When the standard representation of a crystallographic Coxeter group G (with string diagram) is reduced modulo the integer d ≥ 2, one obtains a finite group G which is often the automorphism group of an abstract regular polytope. Building on earlier work in the case that d is an odd prime, we here develop methods to handle composite moduli and completely describe the corresponding modular polyt...

Isoradial dimer models were introduced in Kenyon (Invent Math 150(2):409–439, 2002)— they consist of dimer models whose underlying graph satisfies a simple geometric condition, and whose weight function is chosen accordingly. In this paper, we prove a conjecture of (Kenyon in Invent Math 150(2):409–439, 2002), namely that for periodic isoradial dimer models, the growth rate of the toroidal part...

ABSTRACT Broadcasting is the process of disseminating a message from a node of a communication network to all other nodes as quickly as possible. In this paper we consider Manhattan Street Networks (MSNs) which are mesh-structured, toroidal, directed, regular networks such that locally they resemble the geographical topology of the avenues and streets of Manhattan. Previous work on these networ...

The simplest toroidally compactified string theories exhibit a duality between small and large radii: compactification on a circle, for example, is invariant under R → 1/(2R). Compactification on more general Lorentzian lattices (e.g. toroidal compactification in the presence of background metric, antisymmetric tensor, and gauge fields) yields theories for which a large-small equivalence is not...

We investigate the possibility of inducing a bosonic current which is rotational ( −→ ∇×−→v 6= −→ 0 ) in a pseudo 1D quasi-condensate confined in an optical toroidal trap. The stability of such a current is also analyzed using hydrodynamics approach. We find that such a current is uniform when the circular symmetry is preserved and energetically stable when the modes of elementary excitations a...

REQUIREMENTS AND DESIGN ENVELOPE FOR A VOLUMETRIC NEUTRON SOURCE (VNS) FUSION FACILITY FOR FUSION NUCLEAR TECHNOLOGY DEVELOPMENT. The paper shows that timely development of fusion nuclear technology (FNT) components, e.g. blanket, for DEMO requires the construction and operation of a fusion facility parallel to ITER. This facility, called VNS, will be dedicated to testing, developing and qualif...

We study homogeneous special Lagrangian cones in C with isolated singularities. Our main result constructs an infinite family of special Lagrangian cones in C each of which has a toroidal link. We obtain a detailed geometric description of these tori. We prove a regularity result for special Lagrangian cones in C with a spherical link – any such cone must be a plane. We also construct a one-par...

Building upon the work of [Morelli1,2], we give a coherent presentation of Morelli’s algorithm for the weak and strong factorization of toric birational maps. We also discuss its toroidal extension, which plays a crucial role in the recent solutions [W lodarczyk2,3, Abramovich-Karu-Matsuki-W lodarczyk] of the weak factorization conjecture of general birational maps.

We discuss the first step in the moduli stabilization program a la KKLT for a general class of resolved toroidal type IIB orientifolds. In particular, we discuss their geometry, the topology of the divisors relevant for the D3–brane instantons which can contribute to the superpotential, and some non–trivial aspects of the orientifold action.

In this paper, we derive simple closed-form expressions for the n-queens problem and three related problems in terms of permanents of (0, 1) matrices. These formulas are the first of their kind. Moreover, they provide the first method for solving these problems with polynomial space that has a nontrivial time complexity bound. We then show how a closed form for the number of Latin squares of or...