1,112 research outputs found
Failure detection and isolation investigation for strapdown skew redundant tetrad laser gyro inertial sensor arrays
The degree to which flight-critical failures in a strapdown laser gyro tetrad sensor assembly can be isolated in short-haul aircraft after a failure occurrence has been detected by the skewed sensor failure-detection voting logic is investigated along with the degree to which a failure in the tetrad computer can be detected and isolated at the computer level, assuming a dual-redundant computer configuration. The tetrad system was mechanized with two two-axis inertial navigation channels (INCs), each containing two gyro/accelerometer axes, computer, control circuitry, and input/output circuitry. Gyro/accelerometer data is crossfed between the two INCs to enable each computer to independently perform the navigation task. Computer calculations are synchronized between the computers so that calculated quantities are identical and may be compared. Fail-safe performance (identification of the first failure) is accomplished with a probability approaching 100 percent of the time, while fail-operational performance (identification and isolation of the first failure) is achieved 93 to 96 percent of the time
Analysis of Fourier transform valuation formulas and applications
The aim of this article is to provide a systematic analysis of the conditions
such that Fourier transform valuation formulas are valid in a general
framework; i.e. when the option has an arbitrary payoff function and depends on
the path of the asset price process. An interplay between the conditions on the
payoff function and the process arises naturally. We also extend these results
to the multi-dimensional case, and discuss the calculation of Greeks by Fourier
transform methods. As an application, we price options on the minimum of two
assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ
The Radon transform and its dual for limits of symmetric spaces
The Radon transform and its dual are central objects in geometric analysis on
Riemannian symmetric spaces of the noncompact type. In this article we study
algebraic versions of those transforms on inductive limits of symmetric spaces.
In particular, we show that normalized versions exists on some spaces of
regular functions on the limit. We give a formula for the normalized transform
using integral kernels and relate them to limits of double fibration transforms
on spheres
Gauge Theories with Cayley-Klein and Gauge Groups
Gauge theories with the orthogonal Cayley-Klein gauge groups and
are regarded. For nilpotent values of the contraction
parameters these groups are isomorphic to the non-semisimple Euclid,
Newton, Galilei groups and corresponding matter spaces are fiber spaces with
degenerate metrics. It is shown that the contracted gauge field theories
describe the same set of fields and particle mass as gauge
theories, if Lagrangians in the base and in the fibers all are taken into
account. Such theories based on non-semisimple contracted group provide more
simple field interactions as compared with the initial ones.Comment: 14 pages, 5 figure
Stress Tensor Correlators in the Schwinger-Keldysh Formalism
We express stress tensor correlators using the Schwinger-Keldysh formalism.
The absence of off-diagonal counterterms in this formalism ensures that the +-
and -+ correlators are free of primitive divergences. We use dimensional
regularization in position space to explicitly check this at one loop order for
a massless scalar on a flat space background. We use the same procedure to show
that the ++ correlator contains the divergences first computed by `t Hooft and
Veltman for the scalar contribution to the graviton self-energy.Comment: 14 pages, LaTeX 2epsilon, no figures, revised for publicatio
Motion-Induced Radiation from a Dynamically Deforming Mirror
A path integral formulation is developed to study the spectrum of radiation
from a perfectly reflecting (conducting) surface. It allows us to study
arbitrary deformations in space and time. The spectrum is calculated to second
order in the height function. For a harmonic traveling wave on the surface, we
find many different regimes in which the radiation is restricted to certain
directions. It is shown that high frequency photons are emitted in a beam with
relatively low angular dispersion whose direction can be controlled by the
mechanical deformations of the plate.Comment: 4 pages, 2 eps figues included, final version as appeared in PR
Completeness of evanescent modes in layered dielectrics
In the presence of a dielectric slab, the modes of the free electromagnetic field comprise traveling modes, consisting of incoming, reflected, and transmitted parts, as well as trapped modes that are subject to repeated total internal reflection and emerge as evanescent field outside the slab. Traveling modes have a continuous range of frequencies, but trapped modes occur only at certain discrete frequencies. We solve the problem of which relative weight to use when summing over all modes, as commonly required in perturbative calculations. We demonstrate the correctness of our method by showing the completeness of electromagnetic field modes in the presence of a dielectric slab. We derive a convenient method of summing over all modes by means of a single contour integral, which is very useful in standard quantum electrodynamic calculations
Fluctuations of the Retarded Van der Waals Force
The retarded Van der Waals force between a polarizable particle and a
perfectly conducting plate is re-examined. The expression for this force given
by Casimir and Polder represents a mean force, but there are large fluctuations
around this mean value on short time scales which are of the same order of
magnitude as the mean force itself. However, these fluctuations occur on time
scales which are typically of the order of the light travel time between the
atom and the plate. As a consequence, they will not be observed in an
experiment which measures the force averaged over a much longer time. In the
large time limit, the magnitude of the mean squared velocity of a test particle
due to this fluctuating Van der Waals force approaches a constant, and is
similar to a Brownian motion of a test particle in an thermal bath with an
effective temperature. However the fluctuations are not isotropic in this case,
and the shift in the mean square velocity components can even be negative. We
interpret this negative shift to correspond to a reduction in the velocity
spread of a wavepacket. The force fluctuations discussed in this paper are
special case of the more general problem of stress tensor fluctuations. These
are of interest in a variety of areas fo physics, including gravity theory.
Thus the effects of Van der Waals force fluctuations serve as a useful model
for better understanding quantum effects in gravity theory.Comment: 14 pages, no figure
Quantum Electrodynamics near a Huttner-Barnett dielectric
We build up a consistent theory of quantum electrodynamics in the presence of
macroscopic polarizable media. We use the Huttner-Barnett model of a dispersive
and absorbing dielectric medium and formulate the theory in terms of
interacting quantum fields. We integrate out the damped polaritons by using
diagrammatic techniques and find an exact expression for the displacement field
(photon) propagator in the presence of a dispersive and absorbing dielectric
half-space. This opens a new route to traceable perturbative calculations of
the same kind as in free-space quantum electrodynamics. As a worked-through
example we consider the interaction of a neutral atom with a dispersive and
absorbing dielectric half-space. For that we use the multipolar coupling
of the atomic dipole moment to the
electromagnetic displacement field. We apply the newly developed formalism to
calculate the one-loop correction to the atomic electron propagator and find
the energy-level shift and changes in the spontaneous decay rates for a neutral
atom close to an absorptive dielectric mirror.Comment: 25 pages, 4 figure
On an exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions
We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein
condensate which has dipole-dipole interactions as well as the usual s-wave
contact interaction, in a harmonic trap. Remarkably, despite the non-local
anisotropic nature of the dipolar interaction the solution is an inverted
parabola, as in the pure s-wave case, but with a different aspect ratio.
Various properties such as electrostriction and stability are discussed.Comment: 11 pages, 5 figure
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