743 research outputs found
Stress correlations in glasses
We rigorously establish that, in disordered three-dimensional (3D) isotropic
solids, the stress autocorrelation function presents anisotropic terms that
decay as at long-range, with the distance, as soon as either
pressure or shear stress fluctuations are normal. By normal, we mean that the
fluctuations of stress, as averaged over spherical domains, decay as the
inverse domain volume. Since this property is required for macroscopic stress
to be self-averaging, it is expected to hold generically in all glasses and we
thus conclude that the presence of stress correlation tails is the rule
in these systems. Our proof follows from the observation that, in an infinite
medium, when both material isotropy and mechanical balance hold, (i) the stress
autocorrelation matrix is completely fixed by just two radial functions: the
pressure autocorrelation and the trace of the autocorrelation of stress
deviators; furthermore, these two functions (ii) fix the decay of the
fluctuations of sphere-averaged pressure and deviatoric stresses for windows of
increasing volume. Our conclusion is reached because, due to the precise
analytic relation (i) fixed by isotropy and mechanical balance, the constraints
arising via (ii) from the normality of stress fluctuations demand the spatially
anisotropic stress correlation terms to decay as at long-range. For the
sake of generality, we also examine situations when stress fluctuations are not
normal
Editorial note to "The beginning of the world from the point of view of quantum theory"
This is an editorial note to accompany reprinting as a Golden Oldie in the
Journal of General Relativity and Gravitation of the famous note by Georges
Lemaitre on the quantum birth of the universe, published in Nature in 1931. We
explain why this short (457 words) article can be considered to be the true
"Charter" of the modern Big Bang theory.Comment: This is an editorial comment to accompany reprinting of a classical
paper in the Journal of General Relativity and Gravitation. 16 pages, 2
figure
Alternative Methods of Describing Structure Formation in the Lemaitre-Tolman Model
We describe several new ways of specifying the behaviour of Lemaitre-Tolman
(LT) models, in each case presenting the method for obtaining the LT arbitrary
functions from the given data, and the conditions for existence of such
solutions. In addition to our previously considered `boundary conditions', the
new ones include: a simultaneous big bang, a homogeneous density or velocity
distribution in the asymptotic future, a simultaneous big crunch, a
simultaneous time of maximal expansion, a chosen density or velocity
distribution in the asymptotic future, only growing or only decaying
fluctuations. Since these conditions are combined in pairs to specify a
particular model, this considerably increases the possible ways of designing LT
models with desired properties.Comment: Accepted by Phys Rev D. RevTeX 4, 13 pages, no figures. Part of a
series: gr-qc/0106096, gr-qc/0303016, gr-qc/0309119. Replacement contains
very minor correction
Can we avoid dark energy?
The idea that we live near the centre of a large, nonlinear void has
attracted attention recently as an alternative to dark energy or modified
gravity. We show that an appropriate void profile can fit both the latest
cosmic microwave background and supernova data. However, this requires either a
fine-tuned primordial spectrum or a Hubble rate so low as to rule these models
out. We also show that measurements of the radial baryon acoustic scale can
provide very strong constraints. Our results present a serious challenge to
void models of acceleration.Comment: 5 pages, 4 figures; minor changes; version published in Phys. Rev.
Let
Symplectic integration of space debris motion considering several Earth's shadowing models
In this work, we present a symplectic integration scheme to numerically
compute space debris motion. Such an integrator is particularly suitable to
obtain reliable trajectories of objects lying on high orbits, especially
geostationary ones. Indeed, it has already been demonstrated that such objects
could stay there for hundreds of years. Our model takes into account the
Earth's gravitational potential, luni-solar and planetary gravitational
perturbations and direct solar radiation pressure. Based on the analysis of the
energy conservation and on a comparison with a high order non-symplectic
integrator, we show that our algorithm allows us to use large time steps and
keep accurate results. We also propose an innovative method to model Earth's
shadow crossings by means of a smooth shadow function. In the particular
framework of symplectic integration, such a function needs to be included
analytically in the equations of motion in order to prevent numerical drifts of
the energy. For the sake of completeness, both cylindrical shadows and penumbra
transitions models are considered. We show that both models are not equivalent
and that big discrepancies actually appear between associated orbits,
especially for high area-to-mass ratios
Light-cone averages in a swiss-cheese universe
We analyze a toy swiss-cheese cosmological model to study the averaging
problem. In our model, the cheese is the EdS model and the holes are
constructed from a LTB solution. We study the propagation of photons in the
swiss-cheese model, and find a phenomenological homogeneous model to describe
observables. Following a fitting procedure based on light-cone averages, we
find that the the expansion scalar is unaffected by the inhomogeneities. This
is because of spherical symmetry. However, the light-cone average of the
density as a function of redshift is affected by inhomogeneities. The effect
arises because, as the universe evolves, a photon spends more and more time in
the (large) voids than in the (thin) high-density structures. The
phenomenological homogeneous model describing the light-cone average of the
density is similar to the concordance model. Although the sole source in the
swiss-cheese model is matter, the phenomenological homogeneous model behaves as
if it has a dark-energy component. Finally, we study how the equation of state
of the phenomenological model depends on the size of the inhomogeneities, and
find that the equation-of-state parameters w_0 and w_a follow a power-law
dependence with a scaling exponent equal to unity. That is, the equation of
state depends linearly on the distance the photon travels through voids. We
conclude that within our toy model, the holes must have a present size of about
250 Mpc to be able to mimic the concordance model.Comment: 20 pages, 14 figures; replaced to fit the version accepted for
publication in Phys. Rev.
