651 research outputs found
A Relativistic Description of Gentry's New Redshift Interpretation
We obtain a new expression of the Friedmann-Robertson-Walker metric, which is
an analogue of a static chart of the de Sitter space-time. The reduced metric
contains two functions, and , which are interpreted as,
respectively, the mass function and the gravitational potential. We find that,
near the coordinate origin, the reduced metric can be approximated in a static
form and that the approximated metric function, , satisfies the
Poisson equation. Moreover, when the model parameters of the
Friedmann-Robertson-Walker metric are suitably chosen, the approximated metric
coincides with exact solutions of the Einstein equation with the perfect fluid
matter. We then solve the radial geodesics on the approximated space-time to
obtain the distance-redshift relation of geodesic sources observed by the
comoving observer at the origin. We find that the redshift is expressed in
terms of a peculiar velocity of the source and the metric function, ,
evaluated at the source position, and one may think that this is a new
interpretation of {\it Gentry's new redshift interpretation}.Comment: 11 pages. Submitted to Modern Physics Letters
Performance of a family of omni and steered antennas for mobile satellite applications
The design and performance of a family of vehicle antennas developed at JPL in support of an emerging US Mobile Satellite Service (MSS) system are described. Test results of the antennas are presented. Trends for future development are addressed. Recommendations on design approaches for vehicle antennas of the first generation MSS are discussed
The Effects of Orbital Motion on LISA Time Delay Interferometry
In an effort to eliminate laser phase noise in laser interferometer
spaceborne gravitational wave detectors, several combinations of signals have
been found that allow the laser noise to be canceled out while gravitational
wave signals remain. This process is called time delay interferometry (TDI). In
the papers that defined the TDI variables, their performance was evaluated in
the limit that the gravitational wave detector is fixed in space. However, the
performance depends on certain symmetries in the armlengths that are available
if the detector is fixed in space, but that will be broken in the actual
rotating and flexing configuration produced by the LISA orbits. In this paper
we investigate the performance of these TDI variables for the real LISA orbits.
First, addressing the effects of rotation, we verify Daniel Shaddock's result
that the Sagnac variables will not cancel out the laser phase noise, and we
also find the same result for the symmetric Sagnac variable. The loss of the
latter variable would be particularly unfortunate since this variable also
cancels out gravitational wave signal, allowing instrument noise in the
detector to be isolated and measured. Fortunately, we have found a set of more
complicated TDI variables, which we call Delta-Sagnac variables, one of which
accomplishes the same goal as the symmetric Sagnac variable to good accuracy.
Finally, however, as we investigate the effects of the flexing of the detector
arms due to non-circular orbital motion, we show that all variables, including
the interferometer variables, which survive the rotation-induced loss of
direction symmetry, will not completely cancel laser phase noise when the
armlengths are changing with time. This unavoidable problem will place a
stringent requirement on laser stability of 5 Hz per root Hz.Comment: 12 pages, 2 figure
Appeals
Master of Regional and Community PlanningDepartment of Landscape Architecture/Regional and Community PlanningStephanie A. RolleyAppellate zoning boards provide aggrieved property owners the ability to appeal bulk zoning regulations which otherwise create an undue hardship on the property owner. However, this process when not monitored, can create the following three primary, twentieth-century criticisms: (1) a high number of cases paired with high rates of approval, (2) applicant properties which lack uniqueness, and (3) the ability to issue conditional use permits (Bryden, 1977; Leary, 1957). In order to test if the three criticisms are relevant in twenty-first-century practices, the research developed a record system for reviewing all state statutes; records and analyzes the actions of appellate zoning boards in ten Kansas municipal governments from 2014-2018, and focuses on the decision trends and themes of Manhattan, Kansas, an appellate zoning board currently subject to criticism. Document analysis, coding, and tracking are used to analyze 676 cases and reveal varying trends and themes among Kansas municipal governments. The most significant finding is that Manhattanâs Board of Zoning Appeals out-paces peer municipal governments with a 17% higher rate of approval, 11% of approved cases fail to meet the uniqueness of property standard and a nearly 10% difference in the percentage of cases paired with conditional use permits. These findings support the validity of twentieth-century criticisms of appellate zoning boards and provide Manhattan, Kansas as a case of potential misuse of appellate zoning statutes
Conservation laws for vacuum tetrad gravity
Ten conservation laws in useful polynomial form are derived from a Cartan
form and Exterior Differential System (EDS) for the tetrad equations of vacuum
relativity. The Noether construction of conservation laws for well posed EDS is
introduced first, and an illustration given, deriving 15 conservation laws of
the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS
and tetrad gravity EDS have parallel structures, with their numbers of
dependent variables, numbers of generating 2-forms and generating 3-forms, and
Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding
symmetries with the same Lorentz algebra, and 10 corresponding conservation
laws.Comment: Final version with additional reference
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Brillouin scatter in a hydrodynamic simulation
A numerical method for modeling stimulated Brillouin scatter (SBS) in a hydrodynamic simulation code is discussed. Preliminary results using the model show that scattering is reduced as shorter wavelengths are used and for spherical symmetry that ion heating by SBS is not significant since the ions cool by expansion
Improving the Sensitivity of LISA
It has been shown in the past, that the six Doppler data streams obtained
LISA configuration can be combined by appropriately delaying the data streams
for cancelling the laser frequency noise. Raw laser noise is several orders of
magnitude above the other noises and thus it is essential to bring it down to
