Dynamical symmetry enhancement near N=2, D=4 gauged supergravity horizons

We show that all smooth Killing horizons with compact horizon sections of 4-dimensional gauged N=2 supergravity coupled to any number of vector multiplets preserve $2 c_1({\cal K})+4 \ell$ supersymmetries, where ${\cal K}$ is a pull-back of the Hodge bundle of the special K\"ahler manifold on the horizon spatial section. We also demonstrate that all such horizons with $c_1({\cal K})=0$ exhibit an SL(2,R) symmetry and preserve either 4 or 8 supersymmetries. If the orbits of the SL(2,R) symmetry are 2-dimensional, the horizons are warped products of AdS2 with the horizon spatial section. Otherwise, the horizon section admits an isometry which preserves all the fields. The proof of these results is centered on the use of index theorem in conjunction with an appropriate generalization of the Lichnerowicz theorem for horizons that preserve at least one supersymmetry. In all $c_1({\cal K})=0$ cases, we specify the local geometry of spatial horizon sections and demonstrate that the solutions are determined by first order non-linear ordinary differential equations on some of the fields.Comment: 60 pages, late

Cosmological Solutions, a New Wick-Rotation, and the First Law of Thermodynamics

We present a modified implementation of the Euclidean action formalism suitable for studying the thermodynamics of a class of cosmological solutions containing Killing horizons. To obtain a real metric of definite signature, we perform a `triple Wick-rotation' by analytically continuing all space-like directions. The resulting Euclidean geometry is used to calculate the Euclidean on-shell action, which defines a thermodynamic potential. We show that for the vacuum de Sitter solution, planar solutions of Einstein-Maxwell theory and a previously found class of cosmological solutions of N = 2 supergravity, this thermodynamic potential can be used to define an internal energy which obeys the first law of thermodynamics. Our approach is complementary to, but consistent with the isolated horizon formalism. For planar Einstein-Maxwell solutions, we find dual solutions in Einstein-anti-Maxwell theory where the sign of the Maxwell term is reversed. These solutions are planar black holes, rather than cosmological solutions, but give rise, upon a standard Wick-rotation to the same Euclidean action and thermodynamic relations

Designers' unified cost model

The Structures Technology Program Office (STPO) at NASA LaRC has initiated development of a conceptual and preliminary designers' cost prediction model. The model will provide a technically sound method for evaluating the relative cost of different composite structural designs, fabrication processes, and assembly methods that can be compared to equivalent metallic parts or assemblies. The feasibility of developing cost prediction software in a modular form for interfacing with state-of-the-art preliminary design tools and computer aided design programs is being evaluated. The goal of this task is to establish theoretical cost functions that relate geometric design features to summed material cost and labor content in terms of process mechanics and physics. The output of the designers' present analytical tools will be input for the designers' cost prediction model to provide the designer with a database and deterministic cost methodology that allows one to trade and synthesize designs with both cost and weight as objective functions for optimization. This paper presents the team members, approach, goals, plans, and progress to date for development of COSTADE (Cost Optimization Software for Transport Aircraft Design Evaluation)

M-Horizons

We solve the Killing spinor equations and determine the near horizon geometries of M-theory that preserve at least one supersymmetry. The M-horizon spatial sections are 9-dimensional manifolds with a Spin(7) structure restricted by geometric constraints which we give explicitly. We also provide an alternative characterization of the solutions of the Killing spinor equation, utilizing the compactness of the horizon section and the field equations, by proving a Lichnerowicz type of theorem which implies that the zero modes of a Dirac operator coupled to 4-form fluxes are Killing spinors. We use this, and the maximum principle, to solve the field equations of the theory for some special cases and present some examples.Comment: 36 pages, latex. Reference added, minor typos correcte

Turbsim: Reliability-based wind turbine simulator,

Abstract-Wind turbine farms are an effective generator of electricity in windy parts of the world, with prices progressing to levels competitive with other sources. Choosing the correct turbine for a given installation requires significant engineering and the current trend leads towards groups of large horizontal axis turbines. Unfortunately, large wind turbines have to contend with large forces and other sources of failure. With the new push to move generation farms offshore where they are less accessible, the issue of reliability becomes more critical. This work investigates the impact of reliability in a life-cycle analysis simulation of a theoretical wind farm in Massachusetts based upon reliability information from a number of academic sources. The simulator, TurbSim, is designed with significant modularity to enable reliability simulation of any turbine with available wind information. Our simulation of a turbine indicated that reliability makes a small but noticeable impact of 1.24% in its output

