811 research outputs found

### Accurate light-time correction due to a gravitating mass

This work arose as an aftermath of Cassini's 2002 experiment \cite{bblipt03},
in which the PPN parameter $\gamma$ was measured with an accuracy
$\sigma_\gamma = 2.3\times 10^{-5}$ and found consistent with the prediction
$\gamma =1$ of general relativity. The Orbit Determination Program (ODP) of
NASA's Jet Propulsion Laboratory, which was used in the data analysis, is based
on an expression for the gravitational delay which differs from the standard
formula; this difference is of second order in powers of $m$ -- the sun's
gravitational radius -- but in Cassini's case it was much larger than the
expected order of magnitude $m^2/b$, where $b$ is the ray's closest approach
distance. Since the ODP does not account for any other second-order terms, it
is necessary, also in view of future more accurate experiments, to
systematically evaluate higher order corrections and to determine which terms
are significant. Light propagation in a static spacetime is equivalent to a
problem in ordinary geometrical optics; Fermat's action functional at its
minimum is just the light-time between the two end points A and B. A new and
powerful formulation is thus obtained. Asymptotic power series are necessary to
provide a safe and automatic way of selecting which terms to keep at each
order. Higher order approximations to the delay and the deflection are
obtained. We also show that in a close superior conjunction, when $b$ is much
smaller than the distances of A and B from the Sun, of order $R$, say, the
second-order correction has an \emph{enhanced} part of order $m^2R/b^2$, which
corresponds just to the second-order terms introduced in the ODP. Gravitational
deflection of the image of a far away source, observed from a finite distance
from the mass, is obtained to $O(m^2)$.Comment: 4 figure

### The effect of the motion of the Sun on the light-time in interplanetary relativistic experiments

In 2002 a measurement of the effect of solar gravity upon the phase of
coherent microwave beams passing near the Sun has been carried out with the
Cassini mission, allowing a very accurate measurement of the PPN parameter
$\gamma$. The data have been analyzed with NASA's Orbit Determination Program
(ODP) in the Barycentric Celestial Reference System, in which the Sun moves
around the centre of mass of the solar system with a velocity $v_\odot$ of
about 10 m/sec; the question arises, what correction this implies for the
predicted phase shift. After a review of the way the ODP works, we set the
problem in the framework of Lorentz (and Galilean) transformations and evaluate
the correction; it is several orders of magnitude below our experimental
accuracy. We also discuss a recent paper \cite{kopeikin07}, which claims wrong
and much larger corrections, and clarify the reasons for the discrepancy.Comment: Final version accepted by Classical and Quantum Gravity (8 Jan. 2008

### Synthetic LISA: Simulating Time Delay Interferometry in a Model LISA

We report on three numerical experiments on the implementation of Time-Delay
Interferometry (TDI) for LISA, performed with Synthetic LISA, a C++/Python
package that we developed to simulate the LISA science process at the level of
scientific and technical requirements. Specifically, we study the laser-noise
residuals left by first-generation TDI when the LISA armlengths have a
realistic time dependence; we characterize the armlength-measurements
accuracies that are needed to have effective laser-noise cancellation in both
first- and second-generation TDI; and we estimate the quantization and
telemetry bitdepth needed for the phase measurements. Synthetic LISA generates
synthetic time series of the LISA fundamental noises, as filtered through all
the TDI observables; it also provides a streamlined module to compute the TDI
responses to gravitational waves according to a full model of TDI, including
the motion of the LISA array and the temporal and directional dependence of the
armlengths. We discuss the theoretical model that underlies the simulation, its
implementation, and its use in future investigations on system characterization
and data-analysis prototyping for LISA.Comment: 18 pages, 14 EPS figures, REVTeX 4. Accepted PRD version. See
http://www.vallis.org/syntheticlisa for information on the Synthetic LISA
software packag

### Cosmological Constraints on the Very Low Frequency Gravitational-Wave Background

While there are no strong observational constraints on the gravitational wave
background across six or more orders of magnitude between 10^{-16} Hz and
10^{-10} Hz and it is difficult to get a constraint below 10^{-12}Hz using
objects in our Galaxy, we suggest that the anisotropy pattern of time variation
of the redshift related to a sample of high redshift objects can be used to
constrain the gravitational wave background around 10^{-12} Hz. Useful
observations for the monitoring of an anisotropy signal in a global redshift
change include spectroscopic observations of the Ly-alpha forest in absorption
towards a sample of quasars, redshifted 21 cm line observations either in
absorption or emission towards a sample of neutral HI regions before or during
reionization, and high frequency (0.1 Hz to 1
Hz) gravitational wave analysis of a sample of neutron star--neutron star
binaries detected with gravitational wave instruments such as the Decihertz
Interferometer Gravitational Wave Observatory (DECIGO). The low frequency
background can also be constrained by arcsecond-scale anisotropy observations
of the CMB. For reasonable observations in the future involving extragalactic
sources, we find best limits at the level of \Omega_{GW} < 10^{-5} at a
frequency around 10^{-12} Hz while the eventual ultimate limit one cannot beat
is \Omega_{GW} < 10^{-11}.Comment: 8 pages 2 figure

### Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model

We obtain an exact solution for the motion of a particle driven by a spring
in a Brownian random-force landscape, the Alessandro-Beatrice-Bertotti-Montorsi
(ABBM) model. Many experiments on quasi-static driving of elastic interfaces
(Barkhausen noise in magnets, earthquake statistics, shear dynamics of granular
matter) exhibit the same universal behavior as this model. It also appears as a
limit in the field theory of elastic manifolds. Here we discuss predictions of
the ABBM model for monotonous, but otherwise arbitrary, time-dependent driving.
Our main result is an explicit formula for the generating functional of
particle velocities and positions. We apply this to derive the
particle-velocity distribution following a quench in the driving velocity. We
also obtain the joint avalanche size and duration distribution and the mean
avalanche shape following a jump in the position of the confining spring. Such
non-stationary driving is easy to realize in experiments, and provides a way to
test the ABBM model beyond the stationary, quasi-static regime. We study
extensions to two elastically coupled layers, and to an elastic interface of
internal dimension d, in the Brownian force landscape. The effective action of
the field theory is equal to the action, up to 1-loop corrections obtained
exactly from a functional determinant. This provides a connection to
renormalization-group methods.Comment: 18 pages, 3 figure

### Domain wall dynamics and Barkhausen effect in metallic ferromagnetic materials. II. Experiments

Barkhausen effect (BE) phenomenology in iron‐based ferromagnetic alloys is investigated by a proper experimental method, in which BE experiments are restricted to the central part of the hysteresis loop, and the amplitude probability distribution, P0(Φ), and power spectrum, F(ω), of the B flux rate Φ are measured under controlled values of the magnetization rate and differential permeability μ. It is found that all of the experimental data are approximately consistent with the law P0(Φ)∝Φ−1 exp(−Φ/〈Φ〉), where all dependencies on and μ are described by the single dimensionless parameter >0. Also the parameters describing the shape of F(ω) are found to obey remarkably simple and general laws of dependence on and μ. The experimental results are interpreted by means of the Langevin theory of domain‐wall dynamics proposed in a companion paper. The theory is in good agreement with experiments, and permits one to reduce the basic aspects of BE phenomenology to the behavior of two parameters describing the stochastic fluctuations of the local coercive field experienced by a moving domain wall

### Functional Integration Approach to Hysteresis

A general formulation of scalar hysteresis is proposed. This formulation is
based on two steps. First, a generating function g(x) is associated with an
individual system, and a hysteresis evolution operator is defined by an
appropriate envelope construction applied to g(x), inspired by the overdamped
dynamics of systems evolving in multistable free energy landscapes. Second, the
average hysteresis response of an ensemble of such systems is expressed as a
functional integral over the space G of all admissible generating functions,
under the assumption that an appropriate measure m has been introduced in G.
The consequences of the formulation are analyzed in detail in the case where
the measure m is generated by a continuous, Markovian stochastic process. The
calculation of the hysteresis properties of the ensemble is reduced to the
solution of the level-crossing problem for the stochastic process. In
particular, it is shown that, when the process is translationally invariant
(homogeneous), the ensuing hysteresis properties can be exactly described by
the Preisach model of hysteresis, and the associated Preisach distribution is
expressed in closed analytic form in terms of the drift and diffusion
parameters of the Markovian process. Possible applications of the formulation
are suggested, concerning the interpretation of magnetic hysteresis due to
domain wall motion in quenched-in disorder, and the interpretation of critical
state models of superconducting hysteresis.Comment: 36 pages, 9 figures, to be published on Phys. Rev.

### Self-organized criticality in the hysteresis of the Sherrington - Kirkpatrick model

We study hysteretic phenomena in random ferromagnets. We argue that the angle
dependent magnetostatic (dipolar) terms introduce frustration and long range
interactions in these systems. This makes it plausible that the Sherrington -
Kirkpatrick model may be able to capture some of the relevant physics of these
systems. We use scaling arguments, replica calculations and large scale
numerical simulations to characterize the hysteresis of the zero temperature SK
model. By constructing the distribution functions of the avalanche sizes,
magnetization jumps and local fields, we conclude that the system exhibits
self-organized criticality everywhere on the hysteresis loop.Comment: 4 pages, 4 eps figure

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