Problems and advances in monitoring horizontal strain

The modern instrumentation is described for use in geodesy for the detection of the deformations of the crust of the earth. Problems are listed. Needs are discussed for the survey of the physical quantities of interest in geodesy, geology, geophysics, and engineering such as the strain invariants, the optimal network of baselines and the accuracy. An analytic method is also given for the computation of the effect of a source of dilatation in a spherical earth

Altimetry data and the elastic stress tensor of subduction zones

The stress field in the lithosphere caused by the distribution of density anomalies associated to the geoidal undulations observed by the GEOS-3 and SEASAT Earth satellites in the Tonga region was studied. Different models of the lithosphere were generated with different assumptions on the density distribution and geometry, all generating a geoid profile almost identical to the observed one. The first model is the Airy isostatic hypothesis which consists of a crust of density 2.85 laying on a lithosphere of density 3.35. The models obtained with different compensation depths give residual shortwavelength anomalies of the order of several tens of mgal and several tens of meters geoidal undulations. It indicates that there is no isostasy of the Airy type in the Tonga region because the observed geoid has very smooth undulation of about 25 m over a distance of 2000 km. The Pratt isostatic hypothesis is used in a model consisting of a crust of variable density laying on a lithosphere of higher density. This model gives smaller residual anomalies but still shows that there is no isostasy of the Pratt type in the Tonga region because the observed geoidal undulation are much smaller and smoother than the residual undulations associated to the Pratt model of isostasy

Fractional Fokker-Planck Equation for Ultraslow Kinetics

Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability distribution of particle's position at long times is a double-sided exponential. We show that such behaviors can be adequately described by a distributed-order fractional Fokker-Planck equations with a power-law weighting-function. We discuss the equations and the properties of their solutions, and connect this description with a scheme based on continuous-time random walks

Highly Degenerate Harmonic Mean Curvature Flow

We study the evolution of a weakly convex surface $\Sigma_0$ in $\R^3$ with flat sides by the Harmonic Mean Curvature flow. We establish the short time existence as well as the optimal regularity of the surface and we show that the boundaries of the flat sides evolve by the curve shortening flow. It follows from our results that a weakly convex surface with flat sides of class $C^{k,\gamma}$, for some $k\in \mathbb{N}$ and $0 < \gamma \leq 1$, remains in the same class under the flow. This distinguishes this flow from other, previously studied, degenerate parabolic equations, including the porous medium equation and the Gauss curvature flow with flat sides, where the regularity of the solution for $t >0$ does not depend on the regularity of the initial data

RR Lyrae variables in Galactic globular clusters - I: The observational scenario

In this paper we revisit observational data concerning RR Lyrae stars in Galactic globular clusters, presenting frequency histograms of fundamentalized periods for the 32 clusters having more than 12 pulsators with well recognized period and pulsation mode. One finds that the range of fundamentalized periods covered by the variables in a given cluster remains fairly constant in varying the cluster metallicity all over the metallicity range spanned by the cluster sample, with the only two exceptions given by M15 and NGC6441. We conclude that the width in temperature of the RR Lyrae instability strip appears largely independent of the cluster metallicity. At the same time, it appears that the fundamentalized periods are not affected by the predicted variation of pulsators luminosity with metal abundance, indicating the occurrence of a correlated variation in the pulsator mass. We discuss mean periods in a selected sample of statistically significant "RR rich" clusters with no less than 10 RRab and 5 RRc variables. One finds a clear evidence for the well known Oosterhoff dichotomy in the mean period of ab-type variables, together with a similarly clear evidence for a constancy of the mean fundamentalized period in passing from Oosterhoff type II to type I clusters. On this basis, the origin of the Oosterhoff dichotomy is discussed, presenting evidence against a strong dependence of the RR Lyrae luminosity on the metal content.Comment: 9 pages, 6 figures. Accepted for publication on A&

Principal Portfolios: Recasting the Efficient Frontier

A new method of analyzing the efficient portfolio problem under the assumption that short sales are allowed is presented. It is based on the remarkable finding that the original asset set can be reorganized as a set of uncorrelated portfolios, here named principal portfolios. The original problem of portfolio selection from the existing, correlated assets is thereby traded for the reduced problem of choosing from a set of uncorrelated portfolios. These portfolios constitute a new investment environment of uncorrelated assets, thereby providing significant conceptual and practical simplification in any portfolio optimization process such as the determination of the efficient frontier. The principal portfolio analysis of the efficient frontier reveals new features of the volatility structure of the optimal portfolios.

Detecting the Stimulated Decay of Axions at Radio Frequencies

Assuming axion-like particles account for the entirety of the dark matter in the Universe, we study the possibility of detecting their decay into photons at radio frequencies. We discuss different astrophysical targets, such as dwarf spheroidal galaxies, the Galactic Center and halo, and galaxy clusters. The presence of an ambient radiation field leads to a stimulated enhancement of the decay rate; depending on the environment and the mass of the axion, the effect of stimulated emission may amplify the photon flux by serval orders of magnitude. For axion-photon couplings allowed by astrophysical and laboratory constraints(and possibly favored by stellar cooling), we find the signal to be within the reach of next-generation radio telescopes such as the Square Kilometer Array.Comment: Minor changes, references added, matches published versio