Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes

Scaling analysis reveals striking regularities in earthquake occurrence. The time between any one earthquake and that following it is random, but it is described by the same universal-probability distribution for any spatial region and magnitude range considered. When time is expressed in rescaled units, set by the averaged seismic activity, the self-similar nature of the process becomes apparent. The form of the probability distribution reveals that earthquakes tend to cluster in time, beyond the duration of aftershock sequences. Furthermore, if aftershock sequences are analysed in an analogous way, yet taking into account the fact that seismic activity is not constant but decays in time, the same universal distribution is found for the rescaled time between events.Comment: short paper, only 2 figure

A critical-density closed Universe in Brans-Dicke theory

In a Brans-Dicke (BD) cosmological model, the energy density associated with some scalar field decreases as \displaystyle a^{{-2}(\frac{\omega_{o}+ {\frac12}%}{\omega_{o}+1})} with the scale factor $a(t)$ of the Universe, giving a matter with an Equation of state $\displaystyle p=-{1/3}(\frac{2+\omega_{o}}{1+\omega_{o}}) \rho$. In this model, the Universe could be closed but still have a nonrelativistic-matter density corresponding to its critical value, $\Omega_{o}=1$. Different cosmological expressions, such as, luminosity distance, angular diameter, number count and ratio of the redshift tickness-angular size, are determined in terms of the redshift for this model.Comment: To appear in MNRAS, 7 pages, 5 eps figure

Nonlinear theory and tests of earthquake recurrence times

We develop an efficient numerical scheme to solve accurately the set of nonlinear integral equations derived previously in (Saichev and Sornette, 2007), which describes the distribution of inter-event times in the framework of a general model of earthquake clustering with long memory. Detailed comparisons between the linear and nonlinear versions of the theory and direct synthetic catalogs show that the nonlinear theory provides an excellent fit to the synthetic catalogs, while there are significant biases resulting from the use of the linear approximation. We then address the suggestions proposed by some authors to use the empirical distribution of inter-event times to obtain a better determination of the so-called clustering parameter. Our theory and tests against synthetic and empirical catalogs find a rather dramatic lack of power for the distribution of inter-event times to distinguish between quite different sets of parameters, casting doubt on the usefulness of this statistics for the specific purpose of identifying the clustering parameter.Comment: 31 pages including 11 figure

Testing the equivalence principle: why and how?

Part of the theoretical motivation for improving the present level of testing of the equivalence principle is reviewed. The general rationale for optimizing the choice of pairs of materials to be tested is presented. One introduces a simplified rationale based on a trichotomy of competing classes of theoretical models.Comment: 11 pages, Latex, uses ioplppt.sty, submitted to Class. Quantum Gra

Universality in solar flare and earthquake occurrence

Earthquakes and solar flares are phenomena involving huge and rapid releases of energy characterized by complex temporal occurrence. By analysing available experimental catalogs, we show that the stochastic processes underlying these apparently different phenomena have universal properties. Namely both problems exhibit the same distributions of sizes, inter-occurrence times and the same temporal clustering: we find afterflare sequences with power law temporal correlations as the Omori law for seismic sequences. The observed universality suggests a common approach to the interpretation of both phenomena in terms of the same driving physical mechanism

Matter-gravity couplings and Lorentz violation

The gravitational couplings of matter are studied in the presence of Lorentz and CPT violation. At leading order in the coefficients for Lorentz violation, the relativistic quantum hamiltonian is derived from the gravitationally coupled minimal Standard-Model Extension. For spin-independent effects, the nonrelativistic quantum hamiltonian and the classical dynamics for test and source bodies are obtained. A systematic perturbative method is developed to treat small metric and coefficient fluctuations about a Lorentz-violating and Minkowski background. The post-newtonian metric and the trajectory of a test body freely falling under gravity in the presence of Lorentz violation are established. An illustrative example is presented for a bumblebee model. The general methodology is used to identify observable signals of Lorentz and CPT violation in a variety of gravitational experiments and observations, including gravimeter measurements, laboratory and satellite tests of the weak equivalence principle, antimatter studies, solar-system observations, and investigations of the gravitational properties of light. Numerous sensitivities to coefficients for Lorentz violation can be achieved in existing or near-future experiments at the level of parts in 10^3 down to parts in 10^{15}. Certain coefficients are uniquely detectable in gravitational searches and remain unmeasured to date.Comment: 59 pages two-column REVTe

The Full-sky Astrometric Mapping Explorer -- Astrometry for the New Millennium

FAME is designed to perform an all-sky, astrometric survey with unprecedented accuracy. It will create a rigid astrometric catalog of 4x10^7 stars with 5 < m_V < 15. For bright stars, 5 < m_V < 9, FAME will determine positions and parallaxes accurate to < 50 microarcseconds, with proper motion errors < 50 microarcseconds/year. For fainter stars, 9 < m_V < 15, FAME will determine positions and parallaxes accurate to < 500 microarcseconds, with proper motion errors < 500 microarcseconds/year. It will also collect photometric data on these 4 x 10^7 stars in four Sloan DSS colors.Comment: 6 pages, 4 figures, to appear in "Working on the Fringe

A note on light velocity anisotropy

It is proved that in experiments on or near the Earth, no anisotropy in the one-way velocity of light may be detected. The very accurate experiments which have been performed to detect such an effect are to be considered significant tests of both special relativity and the equivalence principleComment: 8 pages, LaTex, Gen. Relat. Grav. accepte

Monopole Inflation in Brans-Dicke Theory

According to previous work, topological defects expand exponentially without an end if the vacuum expectation value of the Higgs field is of the order of the Planck mass. We extend the study of inflating topological defects to the Brans-Dicke gravity. With the help of numerical simulation we investigate the dynamics and spacetime structure of a global monopole. Contrary to the case of the Einstein gravity, any inflating monopole eventually shrinks and takes a stable configuration. We also discuss cosmological constraints on the model parameters.Comment: 17 pages, revtex, including figures, discussions in more general theories are added, to appear in Phys. Rev.

Quintessence, the Gravitational Constant, and Gravity

Dynamical vacuum energy or quintessence, a slowly varying and spatially inhomogeneous component of the energy density with negative pressure, is currently consistent with the observational data. One potential difficulty with the idea of quintessence is that couplings to ordinary matter should be strongly suppressed so as not to lead to observable time variations of the constants of nature. We further explore the possibility of an explicit coupling between the quintessence field and the curvature. Since such a scalar field gives rise to another gravity force of long range (\simg H^{-1}_0), the solar system experiments put a constraint on the non-minimal coupling: |\xi| \siml 10^{-2}.Comment: 9 pages, a version to be published in Phys.Rev.