8,583 research outputs found
On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces
We study the recurrence and ergodicity for the billiard on noncompact
polygonal surfaces with a free, cocompact action of or . In the
-periodic case, we establish criteria for recurrence. In the more difficult
-periodic case, we establish some general results. For a particular
family of -periodic polygonal surfaces, known in the physics literature
as the wind-tree model, assuming certain restrictions of geometric nature, we
obtain the ergodic decomposition of directional billiard dynamics for a dense,
countable set of directions. This is a consequence of our results on the
ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure
Higher order corrections to the Newtonian potential in the Randall-Sundrum model
The general formalism for calculating the Newtonian potential in fine-tuned
or critical Randall-Sundrum braneworlds is outlined. It is based on using the
full tensor structure of the graviton propagator. This approach avoids the
brane-bending effect arising from calculating the potential for a point source.
For a single brane, this gives a clear understanding of the disputed overall
factor 4/3 entering the correction. The result can be written on a compact form
which is evaluated to high accuracy for both short and large distances.Comment: 12 pages, LaTeX2e with RevTeX4, 3 postscript figures; Minor
corrections, references update
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
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.
A hybrid lagrangian-eulerian approach for simulation of bubble dynamics
A mutiscale numerical approach is developed for the investigation of bubbly flows in turbulent environments. This consists of two different numerical approaches capable of capturing the bubble dynamics at different scales depending upon the relative size of the bubbles compared to the grid resolution: (i) fully resolved simulations (FRS) wherein the bubble dynamics and deformation are completely resolved, and (ii) subgrid, discrete bubble model where the bubbles are not resolved by the computational grid. For fully resolved simulations, a novel approach combining a particle-based, mesh-free technique with a finite-volume flow solver, is developed. The approach uses marker points around the interface and advects the signed distance to the interface in a Lagrangian frame. Interpolation kernel based derivative calculations typical of particle methods are used to extract the interface normal and curvature from unordered marker points. Unlike front-tracking methods, connectivity between the marker points is not necessary. For underresolved bubbles, a mixture-theory based Eulerian-Lagrangian approach accounting for volumetric displacements due to bubble motion and size variations is developed. The bubble dynamics is modeled by Rayleigh-Plesset equations using an adaptive timestepping scheme. A detailed verification and validation study of both approaches is performed to test the accuracy of the method on a variety of single and multiple bubble problems to show good predictive capability. Interaction of bubbles with a traveling vortex tube is simulated and compared with experimental data of Sridhar and Katz [1] to show good agreement.http://deepblue.lib.umich.edu/bitstream/2027.42/84270/1/CAV2009-final74.pd
Gravitational Waves from coalescing binaries: Estimation of parameters
The paper presents a statistical model which reproduces the results of Monte
Carlo simulations to estimate the parameters of the gravitational wave signal
from a coalesing binary system. The model however is quite general and would be
useful in other parameter estimation problems.Comment: LaTeX with RevTeX macros, 4 figure
Addendum to: Capillary floating and the billiard ball problem
We compare the results of our earlier paper on the floating in neutral
equilibrium at arbitrary orientation in the sense of Finn-Young with the
literature on its counterpart in the sense of Archimedes. We add a few remarks
of personal and social-historical character.Comment: This is an addendum to my article Capillary floating and the billiard
ball problem, Journal of Mathematical Fluid Mechanics 14 (2012), 363 -- 38
Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations
Assuming that general relativity is the correct theory of gravity in the
strong field limit, can gravitational wave observations distinguish between
black hole and other compact object sources? Alternatively, can gravitational
wave observations provide a test of one of the fundamental predictions of
general relativity? Here we describe a definitive test of the hypothesis that
observations of damped, sinusoidal gravitational waves originated from a black
hole or, alternatively, that nature respects the general relativistic no-hair
theorem. For astrophysical black holes, which have a negligible charge-to-mass
ratio, the black hole quasi-normal mode spectrum is characterized entirely by
the black hole mass and angular momentum and is unique to black holes. In a
different theory of gravity, or if the observed radiation arises from a
different source (e.g., a neutron star, strange matter or boson star), the
spectrum will be inconsistent with that predicted for general relativistic
black holes. We give a statistical characterization of the consistency between
the noisy observation and the theoretical predictions of general relativity,
together with a numerical example.Comment: 19 pages, 7 figure
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