The Microcanonical Functional Integral. I. The Gravitational Field

The gravitational field in a spatially finite region is described as a microcanonical system. The density of states $\nu$ is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by {\it any} real stationary axisymmetric black hole, then in this same approximation $\ln\nu$ is shown to equal 1/4 the area of the black hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of $\nu$ that lead to "imaginary time" functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function.Comment: 29 pages, plain Te

Scheduling Ocean Transportation of Crude Oil

Management Science, 33, p. 335-346. (Nominated for 1987 International Management Science Achievement Award.)The article of record as published may be found at http://links.jstor.org/sici?sici=0025-1909%28198703%2933%3A3%3C335%3ASOTOCO%3E2.0.CO%3B2-FNominated for 1987 International Management Science Achievement Award.A crude oil tankerscheduling problem faced by a major oil company is presented and solved using an elastic set partitioning model. The model takes into account all fleet cost components, including the opportunity cost of ship time, port and canal charges, and demurrage and bunker fuel. The model determines optimalspeeds for the ships and the best routing of ballast (empty) legs, as well as which cargos to load on controlled ships and which to spot charter. All feasible schedules are generated, the cost of each is accurately determined and the best set of schedules is selected. For the problems encountered, optimal integer solutions to set partitioning problems with thousands of binary variables have been achieved in less than a minute

Detection of an Extrasolar Planet Atmosphere

We report high precision spectrophotometric observations of four planetary transits of HD 209458, in the region of the sodium resonance doublet at 589.3 nm. We find that the photometric dimming during transit in a bandpass centered on the sodium feature is deeper by (2.32 +/- 0.57) x 10^{-4} relative to simultaneous observations of the transit in adjacent bands. We interpret this additional dimming as absorption from sodium in the planetary atmosphere, as recently predicted from several theoretical modeling efforts. Our model for a cloudless planetary atmosphere with a solar abundance of sodium in atomic form predicts more sodium absorption than we observe. There are several possibilities that may account for this reduced amplitude, including reaction of atomic sodium into molecular gases and/or condensates, photoionization of sodium by the stellar flux, a low primordial abundance of sodium, or the presence of clouds high in the atmosphere.Comment: 26 pages, 8 figures, accepted by ApJ 2001 November 1

Extracting particle freeze-out phase-space densities and entropies from sources imaged in heavy-ion reactions

The space-averaged phase-space density and entropy per particle are both fundamental observables which can be extracted from the two-particle correlation functions measured in heavy-ion collisions. Two techniques have been proposed to extract the densities from correlation data: either by using the radius parameters from Gaussian fits to meson correlations or by using source imaging, which may be applied to any like pair correlation. We show that the imaging and Gaussian fits give the same result in the case of meson interferometry. We discuss the concept of an equivalent instantaneous source on which both techniques rely. We also discuss the phase-space occupancy and entropy per particle. Finally, we propose an improved formula for the phase-space occupancy that has a more controlled dependence on the uncertainty of the experimentally measured source functions.Comment: 14 pages, final version, to appear PRC. Fixed typos, added refs. for last section, added discussions of imaging and d/p ratio

Modifying the Einstein Equations off the Constraint Hypersuface

A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the gravitational field variables are modified by the addition of terms that are linear and nonlocal in the constraints. These terms are obtained from solutions of the linearized Einstein constraints.Comment: 4 pages, 1 figure, uses REVTe

Solving Defender-Attacker-Defender Models for Infrastructure Defense

In Operations Research, Computing, and Homeland Defense, R.K. Wood and R.F. Dell, editors, INFORMS, Hanover, MD, pp. 28-49.The article of record as published may be located at http://dx.doi.org10.1287/ics.2011.0047This paper (a) describes a defender-attacker-defender sequential game model (DAD) to plan defenses for an infrastructure system that will enhance that system's resilience against attacks for an intelligent adversary, (b) describes a realistic formulation of DAD for defending a transportation network, (c) develops a decomposition algorithm for solving this instance of DAD and others, and (d) demonstrates the solution of a small transportation-network example. A DAD model generally evaluates system operation through the solution of an optimization model, and the decomposition algorithm developed here requires only that this system-operation model be continuous and convex. For example, our transportation-network example incorporates a congestion model with a (convex) nonlinear objective function and linear constraints

Optical trapping with "on-demand" two-photon luminescence using Cr:LiSAF laser with optically addressed saturable Bragg reflector

We demonstrate a diode-pumped Cr:LiSAF laser with controllable and reliable fast switching between its continuous-wave and mode-locked states of operation using an optically-addressed semiconductor Bragg reflector, permitting dyed microspheres to be continuously trapped and monitored using a standard microscope imaging and on-demand two-photon-excited luminescence techniques

Determining conductivity and mobility values of individual components in multiphase composite Cu_(1.97)Ag_(0.03)Se

The intense interest in phase segregation in thermoelectrics as a means to reduce the lattice thermal conductivity and to modify the electronic properties from nanoscale size effects has not been met with a method for separately measuring the properties of each phase assuming a classical mixture. Here, we apply effective medium theory for measurements of the in-line and Hall resistivity of a multiphase composite, in this case Cu_(1.97) Ag_(0.03)Se. The behavior of these properties with magnetic field as analyzed by effective medium theory allows us to separate the conductivity and charge carrier mobility of each phase. This powerful technique can be used to determine the matrix properties in the presence of an unwanted impurity phase, to control each phase in an engineered composite, and to determine the maximum carrier concentration change by a given dopant, making it the first step toward a full optimization of a multiphase thermoelectric material and distinguishing nanoscale effects from those of a classical mixture

Optimized Discretization of Sources Imaged in Heavy-Ion Reactions

We develop the new method of optimized discretization for imaging the relative source from two particle correlation functions. In this method, the source resolution depends on the relative particle separation and is adjusted to available data and their errors. We test the method by restoring assumed pp sources and then apply the method to pp and IMF data. In reactions below 100 MeV/nucleon, significant portions of the sources extend to large distances (r > 20 fm). The results from the imaging show the inadequacy of common Gaussian source-parametrizations. We establish a simple relation between the height of the pp correlation function and the source value at short distances, and between the height and the proton freeze-out phase-space density.Comment: 36 pages (inc. 9 figures), RevTeX, uses epsf.sty. Submitted to Phys. Rev.

Effective Potential of a Black Hole in Thermal Equilibrium with Quantum Fields

Expectation values of one-loop renormalized thermal equilibrium stress-energy tensors of free conformal scalars, spin-${1 \over 2}$ fermions and U(1) gauge fields on a Schwarzschild black hole background are used as sources in the semi-classical Einstein equation. The back-reaction and new equilibrium metric are solved for at $O({\hbar})$ for each spin field. The nature of the modified black hole spacetime is revealed through calculations of the effective potential for null and timelike orbits. Significant novel features affecting the motions of both massive and massless test particles show up at lowest order in $\epsilon= (M_{Pl}/M)^2 < 1$, where $M$ is the renormalized black hole mass, and $M_{Pl}$ is the Planck mass. Specifically, we find the tendency for \underline{stable} circular photon orbits, an increase in the black hole capture cross sections, and the existence of a gravitationally repulsive region associated with the black hole which is generated from the U(1) back-reaction. We also consider the back-reaction arising from multiple fields, which will be useful for treating a black hole in thermal equilibrium with field ensembles belonging to gauge theories.Comment: 25 pages (not including seven figures), VAND-TH-93-6. Typed in Latex, uses RevTex macro