Related papers: Small Winding-Number Expansion: Vortex Solutions a…
We study numerically the magnetic susceptibility of the hierarchical model with Ising spins ($\sigma =\pm 1$) above the critical temperature and for two values of the epsilon parameter. The integrations are performed exactly, using…
A method is developed to compute minimal energy vortex lattices in a general Ginzburg-Landau model of a superconductor subjected to an applied magnetic field. The model may have any number of components and may be spatially anisotropic. The…
We study the splitting dynamics of giant vortices in dilute Bose-Einstein condensates by numerically integrating the three-dimensional Gross-Pitaevskii equation in time. By taking advantage of tetrahedral tiling in the spatial…
The ratios $R_{2k}$ of renormalized coupling constants $g_{2k}$ that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar…
We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this…
We consider renormalization of the central charge and the mass of the ${\cal N}=2$ supersymmetric Abelian vortices in 2+1 dimensions. We obtain ${\cal N}=2$ supersymmetric theory in 2+1 dimensions by dimensionally reducing the ${\cal N}=1$…
In this work, we propose an exponentially generalized Abelian model. We investigated the presence of vortex structures in models coupled to Maxwell and Chern-Simons fields. We chose to investigate the dynamics of the complex scalar field in…
We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem for the winding number as the time horizon tends to infinity.…
The incompressible Navier-Stokes equations in R^3 are shown to admit a unique axisymmetric solution without swirl if the initial vorticity is a circular vortex filament with arbitrarily large circulation Reynolds number. The emphasis is on…
We construct exact vortex solutions in 3+1 dimensions to a theory which is an extension, due to Gies, of the Skyrme-Faddeev model, and that is believed to describe some aspects of the low energy limit of the pure SU(2) Yang-Mills theory.…
We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk…
We investigate optical Tamm states supported by a dielectric grating placed on top of a distributed Bragg reflector. It is found that under certain conditions the Tamm state may become a bound state in the continuum. The bound state, in its…
In this paper we apply the approach of formal asymptotic expansions and perturbation theory to derive a new highly nonlinear shallow-water model from the full governing equations for two dimensional incompressible fluid with constant…
A detailed study of vortices is presented in Ginzburg-Landau (or Abelian Higgs) models with two complex scalars (order parameters) assuming a general U(1)$\times$U(1) symmetric potential. Particular emphasis is given to the case, when only…
We have extended through beta^{23} the high-temperature expansion of the second field derivative of the susceptibility for Ising models of general spin, with nearest-neighbor interactions, on the simple cubic and the body-centered cubic…
In this paper, we consider the concentration property of solutions to the dispersive Ginzburg-Landau (or Gross-Pitaevskii) equation in three dimensions. On a spatial domain, it has long been conjectured that such a solution concentrates…
The main result is that given a generic self-similarly expanding configuration of 3 point vortices that start sufficiently far out, we can instead take compactly supported vorticity functions, and the resulting solution to 2D incompressible…
A solution of the vortex type is given in a six-dimensional $SU(2)\times U(1)$ pure gauge theory coupled to Einstein gravity in a compactified background geometry. We construct the solution of an effective abelian Higgs model in terms of…
We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by re-calculating the critical exponents of O(N)-symmetric $\vp^4$ theory. From only…
The large-N expansion technique is tested via an anomalous, soft-core potential which admits the tunneling through its central barrier. The precision of the approximation is found sensitive to the asymptotic component of the interaction.…