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, $M(T,R)$ and $\Psi(T,R)$, 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, $\Psi(R)$, 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, $\Psi(R)$, 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 Manhattan’s 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

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

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

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

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