Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra

We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good 3-orbifolds with planar singular locus and underlying manifold the 3-sphere. The volume bounds follow from techniques related to the proof of Thurston's Orbifold Theorem, Schl\"afli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.Comment: 36 pages, 19 figure

EXPLICT CALULATIONS OF HOMOCLINIC TANGLES SURROUNDING MAGNETIC ISLANDS IN TOKAMAKS

We present explicit calculations of the complicated geometric objects known as homoclinic tangles that surround magnetic islands in the Poincare mapping of a tokamak's magnetic field. These tangles are shown to exist generically in the magnetic field of all toroidal confinement systems. The geometry of these tangles provides an explanation for the stochasticity known to occur near the X-points of the Poincare mapping. Furthermore, the intersection of homoclinic tangles from different resonances provides an explicit mechanism for the non-diffusive transport of magnetic field lines between these resonance layers