
Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schr\"{o}dinger equation. The existence and stability of vortex…
We study stability of solitary vortices in the two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov-de Gennes equations and running direct simulations…
Particles confined in droplets are called compound particles. They are encountered in various biological and soft matter systems. Hydrodynamics can play a decisive role in determining the configuration and stability of these multiphase…
We investigate energetic stability of vortices near the surface of a Bose-Einstein condensate. From an energy functional of a rotating Bose-Einstein condensate, written in terms of variables local to the surface, and a suitable trial…
The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this…
We study logarithmic spiraling solutions to the 2d incompressible Euler equations which solve a nonlinear transport system on $\mathbb{S}$. We show that this system is locally well-posed in $L^p, p\geq 1$ as well as for atomic measures,…
We briefly discuss energy, normal modes and dynamics of a vortex in a trapped Bose-Einstein condensate. Theoretical results are compared with current experiments.
We study the evolution of solutions to the 2D Euler equations whose vorticity is sharply concentrated in the Wasserstein sense around a finite number of points. Under the assumption that the vorticity is merely $L^p$ integrable for some…
We study the stability of the vortex in a 2D model of continuous compressible media in a uniformly rotating reference frame. As it is known, the axisymmetric vortex in a fixed reference frame is stable with respect to asymmetric…
Based on the London approximation, we investigate numerically the stability of the elementary configurations of entanglement, the twisted-pair and the twisted-triplet, in the vortex-lattice and -liquid phases. We find that, except for the…
In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's…
We investigate the stability of a uniform elliptical vortex in a two-dimensional incompressible Euler fluid. It's demonstrated that for small eccentricities, the vortex relaxes to a core-halo structure that undergoes rigid rotation with the…