3,182 research outputs found
Gravity Waves, Chaos, and Spinning Compact Binaries
Spinning compact binaries are shown to be chaotic in the Post-Newtonian
expansion of the two body system. Chaos by definition is the extreme
sensitivity to initial conditions and a consequent inability to predict the
outcome of the evolution. As a result, the spinning pair will have
unpredictable gravitational waveforms during coalescence. This poses a
challenge to future gravity wave observatories which rely on a match between
the data and a theoretical template.Comment: Final version published in PR
Temperature-dependent relaxation times in a trapped Bose-condensed gas
Explicit expressions for all the transport coefficients have recently been
found for a trapped Bose condensed gas at finite temperatures. These transport
coefficients are used to define the characteristic relaxation times, which
determine the crossover between the mean-field collisionless and the two-fluid
hydrodynamic regime. These relaxation times are evaluated as a function of the
position in the trap potential. We show that all the relaxation times are
dominated by the collisions between the condensate and the non-condensate
atoms, and are much smaller than the standard classical collision time used in
most of the current literature. The 1998 MIT study of the collective modes at
finite temperature is shown to have been well within the two-fluid hydrodynamic
regime.Comment: 4 pages, 3 figures, to be published in Phys. Rev.
The Challenges in Gravitational Wave Astronomy for Space-Based Detectors
The Gravitational Wave (GW) universe contains a wealth of sources which, with
the proper treatment, will open up the universe as never before. By observing
massive black hole binaries to high redshifts, we should begin to explore the
formation process of seed black holes and track galactic evolution to the
present day. Observations of extreme mass ratio inspirals will allow us to
explore galactic centers in the local universe, as well as providing tests of
General Relativity and constraining the value of Hubble's constant. The
detection of compact binaries in our own galaxy may allow us to model stellar
evolution in the Milky Way. Finally, the detection of cosmic (super)strings and
a stochastic background would help us to constrain cosmological models.
However, all of this depends on our ability to not only resolve sources and
carry out parameter estimation, but also on our ability to define an optimal
data analysis strategy. In this presentation, I will examine the challenges
that lie ahead in GW astronomy for the ESA L3 Cosmic Vision mission, eLISA.Comment: 12 pages. Plenary presentation to appear in the Proceedings of the
Sant Cugat Forum on Astrophysics, Sant Cugat, April 22-25, 201
Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models
Chemical reactions inside cells occur in compartment volumes in the range of
atto- to femtolitres. Physiological concentrations realized in such small
volumes imply low copy numbers of interacting molecules with the consequence of
considerable fluctuations in the concentrations. In contrast, rate equation
models are based on the implicit assumption of infinitely large numbers of
interacting molecules, or equivalently, that reactions occur in infinite
volumes at constant macroscopic concentrations. In this article we compute the
finite-volume corrections (or equivalently the finite copy number corrections)
to the solutions of the rate equations for chemical reaction networks composed
of arbitrarily large numbers of enzyme-catalyzed reactions which are confined
inside a small sub-cellular compartment. This is achieved by applying a
mesoscopic version of the quasi-steady state assumption to the exact
Fokker-Planck equation associated with the Poisson Representation of the
chemical master equation. The procedure yields impressively simple and compact
expressions for the finite-volume corrections. We prove that the predictions of
the rate equations will always underestimate the actual steady-state substrate
concentrations for an enzyme-reaction network confined in a small volume. In
particular we show that the finite-volume corrections increase with decreasing
sub-cellular volume, decreasing Michaelis-Menten constants and increasing
enzyme saturation. The magnitude of the corrections depends sensitively on the
topology of the network. The predictions of the theory are shown to be in
excellent agreement with stochastic simulations for two types of networks
typically associated with protein methylation and metabolism.Comment: 13 pages, 4 figures; published in The Journal of Chemical Physic
Extracting galactic binary signals from the first round of Mock LISA Data Challenges
We report on the performance of an end-to-end Bayesian analysis pipeline for
detecting and characterizing galactic binary signals in simulated LISA data.
