A method for mapping known cylindrical magnetovac solutions to solutions in torus coordinates is developed. Identification of the cylinder ends changes topology from R1 × S1 to S1 × S1. An analytic Einstein–Maxwell solution for a toroidal magnetic field in tori is presented. The toroidal interior is matched to an asymptotically flat vacuum exterior, connected by an Israel boundary layer. PACS n...

A perturbation theoretic approach is proposed as an efficient characterization tool for a tapered fiber coupled ultrahigh-quality factor Q toroidal microcavity with a small inverse aspect ratio. The Helmholtz equation with an assumption of quasi-TE/TM modes in local toroidal coordinates is solved via a power series expansion in terms of the inverse aspect ratio and the expanded eigenmode soluti...

We start from a study of the density-potential relation for classical homeoids in terms of an asymptotic expansion for small deviations from spherical symmetry. We then show that such expansion is a useful device that allows us to construct a variety of exact density-potential pairs with spheroidal, toroidal, or triaxial shapes for which the deviation from spherical symmetry is finite. As concr...

The ’anholonomic frame’ method [1–3] is applied for constructing new classes of exact solutions of vacuum Einstein equations with off–diagonal metrics in 4D and 5D gravity. We examine several black tori solutions generated by anholonomic transforms with non–trivial topology of the Schwarzshild metric, which have a static toroidal horizon. We define ansatz and parametrizations which contain warp...

We study a strongly adsorbed flexible polyelectrolyte chain on tori. In this generalized Thomson problem, the patterns of the adsorbed chain are analyzed in the space of the toroidal coordinates and in terms of the orientation of each chain segment. Various patterns are found, including double spirals, disclination-like structures, Janus tori, and uniform wrappings, arising from the long-range ...

The aim of this paper is to study a finite element numerical approximation of steady flows of an incompressible viscoelastic Oldroyd-B fluid in curved pipes of arbitrary cross-section and curvature ratio. Using rectangular toroidal coordinates, existence and uniqueness of approximated solutions are proved as well as a priori error estimates, under a natural restriction on the pipe curvature ratio.

A simple rendering method is presented to avoid vertex seams in cylindrical and toroidal uv-mappings used for texture mapping (a vertex seam is a vertex duplication of a polygonal mesh with different texture coordinates assigned to the two geometrically coinciding copies). As a result, the method leads for simpler, leaner, replication-free data structures. Is also allows for an higher degree of...

Asymptotic solutions are presented for Stokes flow near circular rims in three dimensional geometries. Using nonstandard toroidal coordinates, asymptotic analytical expressions are derived for different corner angles. In comparison to the two-dimensional case, an extra critical corner angle value is derived, below which the swirling behavior of a particle is absent. Illustrations of the motion ...