Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties

We use the gauged linear sigma model introduced by Witten to calculate instanton expansions for correlation functions in topological sigma models with target space a toric variety $V$ or a Calabi--Yau hypersurface $M \subset V$. In the linear model the instanton moduli spaces are relatively simple objects and the correlators are explicitly computable; moreover, the instantons can be summed, leading to explicit solutions for both kinds of models. In the case of smooth $V$, our results reproduce and clarify an algebraic solution of the $V$ model due to Batyrev. In addition, we find an algebraic relation determining the solution for $M$ in terms of that for $V$. Finally, we propose a modification of the linear model which computes instanton expansions about any limiting point in the moduli space. In the smooth case this leads to a (second) algebraic solution of the $M$ model. We use this description to prove some conjectures about mirror symmetry, including the previously conjectured ``monomial-divisor mirror map'' of Aspinwall, Greene, and Morrison.Comment: 91 pages and 3 figures, harvmac with epsf (Changes in this version: one minor correction, one clarification, one new reference

The processing and properties of syntactic Al foams containing low cost expanded glass particles

Expanded glass particles (EGP) are used to manufacture Al syntactic foams using a simple vacuum casting method. Clamping of the casting in the stainless steel mold is observed when preheating the mold to >400 C, causing damage to the EGP, resulting in a weaker foam but with the significant advantage of eliminating the yield drop, improving the energy absorption characteristics. The same effect in castings that are not clamped (for mold preheats <400 °C) can be achieved by quenching in liquid nitrogen. These “low strength” syntactic metal foams are a cost-effective alternative to metal foams and porous metals (in terms of specific strength, stiffness, and energy absorption) rather than “conventional” syntactic foams which contain smaller, stronger, hollow microspheres

Collapsing D-branes in one-parameter models and small/large radius duality

We finalize the study of collapsing D-branes in one-parameter models by completing the analysis of the associated hypergeometric hierarchy. This brings further evidence that the phenomenon of collapsing 6-branes at the mirror of the `conifold' point in IIA compactifications on one-parameter Calabi-Yau manifolds is generic. It also completes the reduction of the study of higher periods in one-parameter models to a few families which display characteristic behaviour. One of the models we consider displays an exotic form of small-large radius duality, which is a consequence of an ``accidental'' discrete symmetry of its moduli space. We discuss the implementation of this symmetry at the level of the associated type II string compactification and its action on D-brane states. We also argue that this model admits two special Lagrangian fibrations and that the symmetry can be understood as their exchange.Comment: 34 pages, 12 figure

The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Assessing the Effectiveness of In-Vehicle Highway Back-of-Queue Alerting System

This paper proposes an in-vehicle back-of-queue alerting system that is able to issue alerting messages to drivers on highways approaching traffic queues. A prototype system was implemented to deliver the in-vehicle alerting messages to drivers via an Android-based smartphone app. To assess its effectiveness, a set of test scenarios were designed and implemented on a state-of-the-art driving simulator. Subjects were recruited and their testing data was collected under two driver states (normal and distracted) and three alert types (no alerts, roadside alerts, and in-vehicle auditory alerts). The effectiveness was evaluated using three parameters of interest: 1) the minimum Time-to-Collision (mTTC), 2) the maximum deceleration, and 3) the maximum lateral acceleration. Statistical models were utilized to examine the usefulness and benefits of each alerting type. The results show that the in-vehicle auditory alert is the most effective way for delivering alerting messages to drivers. More specifically, it significantly increases the mTTC (30% longer than that of 'no warning') and decreases the maximum lateral acceleration (60% less than that of 'no warning'), which provides drivers with more reaction time and improves driving stability of their vehicles. The effects of driver distraction significantly decrease the efficiency of roadside traffic sign alert. More specifically, when the driver is distracted, the roadside traffic sign alert performs significantly worse in terms of mTTC compared with that of normal driving. This highlights the importance of the in-vehicle auditory alert when the driver is distracted

Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2 quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur

Antibody immobilization within glass microstructured fibers: A route to sensitive and selective biosensors

Glass microstructured optical fibers have been rendered biologically active for the first time via the immobilization of antibodies within the holes in the fiber cross-section. This has been done by introducing coating layers to the internal surfaces of soft glass fibers. The detection of proteins that bind to these antibodies has been demonstrated experimentally within this system via the use of fluorescence labeling. The approach combines the sensitivity resulting from the long interaction lengths of filled fibers with the selectivity provided by the use of antibodies.Yinlan Ruan, Tze Cheung Foo, Stephen Warren-Smith, Peter Hoffmann, Roger C. Moore, Heike Ebendorff-Heidepriem, Tanya M. Monr

Fluorescence-based sensing with optical nanowires: a generalized model and experimental validation

A model for the fluorescence sensing properties of small-core high-refractive-index fibers (optical nanowires) is developed and compared quantitatively with experiment. For the first time, higher-order modes and loss factors relevant to optical nanowires are included, which allows the model to be compared effectively with experiment via the use of fluorophore filled suspended optical nanowires. Numerical results show that high-index materials are beneficial for fluorescence-based sensing. However, both numerical and experimental results show that the fluorescence signal is relatively insensitive to core size, except for low concentration sensing where nanoscale fiber cores are advantageous due to the increased evanescent field power.Stephen C. Warren-Smith, Shahraam Afshar V. and Tanya M. Monr