Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves

We consider the F-theory description of non-simply-connected gauge groups appearing in the E8 x E8 heterotic string. The analysis is closely tied to the arithmetic of torsion points on an elliptic curve. The general form of the corresponding elliptic fibration is given for all finite subgroups of E8 which are applicable in this context. We also study the closely-related question of point-like instantons on a K3 surface whose holonomy is a finite group. As an example we consider the case of the heterotic string on a K3 surface having the E8 gauge symmetry broken to (E6 x SU(3))/Z3 or SU(9)/Z3 by point-like instantons with Z3 holonomy.Comment: 15 pages, 2 embedded figures, some spurious U(1)'s remove

Tiltrotor research aircraft composite blade repairs: Lessons learned

The XV-15, N703NA Tiltrotor Research Aircraft located at the NASA Ames Research Center, Moffett Field, California, currently uses a set of composite rotor blades of complex shape known as the advanced technology blades (ATBs). The main structural element of the blades is a D-spar constructed of unidirectional, angled fiberglass/graphite, with the aft fairing portion of the blades constructed of a fiberglass cross-ply skin bonded to a Nomex honeycomb core. The blade tip is a removable laminate shell that fits over the outboard section of the spar structure, which contains a cavity to retain balance weights. Two types of tip shells are used for research. One is highly twisted (more than a conventional helicopter blade) and has a hollow core constructed of a thin Nomex-honeycomb-and-fiberglass-skin sandwich; the other is untwisted with a solid Nomex honeycomb core and a fiberglass cross-ply skin. During initial flight testing of the blades, a number of problems in the composite structure were encountered. These problems included debonding between the fiberglass skin and the honeycomb core, failure of the honeycomb core, failures in fiberglass splices, cracks in fiberglass blocks, misalignment of mated composite parts, and failures of retention of metal fasteners. Substantial time was spent in identifying and repairing these problems. Discussed here are the types of problems encountered, the inspection procedures used to identify each problem, the repairs performed on the damaged or flawed areas, the level of criticality of the problems, and the monitoring of repaired areas. It is hoped that this discussion will help designers, analysts, and experimenters in the future as the use of composites becomes more prevalent

Topological Defects on the Lattice I: The Ising model

In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang-Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers-Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.Comment: 45 pages, 9 figure

Highly Stretchable MoS2_2 Kirigami

We report the results of classical molecular dynamics simulations focused on studying the mechanical properties of MoS$_{2}$ kirigami. Several different kirigami structures were studied based upon two simple non-dimensional parameters, which are related to the density of cuts, as well as the ratio of the overlapping cut length to the nanoribbon length. Our key finding is significant enhancements in tensile yield (by a factor of four) and fracture strains (by a factor of six) as compared to pristine MoS$_{2}$ nanoribbons. These results in conjunction with recent results on graphene suggest that the kirigami approach may be a generally useful one for enhancing the ductility of two-dimensional nanomaterials