Expansion-Free Evolving Spheres Must Have Inhomogeneous Energy Density Distributions
In a recent paper a systematic study on shearing expansion-free spherically
symmetric distributions was presented. As a particular case of such systems,
the Skripkin model was mentioned, which corresponds to a nondissipative perfect
fluid with a constant energy density. Here we show that such a model is
inconsistent with junction conditions. It is shown that in general for any
nondissipative fluid distribution, the expansion-free condition requires the
energy density to be inhomogeneous. As an example we consider the case of dust,
which allows for a complete integration.Comment: 8 pages, Latex. To appear in Phys. Rev.D. Typos correcte
More examples of structure formation in the Lemaitre-Tolman model
In continuing our earlier research, we find the formulae needed to determine
the arbitrary functions in the Lemaitre-Tolman model when the evolution
proceeds from a given initial velocity distribution to a final state that is
determined either by a density distribution or by a velocity distribution. In
each case the initial and final distributions uniquely determine the L-T model
that evolves between them, and the sign of the energy-function is determined by
a simple inequality. We also show how the final density profile can be more
accurately fitted to observational data than was done in our previous paper. We
work out new numerical examples of the evolution: the creation of a galaxy
cluster out of different velocity distributions, reflecting the current data on
temperature anisotropies of CMB, the creation of the same out of different
density distributions, and the creation of a void. The void in its present
state is surrounded by a nonsingular wall of high density.Comment: LaTeX 2e with eps figures. 30 pages, 11 figures, 30 figure files.
Revision matches published versio
Optically tunable nuclear magnetic resonance in a single quantum dot
We report optically detected nuclear magnetic resonance (ODNMR) measurements on small ensembles of nuclear spins in single GaAs quantum dots. Using ODNMR we make direct measurements of the inhomogeneous Knight field from a photoexcited electron which acts on the nuclei in the dot. The resulting shifts of the NMR peak can be optically controlled by varying the electron occupancy and its spin orientation, and lead to strongly asymmetric line shapes at high optical excitation. The all-optical control of the NMR line shape will enable position-selective control of small groups of nuclear spins inside a dot
Analytical and numerical study of the ground-track resonances of Dawn orbiting Vesta
The aim of Dawn mission is the acquisition of data from orbits around two
bodies, (4)Vesta and (1)Ceres, the two most massive asteroids. Due to the low
thrust propulsion, Dawn will slowly cross and transit through ground-track
resonances, where the perturbations on Dawn orbit may be significant. In this
context, to safety go the Dawn mission from the approach orbit to the lowest
science orbit, it is essential to know the properties of the crossed
resonances. This paper analytically investigates the properties of the major
ground-track resonances (1:1, 1:2, 2:3 and 3:2) appearing for Vesta orbiters:
location of the equilibria, aperture of the resonances and period at the stable
equilibria. We develop a general method using an averaged Hamiltonian
formulation with a spherical harmonic approximation of the gravity field. If
the values of the gravity field coefficient change, our method stays correct
and applicable. We also discuss the effect of one uncertainty on the C20 and
C22 coefficients on the properties of the 1:1 resonance. These results are
checked by numerical tests. We determine that the increase of the eccentricity
appearing in the 2:3 resonance is due to the C22 and S22 coefficients.
Our method can be easily adapted to missions similar to Dawn because,
contrarily to the numerical results, the analytical formalism stays the same
and is valid for a wide range of physical parameters of the asteroid (namely
the shape and the mass) as well as for different spacecraft orbits.
Finally we numerically study the probability of the capture in resonance 1:1.
Our paper reproduces, explains and supplements the results of Tricarico and
Sykes (2010).Comment: 34 pages, 9 figures, 10 Table
- …