the level of shot, acceleration noises. A rigorous and systematic formalism
using the techniques of computational commutative algebra was developed which
generates all the data combinations cancelling the laser frequency noise. The
relevant data combinations form a first module of syzygies. In this paper we
use this formalism for optimisation of the LISA sensitivity by analysing the
noise and signal covariance matrices. The signal covariance matrix, averaged
over polarisations and directions, is calculated for binaries whose frequency
changes at most adiabatically. We then present the extremal SNR curves for all
the data combinations in the module. They correspond to the eigenvectors of the
noise and signal covariance matrices. We construct LISA `network' SNR by
combining the outputs of the eigenvectors which improves the LISA sensitivity
substantially. The maximum SNR curve can yield an improvement upto 70 % over
the Michelson, mainly at high frequencies, while the improvement using the
network SNR ranges from 40 % to over 100 %. Finally, we describe a simple toy
model, in which LISA rotates in a plane. In this analysis, we estimate the
improvement in the LISA sensitivity, if one switches from one data combination
to another as it rotates. Here the improvement in sensitivity, if one switches
optimally over three cyclic data combinations of the eigenvector is about 55 %
on an average over the LISA band-width. The corresponding SNR improvement is 60
%, if one maximises over the module.Comment: 16 pages, 10 figures, Submitted to Class. Quant. Gravit
Time-Delay Interferometry
Equal-arm interferometric detectors of gravitational radiation allow phase
measurements many orders of magnitude below the intrinsic phase stability of
the laser injecting light into their arms. This is because the noise in the
laser light is common to both arms, experiencing exactly the same delay, and
thus cancels when it is differenced at the photo detector. In this situation,
much lower level secondary noises then set overall performance. If, however,
the two arms have different lengths (as will necessarily be the case with
space-borne interferometers), the laser noise experiences different delays in
the two arms and will hence not directly cancel at the detector. In order to
solve this problem, a technique involving heterodyne interferometry with
unequal arm lengths and independent phase-difference readouts has been
proposed. It relies on properly time-shifting and linearly combining
independent Doppler measurements, and for this reason it has been called
Time-Delay Interferometry (or TDI). This article provides an overview of the
theory and mathematical foundations of TDI as it will be implemented by the
forthcoming space-based interferometers such as the Laser Interferometer Space
Antenna (LISA) mission. We have purposely left out from this first version of
our ``Living Review'' article on TDI all the results of more practical and
experimental nature, as well as all the aspects of TDI that the data analysts
will need to account for when analyzing the LISA TDI data combinations. Our
forthcoming ``second edition'' of this review paper will include these topics.Comment: 51 pages, 11 figures. To appear in: Living Reviews. Added conten
Algebraic approach to time-delay data analysis for LISA
Cancellation of laser frequency noise in interferometers is crucial for
attaining the requisite sensitivity of the triangular 3-spacecraft LISA
configuration. Raw laser noise is several orders of magnitude above the other
noises and thus it is essential to bring it down to the level of other noises
such as shot, acceleration, etc. Since it is impossible to maintain equal
distances between spacecrafts, laser noise cancellation must be achieved by
appropriately combining the six beams with appropriate time-delays. It has been
shown in several recent papers that such combinations are possible. In this
paper, we present a rigorous and systematic formalism based on algebraic
geometrical methods involving computational commutative algebra, which
generates in principle {\it all} the data combinations cancelling the laser
frequency noise. The relevant data combinations form the first module of
syzygies, as it is called in the literature of algebraic geometry. The module
is over a polynomial ring in three variables, the three variables corresponding
to the three time-delays around the LISA triangle. Specifically, we list
several sets of generators for the module whose linear combinations with
polynomial coefficients generate the entire module. We find that this formalism
can also be extended in a straight forward way to cancel Doppler shifts due to
optical bench motions. The two modules are infact isomorphic.
We use our formalism to obtain the transfer functions for the six beams and
for the generators. We specifically investigate monochromatic gravitational
wave sources in the LISA band and carry out the maximisiation over linear
combinations of the generators of the signal-to-noise ratios with the frequency
and source direction angles as parameters.Comment: 27 Pages, 6 figure
Sensitivity and parameter-estimation precision for alternate LISA configurations
We describe a simple framework to assess the LISA scientific performance
(more specifically, its sensitivity and expected parameter-estimation precision
for prescribed gravitational-wave signals) under the assumption of failure of
one or two inter-spacecraft laser measurements (links) and of one to four
intra-spacecraft laser measurements. We apply the framework to the simple case
of measuring the LISA sensitivity to monochromatic circular binaries, and the
LISA parameter-estimation precision for the gravitational-wave polarization
angle of these systems. Compared to the six-link baseline configuration, the
five-link case is characterized by a small loss in signal-to-noise ratio (SNR)
in the high-frequency section of the LISA band; the four-link case shows a
reduction by a factor of sqrt(2) at low frequencies, and by up to ~2 at high
frequencies. The uncertainty in the estimate of polarization, as computed in
the Fisher-matrix formalism, also worsens when moving from six to five, and
then to four links: this can be explained by the reduced SNR available in those
configurations (except for observations shorter than three months, where five
and six links do better than four even with the same SNR). In addition, we
prove (for generic signals) that the SNR and Fisher matrix are invariant with
respect to the choice of a basis of TDI observables; rather, they depend only
on which inter-spacecraft and intra-spacecraft measurements are available.Comment: 17 pages, 4 EPS figures, IOP style, corrected CQG versio
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