460 research outputs found
Rigid motions in Einstein spaces
Rigid motion in Einstein space-time using dyadic formulation of general relativit
The implications of precise timekeeping of Doppler gravitational wave observations
Gravitational radiation from galactic and extragalactic astrophysical sources will induce spatial strains in the solar system, strains which can be measured directly by the Doppler radio link to distant spacecraft. Current noise sources in Pioneer and Voyager Doppler data are delineated and a comparison is made with expected signal levels from gravitational wave sources. The main conclusion is that it is possible to detect gravitational radiation with current DSN hydrogen maser systems stable in fractional frequency + or - 2 x 10 to the minus 14th power over 1000 sec. In the future, however, a serious Doppler observational program in gravitational wave astronomy will require frequency systems stable to at least 10 to the minus 16th power, but at the same time the current single frequency S-band uplink transmission will have to be replaced by a dual frequency capability
SyZyGy: A Straight Interferometric Spacecraft System for Gravity Wave Observations
We apply TDI, unfolding the general triangular configuration, to the special
case of a linear array of three spacecraft. We show that such an array
("SyZyGy") has, compared with an equilateral triangle GW detector of the same
scale, degraded (but non-zero) sensitivity at low-frequencies (f<<c/(arrany
size)) but similar peak and high-frequency sensitivities to GWs. Sensitivity
curves are presented for SyZyGys having various arm-lengths. A number of
technical simplifications result from the linear configuration. These include
only one faceted (e.g., cubical) proof mass per spacecraft, intra-spacecraft
laser metrology needed only at the central spacecraft, placement in a single
appropriate orbit can reduce Doppler drifts so that no laser beam modulation is
required for ultra-stable oscillator noise calibration, and little or no
time-dependent articulation of the telescopes to maintain pointing. Because
SyZyGy's sensitivity falls off more sharply at low frequency than that of an
equilateral triangular array, it may be more useful for GW observations in the
band between those of ground-based interferometers (10-2000 Hz) and LISA (.1
mHz-.1 Hz). A SyZyGy with ~1 light- second scale could, for the same
instrumental assumptions as LISA, make obseervations in this intermediate
frequency GW band with 5 sigma sensitivity to sinusoidal waves of ~2.5 x 10^-23
in a year's integration.Comment: 13 pages, 6 figures; typos corrected, figure modified, references
adde
Hyperbolic Equations for Vacuum Gravity Using Special Orthonormal Frames
By adopting Nester's higher dimensional special orthonormal frames (HSOF) the
tetrad equations for vacuum gravity are put into first order symmetric
hyperbolic (FOSH) form with constant coefficients, independent of any time
slicing or coordinate specialization.Comment: 14 pages, 3 figures, LaTeX, 13 macros. CQG 14 (1997) 1237-1247 has
algebraic errors. +/- signs in Equations (2), (4) and (5) are here corrected,
and factors of 2 added to Eqs. (18) and (19
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
RECOGNITION OF TAXONOMICALLY SIGNIFICANT CLUSTERS NEAR THE SPECIES LEVEL, USING COMPUTATIONALLY INTENSE METHODS, WITH EXAMPLES FROM THE STEPHANODISCUS NIAGARAE COMPLEX (BACILLARIOPHYCEAE) 1
Since the early 1960s, numerical techniques have produced a wide variety of methods to suggest classifications of organisms based on quantitative measurements. A long-recognized shortcoming of these methods is that they will suggest classifications for any group of organisms and any set of measurements, whether or not the clusters in the suggested classification have any natural meaning or significance. Some progress has been made in assessing the reality of clusters determined by various methods. Data simulated to reflect known cluster structure have been used to test the accuracy of different methods, Various methods have been applied to the same data sets to compare how well they realize various desirable properties. Here we define a data-based model of randomness to represent what might be meant by âno natural basis for subdivision into clustersâ and use it to compare an observed measure of cluster distinctness to the distribution of this measure predicted by this model of randomness. In this way, unwarranted subdivision can be statistically avoided, and significant subdivisions can be investigated with confidence. Our methods are illustrated with some examples from the Stephanodiscus niagarae Ehrenb. species complex. Significant differences in morphologic expression are identified in S. reimerii Theriot and Stoermer in Theriot, S. superiorensis Theriot and Stoermer and S. yellowstonensis Theriot and Stoermer. In addition, statistically significant clusters are identified in S. niagarae populations from different geographic locations and in members of the same population grown in different environments. These results suggest current criteria for resolving diatom taxa may not be sufficient to discern subtle differences that occur between real species.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65691/1/j.0022-3646.1997.01049.x.pd
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
Sensitivity curves for spaceborne gravitational wave interferometers
To determine whether particular sources of gravitational radiation will be
detectable by a specific gravitational wave detector, it is necessary to know
the sensitivity limits of the instrument. These instrumental sensitivities are
often depicted (after averaging over source position and polarization) by
graphing the minimal values of the gravitational wave amplitude detectable by
the instrument versus the frequency of the gravitational wave. This paper
describes in detail how to compute such a sensitivity curve given a set of
specifications for a spaceborne laser interferometer gravitational wave
observatory. Minor errors in the prior literature are corrected, and the first
(mostly) analytic calculation of the gravitational wave transfer function is
presented. Example sensitivity curve calculations are presented for the
proposed LISA interferometer. We find that previous treatments of LISA have
underestimated its sensitivity by a factor of .Comment: 27 pages + 5 figures, REVTeX, accepted for publication in Phys Rev D;
Update reflects referees comments, figure 3 clarified, figure 5 corrected for
LISA baselin
Character Analysis In The Banisteriopsis Campestris Complex (Malpighiaceae), Using Spatial AutoâCorrelation
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149728/1/tax02450.pd
Significance of c/sqrt(2) in Relativistic Physics
In the description of \emph{relative} motion in accelerated systems and
gravitational fields, inertial and tidal accelerations must be taken into
account, respectively. These involve a critical speed that in the first
approximation can be simply illustrated in the case of motion in one dimension.
For one-dimensional motion, such first-order accelerations are multiplied by
, where is the critical speed. If the speed of
relative motion exceeds , there is a sign reversal with consequences that
are contrary to Newtonian expectations.Comment: 7 pages, 1 figure, slightly expanded version accepted for publication
in Class. Quantum Gra
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