Cosmological solutions, a new wick-rotation, and the first law of thermodynamics

We present a modified implementation of the Euclidean action formalism suitable for studying the thermodynamics of a class of cosmological solutions containing Killing horizons. To obtain a real metric of definite signature, we perform a `triple Wick-rotation' by analytically continuing all space-like directions. The resulting Euclidean geometry is used to calculate the Euclidean on-shell action, which defines a thermodynamic potential. We show that for the vacuum de Sitter solution, planar solutions of Einstein-Maxwell theory and a previously found class of cosmological solutions of N = 2 supergravity, this thermodynamic potential can be used to define an internal energy which obeys the first law of thermodynamics. Our approach is complementary to, but consistent with the isolated horizon formalism. For planar Einstein-Maxwell solutions, we find dual solutions in Einstein-anti-Maxwell theory where the sign of the Maxwell term is reversed. These solutions are planar black holes, rather than cosmological solutions, but give rise, upon a standard Wick-rotation to the same Euclidean action and thermodynamic relations.Comment: 80 pages including 27 pages of appendices, 10 figures. Revised version: extended discussion of related results, several references added. Accepted for publication in JHE

Quantization of maximally-charged slowly-moving black holes

We discuss the quantization of a system of slowly-moving extreme Reissner-Nordstrom black holes. In the near-horizon limit, this system has been shown to possess an SL(2,R) conformal symmetry. However, the Hamiltonian appears to have no well-defined ground state. This problem can be circumvented by a redefinition of the Hamiltonian due to de Alfaro, Fubini and Furlan (DFF). We apply the Faddeev-Popov quantization procedure to show that the Hamiltonian with no ground state corresponds to a gauge in which there is an obstruction at the singularities of moduli space requiring a modification of the quantization rules. The redefinition of the Hamiltonian a la DFF corresponds to a different choice of gauge. The latter is a good gauge leading to standard quantization rules. Thus, the DFF trick is a consequence of a standard gauge-fixing procedure in the case of black hole scattering.Comment: Corrected errors in the gauge-fixing procedur

On the Bogomol'nyi bound in Einstein-Maxwell-dilaton gravity

It has been shown that the 4-dimensional Einstein-Maxwell-dilaton theory allows a Bogomol'nyi-type inequality for an arbitrary dilaton coupling constant $\alpha$, and that the bound is saturated if and only if the (asymptotically flat) spacetime admits a nontrivial spinor satisfying the gravitino and the dilatino Killing spinor equations. The present paper revisits this issue and argues that the dilatino equation fails to ensure the dilaton field equation unless the solution is purely electric/magnetic, or the dilaton coupling constant is given by $\alpha=0, \sqrt 3$, corresponding to the Brans-Dicke-Maxwell theory and the Kaluza-Klein reduction of 5-dimensional vacuum gravity, respectively. A systematic classification of the supersymmetric solutions reveals that the solution can be rotating if and only if the solution is dyonic or the coupling constant is given by $\alpha=0, \sqrt 3$. This implies that the theory with $\alpha \ne 0, \sqrt 3$ cannot be embedded into supergravity except for the static truncation. Physical properties of supersymmetric solutions are explored from various points of view.Comment: v2: 23 pages, typos corrected, minor modifications, to appear in CQ

Equal charge black holes and seven dimensional gauged supergravity

We present various supergravity black holes of different dimensions with some U(1) charges set equal in a simple, common form. Black hole solutions of seven dimensional U(1)^2 gauged supergravity with three independent angular momenta and two equal U(1) charges are obtained. We investigate the thermodynamics and the BPS limit of this solution, and find that there are rotating supersymmetric black holes without naked closed timelike curves. There are also supersymmetric topological soliton solutions without naked closed timelike curves that have a smooth geometry.Comment: 24 pages; v2, v3: minor change

Coherent Propagation of Polaritons in Semiconductor Heterostructures: Nonlinear Pulse Transmission in Theory and Experiment

The influence of coherent optical nonlinearities on polariton propagation effects is studied within a theory-experiment comparison. A novel approach that combines a microscopic treatment of the boundary problem in a sample of finite thickness with excitonic and biexcitonic nonlinearities is introduced. Light-polarization dependent spectral changes are analyzed for single-pulse transmission and pump-probe excitation