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Theoretical and numerical studies have shown that large-scale vortices in Protoplanetary discs can result from various hydrodynamical instabilities. Once produced, such vortices can survive nearly unchanged over a large number of rotation…
New exact spatially localized stationary solutions against the background of a zonal flow are found for the (3+1)-dimensional nonlinear non-dissipative quasi-geostrophic potential vorticity equation, which describes Rossby waves and…
Analytical and numerical vortex solutions for the extended Skyrme-Faddeev model in a (3+1) dimensional Minkowski space-time are investigated. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the…
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…
We present molecular dynamics simulations of driven vortices in layered superconductors in the presence of an external homogeneous force and point disorder. We use a model introduced by J.R.Clem for describing 3D vortex lines as stacks of…
In type-II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise…
Superfluids with strong spatial modulation can be experimentally produced in the area of cold atoms under the influence of optical lattices. Here we address $^{87}$Rb bosons at T=0 K in a flat geometry under the influence of a periodic…
An exact analytic solution for the dynamics of vortex pairs is obtained for rapid temperature quenches of a superfluid film starting from the line of critical points below the critical temperature $T_{KT}$. An approximate solution for…
We study the splitting dynamics of giant vortices in dilute Bose-Einstein condensates by numerically integrating the three-dimensional Gross-Pitaevskii equation in time. By taking advantage of tetrahedral tiling in the spatial…
Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the…
The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is…
This paper addresses the question of existence of (not necessarily self-similar) solutions to the 4-vortex problem that lead to total or partial collision. We begin by showing that energy considerations alone imply that, for the general…
We study a 3D model of driven vortices in weakly coupled layered superconductors with strong pinning. Above the critical force $F_c$, we find a plastic flow regime in which pancakes in different layers are uncoupled, corresponding to a…
We consider two types of the time-dependent Ginzburg-Landau equation in 2D bounded domains: the heat-flow equation and the Schroedinger equation. The system of ordinary differential equations is obtained that describes the evolution of the…
We consider the N-vortex problem on a ellipsoid of revolution. Applying standard techniques of classical perturbation theory we construct a sequence of conformal transformations from the ellipsoid into the complex plane. Using these…
Designing effective control for complex three-dimensional flow fields proves to be non-trivial. Oftentimes, intuitive control strategies lead to suboptimal control. To navigate the control space, we utilize a linear parabolized stability…
Quantized vortices in a complex wave field described by a defocusing nonlinear Schr\"odinger equation with a space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external…
Using numerical simulations we study the configurations, dynamics, and melting properties of vortex lattices interacting with elliptical pinning sites at integer matching fields with as many as 27 vortices per pin. Our pinning model is…
We study the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a Chaplygin gas. We prove that the well-known phenomenon of shock formation in simple…
Superfluid phase transitions are discussed from a geometrical perspective as envisaged by Onsager. The approach focuses on vortex loops which close to the critical temperature form a fluctuating vortex tangle. As the transition is…