It is shown that toroidal surfaces that extremize a properly weighted surface integral of the squared normal component of a solenoidal three-vector field capture the local invariant dynamics, in that a field line that is anywhere tangential to the surface must be confined to the surface everywhere. In addition to an elementary three-vector calculus derivation, which relies on a curvilinear toro...

Tutte has shown that every 4-connected planar graph contains a Hamilton cycle. Grünbaum and Nash-Williams independently conjectured that the same is true for toroidal graphs. In this paper, we prove that every 4-connected toroidal graph contains a Hamilton path. Partially supported by NSF grant DMS-9970514 Partially supported by NSF grants DMS-9970527 and DMS-0245530 Partially supported by RGC ...

A Dehn surgery on a knot K in S is exceptional if it produces a reducible, toroidal or Seifert fibred manifold. It is known that a large arborescent knot admits no such surgery unless it is a type II arborescent knot. The main theorem of this paper shows that up to isotopy there are exactly three large arborescent knots admitting exceptional surgery, each of which admits exactly one exceptional...

In this paper we give a linear algorithm to edge partition a toroidal graph, i.e., graph that can be embedded on the orientable surface of genus one without edge crossing, into three forests plus a set of at most three edges. For triangulated toroidal graphs, this algorithm gives a linear algorithm for finding three edge-disjoint spanning trees. This is in a certain way an extension of the well...

The eeects of atomic physics processes such as ionization, charge exchange, and radiation on the linear stability of dissi-pative drift waves are investigated in toroidal geometry both numerically and analytically. edge parameters, overall linear stability is determined by the competition between the destabilizing innuence of ionization and the stabilizing eeect due to the electron temperature ...

We show that the torus in R is a critical point of a sequence of functionalsFn (n = 1, 2, 3, . . .) defined over compact surfaces (closed membranes) in R. When the Lagrange function E is a polynomial of degree n of the mean curvatureH of the torus, the radii (a, r) of the torus are constrained to satisfy a 2 r2 = n−n n2−n−1 , n ≥ 2. A simple generalization of torus in R 3 is a tube of radius r ...

T. A. Raybould,1, ⇤ V. A. Fedotov,1 N. Papasimakis,1 I. Kuprov,2 I. J. Youngs,3 W. T. Chen,4, † D. P. Tsai,4, 5 and N. I. Zheludev1, 6 Optoelectronics Research Centre, University of Southampton, SO17 1BJ, United Kingdom School of Chemistry, University of Southampton, SO17 1BJ, United Kingdom DSTL, Salisbury, United Kingdom Department of Physics, National Taiwan University, Taipei, 10617, Taiwan...

Poulalhon and Schaeffer introduced an elegant method to linearly encode a planar triangulation optimally. The method is based on performing a special depth-first search algorithm on a particular orientation of the triangulation: the minimal Schnyder wood. Recent progress toward generalizing Schnyder woods to higher genus enables us to generalize this method to the toroidal case. In the plane, t...

It is shown theoretically and computationally that helical magnetic field, produced by continuous winding helical coils and without the toroidal coil, can sustain MHD stable high beta plasma. Pressure driven toroidal current (bootstrap current) cancels the external magnetic field and reduces the MHD potential energy, depending on the plasma beta values. Ramp-up of heating power input induces bo...