Entropy and Temperature of Black 3-Branes

We consider slightly non-extremal black 3-branes of type IIB supergravity and show that their Bekenstein-Hawking entropy agrees, up to a mysterious factor, with an entropy derived by counting non-BPS excitations of the Dirichlet 3-brane. These excitations are described in terms of the statistical mechanics of a 3+1 dimensional gas of massless open string states. This is essentially the classic problem of blackbody radiation. The blackbody temperature is related to the temperature of the Hawking radiation. We also construct a solution of type IIB supergravity describing a 3-brane with a finite density of longitudinal momentum. For extremal momentum-carrying 3-branes the horizon area vanishes. This is in agreement with the fact that the BPS entropy of the momentum-carrying Dirichlet 3-branes is not an extensive quantity.Comment: 10 pages, LaTeX, minor revisions. v3: version that appeared in PR

Potential markets for a satellite-based mobile communications system

The objective of the study was to define the market needs for improved land mobile communications systems. Within the context of this objective, the following goals were set: (1) characterize the present mobile communications industry; (2) determine the market for an improved system for mobile communications; and (3) define the system requirements as seen from the potential customer's viewpoint. The scope of the study was defined by the following parameters: (1) markets were confined to U.S. and Canada; (2) range of operation generally exceeded 20 miles, but this was not restrictive; (3) the classes of potential users considered included all private sector users, and non-military public sector users; (4) the time span examined was 1975 to 1985; and (5) highly localized users were generally excluded - e.g., taxicabs, and local paging

A Parameterization of Polynomials on Distributed States and a PIE Representation of Nonlinear PDEs

Partial Integral Equations (PIEs) have previously been used to represent systems of linear (1D) Partial Differential Equations (PDEs) with homogeneous Boundary Conditions (BCs), facilitating analysis and simulation of such distributed-state systems. In this paper, we extend these result to derive an equivalent PIE representation of scalar-valued, 1D, polynomial PDEs, with linear, homogoneous BCs. To derive this PIE representation of polynomial PDEs, we first propose a new definition of polynomials on distributed states $\mathbf{u}\in L_2[a,b]$, that naturally generalizes the concept of polynomials on finite-dimensional states to infinite dimensions. We then define a subclass of distributed polynomials that is parameterized by Partial Integral (PI) operators. We prove that this subclass of polynomials is closed under addition and multiplication, providing formulae for computing the sums and products of such polynomials. Applying these results, we then show how a large class of polynomial PDEs can be represented in terms of distributed PI polynomials, proving equivalence of solutions of the resulting PIE representation to those of the original PDE. Finally, parameterizing quadratic Lyapunov functions by PI operators as well, we formulate a stability test for quadratic PDEs as a linear operator inequality optimization problem, which can be solved using the PIETOOLS software suite. We illustrate how this framework can be used to test stability of several common nonlinear PDEs

A PIE Representation of Coupled Linear 2D PDEs and Stability Analysis using LPIs

We introduce a Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in two spatial variables. PIEs are an algebraic state-space representation of infinite-dimensional systems and have been used to model 1D PDEs and time-delay systems without continuity constraints or boundary conditions -- making these PIE representations amenable to stability analysis using convex optimization. To extend the PIE framework to 2D PDEs, we first construct an algebra of Partial Integral (PI) operators on the function space L_2[x,y], providing formulae for composition, adjoint, and inversion. We then extend this algebra to R^n x L_2[x] x L_2[y] x L_2[x,y] and demonstrate that, for any suitable coupled, linear PDE in 2 spatial variables, there exists an associated PIE whose solutions bijectively map to solutions of the original PDE -- providing conversion formulae between these representations. Next, we use positive matrices to parameterize the convex cone of 2D PI operators -- allowing us to optimize PI operators and solve Linear PI Inequality (LPI) feasibility problems. Finally, we use the 2D LPI framework to provide conditions for stability of 2D linear PDEs. We test these conditions on 2D heat and wave equations and demonstrate that the stability condition has little to no conservatism

A PIE Representation of Delayed Coupled Linear ODE-PDE Systems and Stability Analysis using Convex Optimization

Partial Integral Equations (PIEs) have been used to represent both systems with delay and systems of Partial Differential Equations (PDEs) in one or two spatial dimensions. In this paper, we show that these results can be combined to obtain a PIE representation of any suitably well-posed 1D PDE model with constant delay. In particular, we represent these delayed PDE systems as coupled systems of 1D and 2D PDEs, proving that a PIE representation of both the 1D and 2D subsystems can be derived. Taking the feedback interconnection of these PIE representations, we then obtain a 2D PIE representation of the 1D PDE with delay. We show that this PIE representation can be coupled to that of an Ordinary Differential Equation (ODE) with delay, to obtain a PIE representation of delayed linear ODE-PDE systems. Next, based on the PIE representation, we formulate the problem of stability analysis as a Linear Operator Inequality (LPI) optimization problem which can be solved using the PIETOOLS software suite. We apply the result to several examples from the existing literature involving delay in the dynamics as well as the boundary conditions of the PDE

Hawking Radiation from Non-Extremal D1-D5 Black Hole via Anomalies

We take the method of anomaly cancellation for the derivation of Hawking radiation initiated by Robinson and Wilczek, and apply it to the non-extremal five-dimensional D1-D5 black hole in string theory. The fluxes of the electric charge flow and the energy-momentum tensor from the black hole are obtained. They are shown to match exactly with those of the two-dimensional black body radiation at the Hawking temperature.Comment: 14 page

Manipulations of egg-gallery length to vary brood density in spruce beetle, Dendroctonus rufipennis (Coleoptera: Scolytidae): Effects on brood survival and quality

Different brood densities were produced under a constant bark surface area of the spruce host, by excising egg-producing female <i>Dendroctonus rufipennis</i> from the host material after they had excavated galleries of specified lengths. This procedure allowed a constant attack density. The numbers of adult progeny produced/cm of egg-gallery were significantly greater from bark slabs with short galleries and low densities: the sizes (pronotal widths) of adult progeny of both sexes were also significantly greater from low than from high densities; and the distribution patterns of chromatin differed significantly among high, medium and low densities

Spacetime and the Holographic Renormalization Group

Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our ``interior'' theories is described by a renormalization group equation. The dependence of these flows on the foliation of space encodes bulk geometry.Comment: 12 page