4,371 research outputs found
A stochastic-Lagrangian particle system for the Navier-Stokes equations
This paper is based on a formulation of the Navier-Stokes equations developed
by P. Constantin and the first author (\texttt{arxiv:math.PR/0511067}, to
appear), where the velocity field of a viscous incompressible fluid is written
as the expected value of a stochastic process. In this paper, we take
copies of the above process (each based on independent Wiener processes), and
replace the expected value with times the sum over these
copies. (We remark that our formulation requires one to keep track of
stochastic flows of diffeomorphisms, and not just the motion of particles.)
We prove that in two dimensions, this system of interacting diffeomorphisms
has (time) global solutions with initial data in the space
\holderspace{1}{\alpha} which consists of differentiable functions whose
first derivative is H\"older continuous (see Section \ref{sGexist} for
the precise definition). Further, we show that as the system
converges to the solution of Navier-Stokes equations on any finite interval
. However for fixed , we prove that this system retains roughly
times its original energy as . Hence the limit
and do not commute. For general flows, we only
provide a lower bound to this effect. In the special case of shear flows, we
compute the behaviour as explicitly.Comment: v3: Typo fixes, and a few stylistic changes. 17 pages, 2 figure
The Dirac Equation Is Separable On The Dyon Black Hole Metric
Using the tetrad formalism, we carry out the separation of variables for the
massive complex Dirac equation in the gravitational and electromagnetic field
of a four-parameter (mass, angular momentum, electric and magnetic charges)
black hole.Comment: 13 page
One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter
The quantum entanglement entropy of an eternal black hole is studied. We
argue that the relevant Euclidean path integral is taken over fields defined on
-fold covering of the black hole instanton. The statement that
divergences of the entropy are renormalized by renormalization of gravitational
couplings in the effective action is proved for non-minimally coupled scalar
matter. The relationship of entanglement and thermodynamical entropies is
discussed.Comment: 17 pages, latex, no figure
The Mystery of the Asymptotic Quasinormal Modes of Gauss-Bonnet Black Holes
We analyze the quasinormal modes of -dimensional Schwarzschild black holes
with the Gauss-Bonnet correction in the large damping limit and show that
standard analytic techniques cannot be applied in a straightforward manner to
the case of infinite damping. However, by using a combination of analytic and
numeric techniques we are able to calculate the quasinormal mode frequencies in
a range where the damping is large but finite. We show that for this damping
region the famous appears in the real part of the quasinormal mode
frequency. In our calculations, the Gauss-Bonnet coupling, , is taken
to be much smaller than the parameter , which is related to the black hole
mass.Comment: 12 pages and 5 figure
Progress in development of tapes and magnets made from Bi-2223 superconductors
Long lengths of (Bi,Pb)2Sr2Ca2Cu3O(x) tapes made by powder-in-tube processing have been wound into coils. Performance of the coils has been measured at temperatures of 4.2 to 77 K, and microstructures have been examined by x-ray diffraction and electron microscopy and then related to superconducting properties. A summary of recent results and an overview of future goals are presented
Total electron concentration of the ionosphere over the magnetic equator
This article does not have an abstract
Conical geometry and quantum entropy of a charged Kerr black hole
We apply the method of conical singularities to calculate the tree-level
entropy and its one-loop quantum corrections for a charged Kerr black hole. The
Euclidean geometry for the Kerr-Newman metric is considered. We show that for
an arbitrary periodization in Euclidean space there exists a conical
singularity at the horizon. Its -function like curvatures are
calculated and are shown to behave similar to the static case. The heat kernel
expansion for a scalar field on this conical space background is derived and
the (divergent) quantum correction to the entropy is obtained. It is argued
that these divergences can be removed by renormalization of couplings in the
tree-level gravitational action in a manner similar to that for a static black
hole.Comment: 22 pages, latex, no figures; minor corrections mad
Accelerated detectors in Dirac vacuum: the effects of horizon fluctuations
We consider an Unruh-DeWitt detector interacting with a massless Dirac field.
Assuming that the detector is moving along an hyperbolic trajectory, we modeled
the effects of fluctuations in the event horizon using a Dirac equation with
random coefficients. First, we develop the perturbation theory for the
fermionic field in a random media. Further we evaluate corrections due to the
randomness in the response function associated to different model detectors.Comment: 19 pages, 1 figur
Quantum Entanglement and Teleportation in Higher Dimensional Black Hole Spacetimes
We study the properties of quantum entanglement and teleportation in the
background of stationary and rotating curved space-times with extra dimensions.
We show that a maximally entangled Bell state in an inertial frame becomes less
entangled in curved space due to the well-known Hawking-Unruh effect. The
degree of entanglement is found to be degraded with increasing the extra
dimensions. For a finite black hole surface gravity, the observer may choose
higher frequency mode to keep high level entanglement. The fidelity of quantum
teleporation is also reduced because of the Hawking-Unruh effect. We discuss
the fidelity as a function of extra dimensions, mode frequency, black hole mass
and black hole angular momentum parameter for both bosonic and fermionic
resources.Comment: 15 pages, 10 figures,contents expande
Asymptotic conservation laws in field theory
A new, general, field theoretic approach to the derivation of asymptotic
conservation laws is presented. In this approach asymptotic conservation laws
are constructed directly from the field equations according to a universal
prescription which does not rely upon the existence of Noether identities or
any Lagrangian or Hamiltonian formalisms. The resulting general expressions of
the conservation laws enjoy important invariance properties and synthesize all
known asymptotic conservation laws, such as the ADM energy in general
relativity.Comment: 13 pages, AMS-TeX, amsppt.sty, revised to give a better exposition
(we hope), and to correct some typesetting error
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