Related papers: Vortex Filament Equation for a Regular Polygon
We have experimentally investigated the evolution properties of multiramp fractional vortex beams (MFVBs) in free space, by using a fundamental Gaussian beam reflecting from a phase-modulated spatial light modulator. The issue about the…
Premixed-flame wrinkling is studied via a Michelson-Sivashinsky (MS) type of evolution equation retaining the Darrieus-Landau (DL) instability, a curvature effect and a geometric nonlinearity. Here it also keeps forcing by longitudinal…
We embed a pair of vortices with different topological charges in a Gaussian beam and study its evolution through an astigmatic optical system, a tilted lens. The propagation dynamics is explained by a closed-form analytical expression.…
A theoretical study is presented for the random aspect of an optical vortex inherent in the nonlinear birefringent Kerr effect, which is called the optical spin vortex. We start with the two-component nonlinear Schr\"{o}dinger equation. The…
We consider a self-interacting diffusion $X$ on a smooth compact Riemannian manifold $\mathbb M$, described by the stochastic differential equation \[ dX_t = \sqrt{2} dW_t(X_t)- \beta(t) \nabla V_t(X_t)dt, \] where $\beta$ is suitably…
We study the Euler equations on a rotating unit sphere, focusing on the dynamics of vortex caps. Leveraging the $L^1$-stability of monotone, longitude-independent profiles, we demonstrate that certain ill-prepared initial data within the…
The study explores the development of the vortex line density in superfluids under thermal activation. This problem is of interest to both applied and fundamental research, and has been investigated by many authors in various aspects.…
The local induction equation, approximately describing dynamics of a quantized vortex filament in a trapped Bose-Einstein condensate in the Thomas-Fermi regime on a spatially nonuniform density background $\rho({\bf r})$ and taking…
We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases which are in good agreement with recent, independent experimental results. Our focus is on the sequence and evolution of defects using the…
We consider the $N$-vortex problem on the sphere assuming that all vorticities have equal strength. We investigate relative equilibria (RE) consisting of $n$ latitudinal rings which are uniformly rotating about the vertical axis with…
We prove global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation we consider generalizes two-sphere-valued completely integrable systems…
The energy of a displaced magnetic vortex in a cylindrical particle made of isotropic ferromagnetic material (magnetic dot) is calculated taking into account the magnetic dipolar and the exchange interactions. Under the simplifying…
We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schroedinger equation with harmonic forces. We also argue…
We present a relativistic description of electron vortex beams in a homogeneous magnetic field. Including spin from the beginning reveals that spin-polarized electron vortex beams have a complicated azimuthal current structure, containing…
An infinite family of integrable vortex equations is studied and related to the Cartan geometry of the underlying Riemann surfaces. This Cartan picture gives an interpretation of the vortex equations as the flatness of a non-Abelian…
Optical propagation and vortices in nonlinear media have been intensively studied in modern optical physics. In this paper, we establish constraints regarding the propagation constant and provide an existence theory and numerical…
We show how to regularize vortex sheets by means of smooth, compactly supported vorticities that asymptotically evolve according to the Birkhoff-Rott vortex sheet dynamics. More precisely, consider a vortex sheet initial datum…
The most general vortex solution of the Liouville equation (which arises in non-relativistic Chern-Simons theory) is associated with rational functions, $f(z)=P(z)/Q(z)$ where $P(z)$ and $Q(z)$ are both polynomials, $\deg P<\deg Q\equiv N$.…
For the incompressible Navier-Stokes equations in $R^3$ with low viscosity $\nu>0$, we consider the Cauchy problem with initial vorticity $\omega_0$ that represents an infinitely thin vortex filament of arbitrary given strength $\Gamma$…
We prove linear in time filamentation for perturbations of the Lamb dipole, which is a traveling wave solution to the incompressible Euler equations in $\mathbb{R}^2$. The main ingredient is a recent nonlinear orbital stability result by…