Related papers: The vortex filament equation as a pseudorandom gen…
In this paper we continue our investigation about selfsimilar solutions of the vortex filament equation, also known as the binormal flow (BF) or the localized induction equation (LIE). Our main result is the stability of the selfsimilar…
Optical turbulence is the term that is used being based on the analogy between hydrodynamic and optical equations. The phenomenon of turbulent photon filamentation occurs in lasers and other active optical media at high Fresnel numbers. A…
Numerical simulation has indicated that vortex structures can exist for a long time in the form of quantized filaments on arrays of coupled weakly dissipative nonlinear oscillators in a finite three-dimensional domain under a resonant…
We consider a nonlinear model equation, known as the Localized Induction Equation, describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. We show stability estimates for an arc-shaped vortex filament,…
We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element…
Vortex dynamics in superfluids is investigated in the framework of the nonlinear Schr\"{o}dinger equation. The natural motion of the vortex is of cyclotron type, whose frequency is found to be on the order of phonon velocity divided by the…
The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently-developed accurate and robust tracking algorithm, all quantised vortices are extracted from the fields. The Vinen's…
We theoretically and experimentally studied a novel class of vortex beams named open vortex beams (OVBs). Such beams are generated using Gaussian beams diffracted by partially blocked fork-shaped gratings (PB-FSGs).The analytical model of…
This paper gives an analysis of the movement of n+1 almost parallel filaments or vortices. Starting from a polygonal equilibrium of n vortices with equal circulation and one vortex at the center of the polygon, we find bifurcation of…
We study numerically the motion of the stretched vortex filaments by using the localized induction equation with the stretch and that without the stretch.
In this article we propose a new type of optical vortex, the X-type vortex. This vortex inherits and develops the conventional noncanonical vortex, i.e., it no longer has a constant phase gradient around the center, while the intensity…
This is an analytical study of pinning and spontaneous vortex phase is a system consisting of a superconducting thin film pierced by a long ferromagnetic columnar defect of finite radius $R$. The magnetic fields, screening currents, energy…
We present a numerical study of the self-similar solutions of the Localized Induction Approximation of a vortex filament. These self-similar solutions, which constitute a one-parameter family, develop a singularity at finite time. We study…
Variational autoencoders (VAE) represent a popular, flexible form of deep generative model that can be stochastically fit to samples from a given random process using an information-theoretic variational bound on the true underlying…
We follow the time evolution of a superfluid Fermi gas of resonantly interacting $^6$Li atoms after a phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, its subsequent snaking, and its decay into a…
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…
The aim of this article is to establish a concise proof for a stability result of self-similar solutions of the binormal flow, in some more restrictive cases than in [5]. This equation, also known as the Local Induction Approximation, is a…
Systems of nearly parallel, slender vortex filaments in which angular momentum is conserved are an important simplification of the Navier-Stokes equations where turbulence can be studied in statistical equilibrium. We study the canonical…
Vortices are topological defects of type-II superconductors in an external magnetic field. In a similar fashion to a quantum anomalous Hall insulator, quantum anomalous vortex (QAV) spontaneously nucleates due to orbital-and-spin exchange…
It is well known that a superfluid rotates by forming an array of quantized vortices. A relativistic formulation for superfluid vortex dynamics is required for a range of problems in astrophysics and cosmology, from neutron star interiors…