Global Aspects of T-Duality, Gauged Sigma Models and T-Folds

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to T-duality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.Comment: Minor corrections and addition

Topology Synthesis of Structures Using Parameter Relaxation and Geometric Refinement

Typically, structural topology optimization problems undergo relaxation of certain design parameters to allow the existence of intermediate variable optimum topologies. Relaxation permits the use of a variety of gradient-based search techniques and has been shown to guarantee the existence of optimal solutions and eliminate mesh dependencies. This Technical Publication (TP) will demonstrate the application of relaxation to a control point discretization of the design workspace for the structural topology optimization process. The control point parameterization with subdivision has been offered as an alternative to the traditional method of discretized finite element design domain. The principle of relaxation demonstrates the increased utility of the control point parameterization. One of the significant results of the relaxation process offered in this TP is that direct manufacturability of the optimized design will be maintained without the need for designer intervention or translation. In addition, it will be shown that relaxation of certain parameters may extend the range of problems that can be addressed; e.g., in permitting limited out-of-plane motion to be included in a path generation problem

The many faces of OSp(1|32)

We show that the complete superalgebra of symmetries, including central charges, that underlies F-theories, M-theories and type II string theories in dimensions 12, 11 and 10 of various signatures correspond to rewriting of the same OSp(1|32) algebra in different covariant ways. One only has to distinguish the complex and the unique real algebra. We develop a common framework to discuss all signatures theories by starting from the complex form of OSp(1|32). Theories are distinguished by the choice of basis for this algebra. We formulate dimensional reductions and dualities as changes of basis of the algebra. A second ingredient is the choice of a real form corresponding to a specific signature. The existence of the real form of the algebra selects preferred spacetime signatures. In particular, we show how the real d=10 IIA and IIB superalgebras for various signatures are related by generalized T-duality transformations that not only involve spacelike but also timelike directions. A third essential ingredient is that the translation generator in one theory plays the role of a central charge operator in the other theory. The identification of the translation generator in these algebras leads to the star algebras of Hull, which are characterized by the fact that the positive definite energy operator is not part of the translation generators. We apply our results to discuss different T-dual pictures of the D-instanton solution of Euclidean IIB supergravity.Comment: 30 pages, Latex, using lscape.st

Evolutionary Optimization of a Geometrically Refined Truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset

Heterotic-type IIA duality with fluxes

In this paper we study a possible non-perturbative dual of the heterotic string compactified on K3 x T^2 in the presence of background fluxes. We show that type IIA string theory compactified on manifolds with SU(3) structure can account for a subset of the possible heterotic fluxes. This extends our previous analysis to a case of a non-perturbative duality with fluxes.Comment: 26 pages, minor corrections; version to appear in JHE

Lunar Habitat Optimization Using Genetic Algorithms

Long-duration surface missions to the Moon and Mars will require bases to accommodate habitats for the astronauts. Transporting the materials and equipment required to build the necessary habitats is costly and difficult. The materials chosen for the habitat walls play a direct role in protection against each of the mentioned hazards. Choosing the best materials, their configuration, and the amount required is extremely difficult due to the immense size of the design region. Clearly, an optimization method is warranted for habitat wall design. Standard optimization techniques are not suitable for problems with such large search spaces; therefore, a habitat wall design tool utilizing genetic algorithms (GAs) has been developed. GAs use a "survival of the fittest" philosophy where the most fit individuals are more likely to survive and reproduce. This habitat design optimization tool is a multiobjective formulation of up-mass, heat loss, structural analysis, meteoroid impact protection, and radiation protection. This Technical Publication presents the research and development of this tool as well as a technique for finding the optimal GA search parameters

Toroidal Orientifolds in IIA with General NS-NS Fluxes

Type IIA toroidal orientifolds offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NS-NS and R-R field strengths, but also fluxes that are T-dual to the NS-NS three-form flux. These new ingredients are known as metric fluxes and non-geometric fluxes, and can help stabilize moduli or can lead to other new features. In this paper we study two approaches to these constructions, by effective field theory or by toroidal fibers twisted over a toroidal base. Each approach leads us to important observations, in particular the presence of D-terms in the four-dimensional effective potential in some cases, and a more subtle treatment of the quantization of the general NS-NS fluxes. Though our methods are general, we illustrate each approach on the example of an orientifold of T^6/Z_4.Comment: 59 pages, references adde

Screw dislocation in zirconium: An ab initio study

Plasticity in zirconium is controlled by 1/3 screw dislocations gliding in the prism planes of the hexagonal close-packed structure. This prismatic and not basal glide is observed for a given set of transition metals like zirconium and is known to be related to the number of valence electrons in the d band. We use ab initio calculations based on the density functional theory to study the core structure of screw dislocations in zirconium. Dislocations are found to dissociate in the prism plane in two partial dislocations, each with a pure screw character. Ab initio calculations also show that the dissociation in the basal plane is unstable. We calculate then the Peierls barrier for a screw dislocation gliding in the prism plane and obtain a small barrier. The Peierls stress deduced from this barrier is lower than 21 MPa, which is in agreement with experimental data. The ability of an empirical potential relying on the embedded atom method (EAM) to model dislocations in zirconium is also tested against these ab initio calculations

Habitat Design Optimization and Analysis

Long-duration surface missions to the Moon and Mars will require habitats for the astronauts. The materials chosen for the habitat walls play a direct role in the protection against the harsh environments found on the surface. Choosing the best materials, their configuration, and the amount required is extremely difficult due to the immense size of the design region. Advanced optimization techniques are necessary for habitat wall design. Standard optimization techniques are not suitable for problems with such large search spaces; therefore, a habitat design optimization tool utilizing genetic algorithms has been developed. Genetic algorithms use a "survival of the fittest" philosophy, where the most fit individuals are more likely to survive and reproduce. This habitat design optimization tool is a multi-objective formulation of structural analysis, heat loss, radiation protection, and meteoroid protection. This paper presents the research and development of this tool

Ferromagnetic Wires Composite Media with Tunable Scattering Spectra at Microwaves

We demonstrate composite media with ferromagnetic wires that exhibit a frequency region at the microwave regime with scattering spectra strongly dependent on an external magnetic field or stress. These tunable composite materials have recently been proposed theoretically; however, no direct experimental verification has been reported. We used composite materials with predominantly oriented CoFeCrSiB glass-coated amorphous wires having large magnetoimpedance at GHz frequencies. The free space measurements of reflection and transmission coefficients were conducted in the frequency range 1-8 GHz in the presence of an external static magnetic field or stress applied to the whole sample. In general, the transmission spectra show greater changes in the range of 10dB for a relatively small magnetic field of few Oe or stress of 0.1 MPa. The obtained results are quantitatively consistent with the analytical expressions predicted by the effective medium arguments. The incident electromagnetic wave induces an electrical dipole moment in each wire, the aggregate of which forms the effective dipole response of the whole composite structure in the radiative near or far field region. The field and stress dependences of the effective response arise from a field or tensile stress sensitivity of the ac surface impedance of a ferromagnetic wire. In the vicinity of the antenna resonance the variations in the magneto-impedance of the wire inclusions result in large changes of the total effective response. A number of applications of proposed materials is discussed including the field tunable microwave surfaces and the self-sensing media for the remote non-destructive evaluation of structural materials