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For the model of a compressible barotropic fluid on a two dimensional rotating Riemmanian manifold we discuss a special class of smooth solutions having a form of a steady non-singular vortex moving with a bearing field. The model can be…
We build a minimal model of dissipative vortex dynamics in two spatial dimensions, subject to a kinematic constraint: dipole conservation. The additional conservation law implies anomalously slow decay rates for vortices. We argue that this…
The study of superfluid and Berezinskii-Kosterlitz-Thouless phases in exciton-polaritons requires an understanding of vortex dynamics in a dissipative unconfined condensate. In this article we study the motion of dynamic vortex-antivortex…
Nonconservative evolution problems describe irreversible processes and dissipative effects in a broad variety of phenomena. Such problems are often characterised by a conservative part, which can be modelled as a Hamiltonian term, and a…
Asynchronous rotation in binary stars produces non-radial oscillations that are known to cause observable variability on orbital timescales. The horizontal perturbations of the surface velocity fields are referred to as "tidal flows". In…
A non-relativistic scalar field coupled minimally to electromagnetism supports in the presence of a homogeneous background electric charge density the existence of smooth, finite-energy topologically stable flux vortices. The static…
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…
We study solutions of Ginzburg-Landau-type evolution equations (both dissipative and Hamiltonian) with initial data representing collections of widely-spaced vortices. We show that for long times, the solutions continue to describe…
We present a simple method to compensate for losses in a polariton superfluid. Based on a weak support field, it allows for an extended propagation of a resonantly driven polariton superfluid at a minimal energetic cost. Moreover, this…
We prove the existence of non-constant time periodic vortex solutions to the Gross-Pitaevskii equations for small but \textit{fixed} $\varepsilon > 0.$ The vortices of these solutions follow periodic orbits to the point vortex system of…
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 present a combined experimental and theoretical investigation of the formation and decay kinetics of vortices in two dimensional, compressible quantum turbulence. We follow the temporal evolution of a quantum fluid of exciton polaritons,…
From Hamilton's principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity…
Dissipation can be represented in Hamiltonian mechanics in an extended phase space as a symplectic process. The method uses an auxiliary variable which represents the excitation of unresolved dynamics and a Hamiltonian for the interaction…
In this paper, we systematically examine the stability and dynamics of vortices under the effect of a phenomenological dissipation used as a simplified model for the inclusion of the effect of finite temperatures in atomic Bose-Einstein…
We study tidal interactions in white dwarf binaries in the limiting case of quasi-static tides. The formalism is valid for arbitrary orbital eccentricities and therefore applicable to white dwarf binaries in the Galactic disk as well as…
The evolution of piecewise constant distributions of a conserved quantity related to the frozen-in canonical vorticity in effectively two-dimensional incompressible ideal EMHD flows is analytically investigated by the Hamiltonian method.…
We derive the conservative secular evolution of precessing compact binaries to second post-Newtonian order accuracy, with leading-order spin-orbit, spin-spin and mass quadrupole-monopole contributions included. The emerging closed system of…
We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating the theory as a mechanical system on a configuration space…
We study the conservative dynamics and stationary configurations of a vortex-antivortex pair in a harmonically trapped two-dimensional Bose-Einstein condensate. We establish the conceptual framework for understanding the stationary states…