8,863 research outputs found
The generation of a Gaussian random process in a position parameter
Analog computer method for approximating stationary Gaussian random process depending only on position paramete
The Cosmological Constant and Advanced Gravitational Wave Detectors
Interferometric gravitational wave detectors could measure the frequency
sweep of a binary inspiral [characterized by its chirp mass] to high accuracy.
The observed chirp mass is the intrinsic chirp mass of the binary source
multiplied by , where is the redshift of the source. Assuming a
non-zero cosmological constant, we compute the expected redshift distribution
of observed events for an advanced LIGO detector. We find that the redshift
distribution has a robust and sizable dependence on the cosmological constant;
the data from advanced LIGO detectors could provide an independent measurement
of the cosmological constant.Comment: 13 pages plus 5 figure, LaTeX. Revised and final version, to appear
in Phys. Rev.
Binary inspiral, gravitational radiation, and cosmology
Observations of binary inspiral in a single interferometric gravitational
wave detector can be cataloged according to signal-to-noise ratio and
chirp mass . The distribution of events in a catalog composed of
observations with greater than a threshold depends on the
Hubble expansion, deceleration parameter, and cosmological constant, as well as
the distribution of component masses in binary systems and evolutionary
effects. In this paper I find general expressions, valid in any homogeneous and
isotropic cosmological model, for the distribution with and of
cataloged events; I also evaluate these distributions explicitly for relevant
matter-dominated Friedmann-Robertson-Walker models and simple models of the
neutron star mass distribution. In matter dominated Friedmann-Robertson-Walker
cosmological models advanced LIGO detectors will observe binary neutron star
inspiral events with from distances not exceeding approximately
, corresponding to redshifts of (0.26) for
(), at an estimated rate of 1 per week. As the binary system mass
increases so does the distance it can be seen, up to a limit: in a matter
dominated Einstein-deSitter cosmological model with () that limit
is approximately (1.7) for binaries consisting of two
black holes. Cosmological tests based on catalogs of the
kind discussed here depend on the distribution of cataloged events with
and . The distributions found here will play a pivotal role in testing
cosmological models against our own universe and in constructing templates for
the detection of cosmological inspiraling binary neutron stars and black holes.Comment: REVTeX, 38 pages, 9 (encapsulated) postscript figures, uses epsf.st
Behavior of Piles in Liquefiable Soils During Earthquakes: Analysis and Design Issues
A general picture of the current state of the art and the emerging technology for dealing effectively with the seismic design and analysis of pile foundations in liquefiable soils is presented. Two distinct design cases are considered and illustrated by case histories. One is the static response of pile foundations to the pressures and displacements caused by lateral spreading of liquefied ground. The other is the seismic response of piles to strong shaking accompanied by the development of high pore water pressures or liquefaction. Design for lateral spreading is examined in the context of developments in design practice and the findings from shake table and centrifuge tests. Response of piles to earthquake shaking in liquefiable soils is examined in the context of 1.5m cast in place reinforced concrete piles supporting a 14 storey apartment building
Detecting an association between Ray and Gravitational Wave Bursts
If -ray bursts (GRBs) are accompanied by gravitational wave bursts (GWBs) the correlated output of two gravitational wave detectors evaluated in the moments just prior to a GRB will differ from that evaluated at times not associated with a GRB. We can test for this difference independently of any model of the GWB signal waveform. If we invoke a model for the GRB source population and GWB radiation spectral density we can find a confidence interval or upper limit on the root-mean-square GWB signal amplitude in the detector waveband. To illustrate we adopt a simple, physically motivated model and estimate that initial LIGO detector observations coincident with 1000 GRBs could lead us to exclude, with 95% confidence, associated GWBs with $h_{RMS} be Gaussian or that any inter-detector correlated noise be measured or measurable; it does not require advanced or a priori knowledge of the source waveform; and the limits obtained on the wave-strength improve with the number of observed GRBs
Crustal Oscillations of Slowly Rotating Relativistic Stars
We study low-amplitude crustal oscillations of slowly rotating relativistic
stars consisting of a central fluid core and an outer thin solid crust. We
estimate the effect of rotation on the torsional toroidal modes and on the
interfacial and shear spheroidal modes. The results compared against the
Newtonian ones for wide range of neutron star models and equations of state.Comment: 15 page
On the spin of gravitational bosons
We unearth spacetime structure of massive vector bosons, gravitinos, and
gravitons. While the curvatures associated with these particles carry a
definite spin, the underlying potentials cannot be, and should not be,
interpreted as single spin objects. For instance, we predict that a spin
measurement in the rest frame of a massive gravitino will yield the result 3/2
with probability one half, and 1/2 with probability one half. The simplest
scenario leaves the Riemannian curvature unaltered; thus avoiding conflicts
with classical tests of the theory of general relativity. However, the quantum
structure acquires additional contributions to the propagators, and it gives
rise to additional phases.Comment: Honorable mention, 2002 Gravity Research Foundation Essay
Inertial modes of rigidly rotating neutron stars in Cowling approximation
In this article, we investigate inertial modes of rigidly rotating neutron
stars, i.e. modes for which the Coriolis force is dominant. This is done using
the assumption of a fixed spacetime (Cowling approximation). We present
frequencies and eigenfunctions for a sequence of stars with a polytropic
equation of state, covering a broad range of rotation rates. The modes were
obtained with a nonlinear general relativistic hydrodynamic evolution code. We
further show that the eigenequations for the oscillation modes can be written
in a particularly simple form for the case of arbitrary fast, but rigid
rotation. Using these equations, we investigate some general characteristics of
inertial modes, which are then compared to the numerically obtained
eigenfunctions. In particular, we derive a rough analytical estimate for the
frequency as a function of the number of nodes of the eigenfunction, and find
that a similar empirical relation matches the numerical results with unexpected
accuracy. We investigate the slow rotation limit of the eigenequations,
obtaining two different sets of equations describing pressure and inertial
modes. For the numerical computations we only considered axisymmetric modes,
while the analytic part also covers nonaxisymmetric modes. The eigenfunctions
suggest that the classification of inertial modes by the quantum numbers of the
leading term of a spherical harmonic decomposition is artificial in the sense
that the largest term is not strongly dominant, even in the slow rotation
limit. The reason for the different structure of pressure and inertial modes is
that the Coriolis force remains important in the slow rotation limit only for
inertial modes. Accordingly, the scalar eigenequation we obtain in that limit
is spherically symmetric for pressure modes, but not for inertial modes.Comment: 13 pages, 10 figures Fixed some typos, reformulated a few paragraphs,
added 3 reference
The approach to typicality in many-body quantum systems
The recent discovery that for large Hilbert spaces, almost all (that is,
typical) Hamiltonians have eigenstates that place small subsystems in thermal
equilibrium, has shed much light on the origins of irreversibility and
thermalization. Here we give numerical evidence that many-body lattice systems
generically approach typicality as the number of subsystems is increased, and
thus provide further support for the eigenstate thermalization hypothesis. Our
results indicate that the deviation of many-body systems from typicality
decreases exponentially with the number of systems. Further, by averaging over
a number of randomly-selected nearest-neighbor interactions, we obtain a
power-law for the atypicality as a function of the Hilbert space dimension,
distinct from the power-law possessed by random Hamiltonians.Comment: 6 pages, 2 png figures, revtex
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