相关论文: Evolution of rarefaction pulses into vortex rings
We study the dynamics of vortices in a two-dimensional, non-equilibrium system, described by the compact Kardar-Parisi-Zhang equation, after a sudden quench across the critical region. Our exact numerical solution of the phase-ordering…
We consider the dynamics of a vortex sheet that evolves by the Birkhoff-Rott equations. The fluid evolution is understood as a weak solution of the incompressible Euler equations where the vorticity is given by a delta function on a curve…
We reformulate the Gross-Pitaevskii equation with an external parabolic potential as a discrete dynamical system, by using the basis of Hermite functions. We consider small amplitude stationary solutions with a single node, called dark…
The time dependent evolution of the accretion disk around black hole is computed. The classical description of the $\alpha$-viscosity is adopted so the evolution is driven by the instability operating in the innermost radiation-pressure…
We study the nucleation and dynamics of vortices in rotating lattice potentials where weakly linked condensates are formed with each condensate exhibiting an almost axial symmetry. Due to such a symmetry, the on-site phases acquire a linear…
A mathematical model is constructed for the evolution of spherical perturbations in a cosmological one-component statistical system of completely degenerate scalarly charged fermions with a scalar Higgs interaction. A complete system of…
We analyse the dynamical properties of three-dimensional solitary waves in cylindrically trapped Bose-Einstein condensates. Families of solitary waves bifurcate from the planar dark soliton and include the solitonic vortex, the vortex ring…
The nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric…
Treating the Teukolsky perturbation equation numerically as a 2+1 PDE and smearing the singularities in the particle source term by the use of narrow Gaussian distributions, we have been able to reproduce earlier results for equatorial…
Origin of turbulence in cold accretion disks, particularly in 3D, which is expected to be hydrodynamic but not magnetohydrodynamic, is a big puzzle. While the flow must exhibit some turbulence in support of the transfer of mass inward and…
Two-dimensional decaying turbulent flow is known to approach apparently stable states after a long time evolution. A few theories and models have been so far proposed to account for this relaxation. In this paper, we compare results of…
In this paper, we are concerned with the uniqueness and nonlinear stability of vortex rings for the 3D Euler equation. By utilizing Arnold 's variational principle for steady states of Euler equations and concentrated compactness method…
We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature…
In the article, we describe three-phase finite-gap solutions of the focusing nonlinear Schr\"odinger equation and Kadomtsev-Petviashvili and Hirota equations that exhibit the behavior of almost-periodic "freak waves". We also study the…
We analyze the stability of the vortex lattice in a rotating superfluid against thermal fluctuations associated with the long-wavelength Tkachenko modes of the lattice. Inclusion of only the two-dimensional modes leads formally to…
We rigorously establish the formal asymptotics of Neu for Gross-Pitaevskii vortex dynamics in the plane. Given any integer $n\geq2$, we construct a family of $n$-vortex solutions with vortices of degree $\pm1$, and describe precisely the…
In this paper, we consider the evolution of the Vortex Filament equation (VFE): \begin{equation*} \mathbf X_t = \mathbf Xs \wedge \mathbf Xss, \end{equation*} taking $M$-sided regular polygons with nonzero torsion as initial data. Using…
The dynamical instabilities and ensuing dynamics of singly- and doubly-quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full 3D numerical simulations of the Gross-Pitaevskii equation.…
The one-dimension Russo--Smereka kinetic equation describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid is considered. Reductions of the model to finite component systems are derived. Stability of the bubbly…
In this paper, we study the nonlinear dynamics of an axisymmetric disturbance to the laminar state in non-rotating Poiseuille pipe flows. In particular, we show that the associated Navier-Stokes equations can be reduced to a set of coupled…