940 research outputs found
High gradient directional solidification furnace
A high gradient directional solidification furnace is disclosed which includes eight thermal zones throughout the length of the furnace. In the hot end of the furnace, furnace elements provide desired temperatures. These elements include Nichrome wire received in a grooved tube which is encapsulated y an outer alumina core. A booster heater is provided in the hot end of the furnace which includes toroidal tungsten/rhenium wire which has a capacity to put heat quickly into the furnace. An adiabatic zone is provided by an insulation barrier to separate the hot end of the furnace from the cold end. The old end of the furnace is defined by additional heating elements. A heat transfer plate provides a means by which heat may be extracted from the furnace and conducted away through liquid cooled jackets. By varying the input of heat via the booster heater and output of heat via the heat transfer plate, a desired thermal gradient profile may be provided
General purpose rocket furnace
A multipurpose furnace for space vehicles used for material processing experiments in an outer space environment is described. The furnace contains three separate cavities designed to process samples of the widest possible range of materials and thermal requirements. Each cavity contains three heating elements capable of independent function under the direction of an automatic and programmable control system. A heat removable mechanism is also provided for each cavity which operates in conjunction with the control system for establishing an isothermally heated cavity or a wide range of thermal gradients and cool down rates. A monitoring system compatible with the rocket telemetry provides furnace performance and sample growth rate data throughout the processing cycle
Dirty black holes: Entropy versus area
Considerable interest has recently been expressed in the entropy versus area
relationship for ``dirty'' black holes --- black holes in interaction with
various classical matter fields, distorted by higher derivative gravity, or
infested with various forms of quantum hair. In many cases it is found that the
entropy is simply related to the area of the event horizon: S = k
A_H/(4\ell_P^2). For example, the ``entropy = (1/4) area'' law *holds* for:
Schwarzschild, Reissner--Nordstrom, Kerr--Newman, and dilatonic black holes. On
the other hand, the ``entropy = (1/4) area'' law *fails* for: various types of
(Riemann)^n gravity, Lovelock gravity, and various versions of quantum hair.
The pattern underlying these results is less than clear. This paper
systematizes these results by deriving a general formula for the entropy: S =
{k A_H/(4\ell_P^2)}
+ {1/T_H} \int_\Sigma [rho - {L}_E ] K^\mu d\Sigma_\mu
+ \int_\Sigma s V^\mu d\Sigma_\mu. (K^\mu is the timelike Killing vector,
V^\mu the four velocity of a co--rotating observer.) If no hair is present the
validity of the ``entropy = (1/4) area'' law reduces to the question of whether
or not the Lorentzian energy density for the system under consideration is
formally equal to the Euclideanized Lagrangian. ****** To appear in Physical
Review D 15 July 1993 ****** [Stylistic changes, minor typos fixed, references
updated, discussion of the Born-Infeld system excised]Comment: plain LaTeX, 17 pages, minor revision
Correspondence between Jordan-Einstein frames and Palatini-metric formalisms
We discuss the conformal symmetry between Jordan and Einstein frames
considering their relations with the metric and Palatini formalisms for
modified gravity. Appropriate conformal transformations are taken into account
leading to the evident connection between the gravitational actions in the two
mentioned frames and the Hilbert-Einstein action with a cosmological constant.
We show that the apparent differences between Palatini and metric formalisms
strictly depend on the representation while the number of degrees of freedom is
preserved. This means that the dynamical content of both formalism is
identical.Comment: 6 pages, to appear in Mod. Phys. Lett.
Uniform polynomial rates of convergence for a class of L\'evy-driven controlled SDEs arising in multiclass many-server queues
We study the ergodic properties of a class of controlled stochastic
differential equations (SDEs) driven by -stable processes which arise
as the limiting equations of multiclass queueing models in the Halfin-Whitt
regime that have heavy-tailed arrival processes. When the safety staffing
parameter is positive, we show that the SDEs are uniformly ergodic and enjoy a
polynomial rate of convergence to the invariant probability measure in total
variation, which is uniform over all stationary Markov controls resulting in a
locally Lipschitz continuous drift. We also derive a matching lower bound on
the rate of convergence (under no abandonment). On the other hand, when all
abandonment rates are positive, we show that the SDEs are exponentially ergodic
uniformly over the above-mentioned class of controls. Analogous results are
obtained for L\'evy-driven SDEs arising from multiclass many-server queues
under asymptotically negligible service interruptions. For these equations, we
show that the aforementioned ergodic properties are uniform over all stationary
Markov controls. We also extend a key functional central limit theorem
concerning diffusion approximations so as to make it applicable to the models
studied here
Quantum Cosmology for a Quadratic Theory of Gravity
For pure fourth order () quantum cosmology the
Wheeler-DeWitt equation is solved exactly for the closed homogeneous and
isotropic model. It is shown that by imposing as boundary condition that at the origin of the universe the wave functions behave as suggested by
Vilenkin.Comment: 13 pages, latex,no figure
Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations
We analyze the tensor mode perturbations of static, spherically symmetric
solutions of the Einstein equations with a quadratic Gauss-Bonnet term in
dimension . We show that the evolution equations for this type of
perturbations can be cast in a Regge-Wheeler-Zerilli form, and obtain the exact
potential for the corresponding Schr\"odinger-like stability equation. As an
immediate application we prove that for and , the sign
choice for the Gauss-Bonnet coefficient suggested by string theory, all
positive mass black holes of this type are stable. In the exceptional case , we find a range of parameters where positive mass asymptotically flat
black holes, with regular horizon, are unstable. This feature is found also in
general for .Comment: 7 pages, 1 figure, minor corrections, references adde
Extended Gravity Theories and the Einstein-Hilbert Action
I discuss the relation between arbitrarily high-order theories of gravity and
scalar-tensor gravity at the level of the field equations and the action. I
show that -order gravity is dynamically equivalent to Brans-Dicke
gravity with an interaction potential for the Brans-Dicke field and further
scalar fields. This scalar-tensor action is then conformally equivalent to the
Einstein-Hilbert action with scalar fields. This clarifies the nature and
extent of the conformal equivalence between extended gravity theories and
general relativity with many scalar fields.Comment: 12 pages, Plain Latex, SUSSEX-AST-93/7-
On the fate of singularities and horizons in higher derivative gravity
We study static spherically symmetric solutions of high derivative gravity
theories, with 4, 6, 8 and even 10 derivatives. Except for isolated points in
the space of theories with more than 4 derivatives, only solutions that are
nonsingular near the origin are found. But these solutions cannot smooth out
the Schwarzschild singularity without the appearance of a second horizon. This
conundrum, and the possibility of singularities at finite r, leads us to study
numerical solutions of theories truncated at four derivatives. Rather than two
horizons we are led to the suggestion that the original horizon is replaced by
a rapid nonsingular transition from weak to strong gravity. We also consider
this possibility for the de Sitter horizon.Comment: 15 pages, 3 figures, improvements and references added, to appear in
PR
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