We obtained new periodic solutions in the problems of three and four point vortices moving on a plane. In the case of three vortices, the system is reduced to a Hamiltonian system with one degree of freedom, and it is integrable. In the case of four vortices, the order is reduced to two degrees of freedom, and the system is not integrable. We present relative and absolute choreographies of thre...

In two preceding papers (Infeld and Senatorski 2003 J. Phys.: Condens. Matter 15 5865, Senatorski and Infeld 2004 J. Phys.: Condens. Matter 16 6589) the authors confirmed Feynman's hypothesis on how circular vortices can be created from oppositely polarized pairs of linear vortices (first paper), and then gave examples of the creation of several different circular vortices from one linear pair ...

Convective vortices are common features of atmospheres that absorb lower-entropy-energy at higher temperatures than they reject higher-entropy-energy to space. These vortices range from small to large-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective vortices is important to our understand...

The stability of steady, inviscid vortex pairs in equilibrium with a circular cylinder are studied by discretizing equations derived from contour dynamics. These flows were found previously using different methods in Elcrat, Fornberg, Horn & Miller (2000). There are two families of vortices, one with a pair of counter-rotating vortices standing behind the cylinder, which may be thought of as de...

We use a combination of numerical simulations and experiments to elucidate the structure of the flow of an electrically conducting fluid past a localized magnetic field, called magnetic obstacle. We demonstrate that the stationary flow pattern is considerably more complex than in the wake behind an ordinary body. The steady flow is shown to undergo two bifurcations (rather than one) and to invo...

Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density atomic Bose-Einstein condensates as quantized vortex lines. We discuss unconventional ...

We use a high order accuracy spectral code to carry out two-dimensional time-dependent numerical simulations of vortices in accretion disks. In particular , we examine the stability and the life time of vortices in circumstellar disks around young stellar objects. The results show that cyclonic vortices dissipate quickly, while anticyclonic vortices can survive in the flow for hundreds of orbit...

In this paper, we investigate localized discrete states with a non-zero topological charge (discrete vortices) in a prototypical model of dynamical lattice systems, based on the twoand three-dimensional (2D and 3D) discrete nonlinear Schrödinger (DNLS) equation, with both attractive and repulsive on-site cubic nonlinearity. Systems of two nonlinearly coupled DNLS equations are considered too. W...

Abstract By using the gauge potential decomposition, we discuss the self-dual equation and its solution in Jackiw-Pi model. We obtain a new concrete self-dual equation and find relationship between Chern-Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees of Ψ-mapping. To show the meaning of topological number we give several figures with diff...

Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density atomic Bose-Einstein condensates as quantized vortex lines. We discuss unconventional ...