Our principal analysis tool is the Blocked-Annealed Metropolis Hasting (BAM)
algorithm, which has been optimized to search for tens of thousands of
overlapping signals across the LISA band. The BAM algorithm employs Bayesian
model selection to determine the number of resolvable sources, and provides
posterior distribution functions for all the model parameters. The BAM
algorithm performed almost flawlessly on all the Round 1 Mock LISA Data
Challenge data sets, including those with many highly overlapping sources. The
only misses were later traced to a coding error that affected high frequency
sources. In addition to the BAM algorithm we also successfully tested a Genetic
Algorithm (GA), but only on data sets with isolated signals as the GA has yet
to be optimized to handle large numbers of overlapping signals.Comment: 13 pages, 4 figures, submitted to Proceedings of GWDAW-11 (Berlin,
Dec. '06
A survey of spinning test particle orbits in Kerr spacetime
We investigate the dynamics of the Papapetrou equations in Kerr spacetime.
These equations provide a model for the motion of a relativistic spinning test
particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter
space search for signs of chaotic dynamics by calculating the Lyapunov
exponents for a large variety of initial conditions. We find that the
Papapetrou equations admit many chaotic solutions, with the strongest chaos
occurring in the case of eccentric orbits with pericenters close to the limit
of stability against plunge into a maximally spinning Kerr black hole. Despite
the presence of these chaotic solutions, we show that physically realistic
solutions to the Papapetrou equations are not chaotic; in all cases, the
chaotic solutions either do not correspond to realistic astrophysical systems,
or involve a breakdown of the test-particle approximation leading to the
Papapetrou equations (or both). As a result, the gravitational radiation from
bodies spiraling into much more massive black holes (as detectable, for
example, by LISA, the Laser Interferometer Space Antenna) should not exhibit
any signs of chaos.Comment: Submitted to Phys. Rev. D. Follow-up to gr-qc/0210042. Figures are
low-resolution in order to satisfy archive size constraints; a
high-resolution version is available at http://www.michaelhartl.com/papers
Studying stellar binary systems with the Laser Interferometer Space Antenna using Delayed Rejection Markov chain Monte Carlo methods
Bayesian analysis of LISA data sets based on Markov chain Monte Carlo methods
has been shown to be a challenging problem, in part due to the complicated
structure of the likelihood function consisting of several isolated local
maxima that dramatically reduces the efficiency of the sampling techniques.
Here we introduce a new fully Markovian algorithm, a Delayed Rejection
Metropolis-Hastings Markov chain Monte Carlo method, to efficiently explore
these kind of structures and we demonstrate its performance on selected LISA
data sets containing a known number of stellar-mass binary signals embedded in
Gaussian stationary noise.Comment: 12 pages, 4 figures, accepted in CQG (GWDAW-13 proceedings
Certain aspects of regularity in scalar field cosmological dynamics
We consider dynamics of the FRW Universe with a scalar field. Using
Maupertuis principle we find a curvature of geodesics flow and show that zones
of positive curvature exist for all considered types of scalar field potential.
Usually, phase space of systems with the positive curvature contains islands of
regular motion. We find these islands numerically for shallow scalar field
potentials. It is shown also that beyond the physical domain the islands of
regularity exist for quadratic potentials as well.Comment: 15 pages with 4 figures; typos corrected, final version to appear in
Regular and Chaotic Dynamic
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
The chemical Fokker-Planck equation and the corresponding chemical Langevin
equation are commonly used approximations of the chemical master equation.
These equations are derived from an uncontrolled, second-order truncation of
the Kramers-Moyal expansion of the chemical master equation and hence their
accuracy remains to be clarified. We use the system-size expansion to show that
chemical Fokker-Planck estimates of the mean concentrations and of the variance
of the concentration fluctuations about the mean are accurate to order
for reaction systems which do not obey detailed balance and at
least accurate to order for systems obeying detailed balance,
where is the characteristic size of the system. Hence the chemical
Fokker-Planck equation turns out to be more accurate than the linear-noise
approximation of the chemical master equation (the linear Fokker-Planck
equation) which leads to mean concentration estimates accurate to order
and variance estimates accurate to order . This
higher accuracy is particularly conspicuous for chemical systems realized in
small volumes such as biochemical reactions inside cells. A formula is also
obtained for the approximate size of the relative errors in the concentration
and variance predictions of the chemical Fokker-Planck equation, where the
relative error is defined as the difference between the predictions of the
chemical Fokker-Planck equation and the master equation divided by the
prediction of the master equation. For dimerization and enzyme-catalyzed
reactions, the errors are typically less than few percent even when the
steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy
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