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

Gauge Coupling Unification and Non-Equilibrium Thermal Dark Matter

We study a new mechanism for the production of dark matter in the universe which does not rely on thermal equilibrium. Dark matter is populated from the thermal bath subsequent to inflationary reheating via a massive mediator whose mass is above the reheating scale, T_R. To this end, we consider models with an extra U(1) gauge symmetry broken at some intermediate scale M, of the order of 10^10 -- 10^12 GeV. We show that not only does the model allow for gauge coupling unification (at a higher scale associated with grand unification) but can naturally provide a dark matter candidate which is a Standard Model singlet but charged under the extra U(1). The intermediate scale gauge boson(s) which are predicted in several E6/SO(10) constructions can be a natural mediator between dark matter and the thermal bath. We show that the dark matter abundance, while never having achieved thermal equilibrium, is fixed shortly after the reheating epoch by the relation T_R^3/M^4. As a consequence, we show that the unification of gauge couplings which determines M also fixes the reheating temperature T_R, which can be as high as 10^11 GeV.Comment: 4 pages, 2 figures, 1 tabl

The Lyman Alpha Forest in Hierarchical Cosmologies

The comparison of quasar absorption spectra with numerically simulated spectra from hierarchical cosmological models of structure formation promises to be a valuable tool to discriminate among these models. We present simulation results for the column density, Doppler b parameter, and optical depth probability distributions for five popular cosmological models.Comment: 4 pages, 3 figures, uses aipproc.sty, to appear in the Proceedings of the 9th Annual October Astrophysics Conference in Maryland, "After the Dark Ages: When Galaxies Were Young (the Universe at 2<z<5)", ed. S. S. Holt and E. P. Smith, October 12-14, 199

Interactions between Octet Baryons in the SU_6 Quark model

The baryon-baryon interactions for the complete baryon octet (B_8) are investigated in a unified framework of the resonating-group method, in which the spin-flavor SU_6 quark-model wave functions are employed. Model parameters are determined to reproduce properties of the nucleon-nucleon system and the low-energy cross section data for the hyperon-nucleon interaction. We then proceed to explore B_8 B_8 interactions in the strangeness S=-2, -3 and -4 sectors. The S-wave phase-shift behavior and total cross sections are systematically understood by 1) the spin-flavor SU_6 symmetry, 2) the special role of the pion exchange, and 3) the flavor symmetry breaking.Comment: 11 pages, 6 figures, submitted to Phys. Rev. C (Rapid Communication

Simulating Star Formation and Feedback in Galactic Disk Models

We use a high-resolution grid-based hydrodynamics method to simulate the multi-phase interstellar medium in a Milky Way-size quiescent disk galaxy. The models are global and three-dimensional, and include a treatment of star formation and feedback. We examine the formation of gravitational instabilities and show that a form of the Toomre instability criterion can successfully predict where star formation will occur. Two common prescriptions for star formation are investigated. The first is based on cosmological simulations and has a relatively low threshold for star formation, but also enforces a comparatively low efficiency. The second only permits star formation above a number density of 1000 cm^-3 but adopts a high efficiency. We show that both methods can reproduce the observed slope of the relationship between star formation and gas surface density (although at too high a rate for our adopted parameters). A run which includes feedback from type II supernovae is successful at driving gas out of the plane, most of which falls back onto the disk. This feedback also substantially reduces the star formation rate. Finally, we examine the density and pressure distribution of the ISM, and show that there is a rough pressure equilibrium in the disk, but with a wide range of pressures at a given location (and even wider for the case including feedbackComment: 14 pages, 12 figures, accepted to Astrophysical Journa

Cost Benefit Analysis: Applications and Future Opportunities

Cost Benefit Analysis (CBA or Benefit Cost Analysis — BCA) is an evaluation tool that state transportation agencies can use to compare infrastructure project options across transportation modes and gauge if the discounted value of benefits exceed the costs. CBA lets policymakers compare alternative project proposals to a baseline scenario, or status quo case, under which no investments are made. CBA is used to select which proposal is the most sensible investment—ideally, the project that maximizes benefits while minimizing costs should be chosen. As the use of CBA to evaluate projects and grant applications (e.g., TIGER Discretionary Grants) continues to grow, state transportation agencies must gain knowledge of CBA methodologies, especially if they want to remain competitive for federal funding. This study documents historical trends in CBA from literature and past studies, provides background on how CBA’s are performed, and describes the purpose and basic function of CBAs. The researchers investigated CBA applications and programs that the Kentucky Transportation Cabinet (KYTC) could potentially use to prioritize projects and identify other investment opportunities. This report serves as a primer on the basic elements of CBA, describes what costs and benefits are typically incorporated into analysis, and gives an overview of the formulas that are used to derive costs and benefits. In the transportation context, most benefits are derived from travel time savings and crash reductions. Typical costs include construction and subsequent maintenance.Researchers developed a simple workbook application that KYTC personnel can use run a CBA. The workbook calculates present value of costs and benefits and makes both NPV and BCR available to the user

A New Approach for Simulating Galaxy Cluster Properties

We describe a subgrid model for including galaxies into hydrodynamical cosmological simulations of galaxy cluster evolution. Each galaxy construct- or galcon- is modeled as a physically extended object within which star formation, galactic winds, and ram pressure stripping of gas are modeled analytically. Galcons are initialized at high redshift (z~3) after galaxy dark matter halos have formed but before the cluster has virialized. Each galcon moves self-consistently within the evolving cluster potential and injects mass, metals, and energy into intracluster (IC) gas through a well-resolved spherical interface layer. We have implemented galcons into the Enzo adaptive mesh refinement code and carried out a simulation of cluster formation in a LambdaCDM universe. With our approach, we are able to economically follow the impact of a large number of galaxies on IC gas. We compare the results of the galcon simulation with a second, more standard simulation where star formation and feedback are treated using a popular heuristic prescription. One advantage of the galcon approach is explicit control over the star formation history of cluster galaxies. Using a galactic SFR derived from the cosmic star formation density, we find the galcon simulation produces a lower stellar fraction, a larger gas core radius, a more isothermal temperature profile, and a flatter metallicity gradient than the standard simulation, in better agreement with observations.Comment: 4 pages, 2 figures, submitted for publication in ApJ

Pulsar Wind Nebulae in EGRET Error Boxes

A remarkable number of pulsar wind nebulae (PWN) are coincident with EGRET gamma-ray sources. X-ray and radio imaging studies of unidentified EGRET sources have resulted in the discovery of at least 6 new pulsar wind nebulae (PWN). Stationary PWN (SPWN) appear to be associated with steady EGRET sources with hard spectra, typical for gamma-ray pulsars. Their toroidal morphologies can help determine the geometry of the pulsar which is useful for constraining models of pulsed gamma-ray emission. Rapidly moving PWN (RPWN) with more cometary morphologies seem to be associated with variable EGRET sources in regions where the ambient medium is dense compared to what is typical for the ISM.Comment: 8 pages, 5 figures, to appear in the proceedings of "The Multiwavelength Approach to Unidentified Sources", ed. G. Romero & K.S. Chen