Water-resource records of Brevard County, Florida

The U. S. Geological Survey made a comprehensive investigation of the water resources of Brevard County from 1954 to 1958. The purposes of this investigation were: (1) to determine the occurrence and chemical quality of water in the streams and lakes, (2) to determine the location and the thickness of aquifers, and (3) to determine the occurrence and chemical quality of the ground water. During the period from 1933 to 1954, water records were collected from a few stream-gaging stations and a few observation wells. The purpose of this report is to present basic data collected during these investigations. (Document has 188 pages.

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

Recent developments in perturbation theory

Rayleigh-Schroeder perturbation theory - degenerate and non-degenerate states - quantum chemistry - other perturbation equation

An extended model of the quantum free-electron laser

Previous models of the quantum regime of operation of the Free Electron Laser (QFEL) have performed an averaging and the application of periodic boundary conditions to the coupled Maxwell - Schrodinger equations over short, resonant wavelength intervals of the interaction. Here, an extended, one-dimensional model of the QFEL interaction is presented in the absence of any such averaging or application of periodic boundary conditions, the absence of the latter allowing electron diffusion processes to be modeled throughout the pulse. The model is used to investigate how both the steady-state (CW) and pulsed regimes of QFEL operation are affected. In the steady-state regime it is found that the electrons are confined to evolve as a 2-level system, similar to the previous QFEL models. In the pulsed regime Coherent Spontaneous Emission (CSE) due to the shape of the electron pulse current distribution is shown to be present in the QFEL regime for the first time. However, unlike the classical case, CSE in the QFEL is damped by the effects of quantum diffusion of the electron wavefunction. Electron recoil from the QFEL interaction can also cause a diffusive drift between the recoiled and non-recoiled parts of the electron pulse wavefunction, effectively removing the recoiled part from the primary electron-radiation interaction.Comment: Submitted to Optics Expres

Positivity of Entropy in the Semi-Classical Theory of Black Holes and Radiation

Quantum stress-energy tensors of fields renormalized on a Schwarzschild background violate the classical energy conditions near the black hole. Nevertheless, the associated equilibrium thermodynamical entropy $\Delta S$ by which such fields augment the usual black hole entropy is found to be positive. More precisely, the derivative of $\Delta S$ with respect to radius, at fixed black hole mass, is found to vanish at the horizon for {\it all} regular renormalized stress-energy quantum tensors. For the cases of conformal scalar fields and U(1) gauge fields, the corresponding second derivative is positive, indicating that $\Delta S$ has a local minimum there. Explicit calculation shows that indeed $\Delta S$ increases monotonically for increasing radius and is positive. (The same conclusions hold for a massless spin 1/2 field, but the accuracy of the stress-energy tensor we employ has not been confirmed, in contrast to the scalar and vector cases). None of these results would hold if the back-reaction of the radiation on the spacetime geometry were ignored; consequently, one must regard $\Delta S$ as arising from both the radiation fields and their effects on the gravitational field. The back-reaction, no matter how "small",Comment: 19 pages, RevTe

The postulates of gravitational thermodynamics

The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.Comment: 28 pages, Revtex, no figures. An important sentence and several minor corrections included. To appear in Physical Review

Field Quantization, Photons and Non-Hermitean Modes

Field quantization in three dimensional unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes in both the cavity and external regions. The cavity non-Hermitean modes (NHM) are treated using the paraxial and monochromaticity approximations. The NHM bi-orthogonality relationships are used in a standard canonical quantization procedure based on introducing generalised coordinates and momenta for the electromagnetic (EM) field. The quantum EM field is equivalent to a set of quantum harmonic oscillators (QHO), associated with either the cavity or the external region NHM. This confirms the validity of the photon model in unstable optical systems, though the annihilation and creation operators for each QHO are not Hermitean adjoints. The quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which is sum of independent QHO Hamiltonians for each NHM, but the external field Hamiltonian also includes a coupling term responsible for external NHM photon exchange processes. Cavity energy gain and loss processes is associated with the non-commutativity of cavity and external region operators, given in terms of surface integrals involving cavity and external region NHM functions on the cavity-external region boundary. The spontaneous decay of a two-level atom inside an unstable cavity is treated using the essential states approach and the rotating wave approximation. Atomic transitions leading to cavity NHM photon absorption have a different coupling constant to those leading to photon emission, a feature resulting from the use of NHM functions. Under certain conditions the decay rate is enhanced by the Petermann factor.Comment: 38 pages, tex, 2 figures, ps. General expression for decay rate added. To be published in Journal of Modern Optic

Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the grand canonical ensemble

The thermodynamical properties of the Reissner-Nordstr\"om-anti-de Sitter black hole in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow us to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and charge. The stability conditions imply that there are thermodynamically stable black hole solutions, under certain conditions. Instantons with negative heat capacity are also found.Comment: 15 pages, 9 figures, Revtex. Published version. Changes: figures added to tex

The influence of steps on the dissociation of NO on Pt surfaces: Temperature-programmed desorption studies of NO adsorption on Pt{211}

Temperature-programmed desorption (TPD) has been used to investigate the adsorption of NO on Pt{211} at 300 K and 120 K. Results show that NO dissociation occurs readily on Pt{211}, as evidenced by the observation of N-2 and N2O in the TPD spectrum. Following adsorption at 120 K three NO TPD peaks at 338, 416, and 503 K are observed, in agreement with previous observations. In combination with data acquired in a recent reflection absorption infrared spectroscopy and density functional theory investigation of NO/Pt{211}, these peaks are assigned to the desorption of NO from an O-NO complex, the recombinative desorption of N and O atoms, and to desorption of a step-bridged NO species, respectively. These assignments are in disagreement with previous work, where the high-temperature NO peak was assigned to the desorption of step bound NO and the two low-temperature peaks were assigned to the desorption of NO from terrace sites. TPD spectra recorded following adsorption at 300 K, with a heating rate of 1 K s(-1), show similar features to those recorded following 120 K adsorption. This is also in disagreement with previous observations, where only two NO TPD peaks were observed following adsorption at room temperature. This disagreement can be accounted for by the different heating rates used in the two experiments. (C) 2003 American Institute of Physics