Related papers: Vortex solutions of the evolutionary Ginzburg-Land…
We prove the existence of smooth solutions to the Gross-Pitaevskii equation on $\mathbf{R}^3$ that feature arbitrarily complex quantum vortex reconnections. We can track the evolution of the vortices during the whole process. This permits…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
New exact solutions of relativistic perfect fluid hydrodynamics are described, including the first family of exact rotating solutions. The method used to search for them is an investigation of the relativistic hydrodynamical equations and…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation…
The Hamiltonian equation of motion is studied for a vortex occuring in 2-dimensional Heisenberg ferromagnet of anisotropic type by starting with the effective action for the spin field formulated by the Bloch (or spin) coherent state. The…
Following the analytic approach to thermodynamics developed by Stueckelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations…
Phase transitions between different (i.e. giant and multi-vortex) superconducting states and between the superconducting-normal state of mesoscopic disks and rings are studied in the presence of an external magnetic field by solving the two…
We have developed the quantum hydrodynamic model that describes particles with spin-up and with spin-down in separate. We have derived the equation of the spin current evolution as a part of the set of the quantum hydrodynamics (QHD)…
We provide a novel existence result for energy-variational solutions to a general class of evolutionary partial differential equations. Compared to previous works on this solution concept, the generalization is mainly twofold: a relaxation…
Novel vortex phase and nature of double transition field are investigated by two-component Ginzburg-Landau theory in a situation where fourfold-twofold symmetric superconducting double transition occurs. The deformation from 60 degree…
We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles with compact support propagating over a stationary state…
We study the Ginzburg-Landau model with a nonlocal quartic term as a simple phenomenological model for superconductors in the presence of coupling between the vortex lattice and the underlying crystal lattice. In mean-field theory, our…
Smoke circle vortexes are a typical dynamic phenomenon in nature. The similar circle vortexes phenomenon appears in hurricane, turbulence, and many others. A semi-empirical method is constructed to get some intrinsic understanding about…
In this paper we use bifurcation methods to construct a new family of solutions of the binormal flow, also known as the vortex filament equation, which do not change their form. Our examples are complementary to those obtained by S. Kida in…
Vortex rings are ubiquitous in fluids, with smoke rings being a familiar example. The interaction of multiple vortex rings produces complex dynamical behaviour, such as the leapfrogging motion first analysed by Helmholtz more than a century…
We consider reflection and transmission of 2D quantum wavepackets with phase vortices (also known in optics as spatiotemporal vortex pulses) at potential step-like, delta-function, and rectangular barriers. The presence of a vortex…
We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We…
We study a variational Ginzburg-Landau type model depending on a small parameter $\varepsilon>0$ for (tangent) vector fields on a $2$-dimensional Riemannian manifold $S$. As $\varepsilon\to 0$, these vector fields tend to have unit length…
Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary…