On the detection of gravitational waves through their interaction with particles in storage rings

It is shown that the interaction between a gravitational wave and ultra-relativistic bunches of particles in storage rings can produce a measurable effect on the non-Euclidean geometry of the space -time manifold of high energy rotating particles. Such an interaction causes simultaneous correlated deflections of bunches at different locations in a collider beam around the storage ring. T he radial deflection of a bunch of particles in a beam caused by a gravitational wave perpendicular to the surface of the ring is predicted to have a frequency equal to twice the revolution frequ ency of the bunch, and be modulated by the frequency of the gravitational wave. Using a system of beam position monitors (and possibly a streak camera), every bunch of particles can be monitored and its oscillations reconstructed so that a clear picture of the complete ring can be achieved at any moment. If the storage ring has two counter-rotating beams, noise effects can be reduced by measuring the difference, at a given point all along the beam, of the relative bunch deflections at both rings. The amplitude and frequency of the gravitational wave (and polarisation, if any) ca n then be deduced. Coincidence at different storage rings, with correlated radial deflection amplitudes and frequencies, are also expected. The position of the source can then be deduced. For gravitational waves with frequencies of the order of 100-1000 Hz and amplitudes of the order of $10^{-20}$-$10^{-23}$ the amplitude of the radial deflection can be as large as a milimeter, depen ding on the quality factor as a gravitational wave antenna and the parameters of the collider

Statistics of Earthquakes in Simple Models of Heterogeneous Faults

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distribution of small events combined with characteristic system size events. The studies employ various analytic methods as well as simulations.Comment: 4 pages, RevTex, 3 figures (eps-files), uses eps

Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ``overshoot'') effects (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed.Comment: 21 pages, RevTex, 6 figures (ps, eps

Orienting the Direction of EGFR Activation

Morphogens are typically distributed symmetrically from their source of production. In this issue of Developmental Cell, Peng et al. (2012) demonstrate that a bias in the directionality of protrusions emanating from cells secreting the EGFR ligand Spitz leads to asymmetric activation of the pathway

Phase transitions of a tethered surface model with a deficit angle term

Nambu-Goto model is investigated by using the canonical Monte Carlo simulations on fixed connectivity surfaces of spherical topology. Three distinct phases are found: crumpled, tubular, and smooth. The crumpled and the tubular phases are smoothly connected, and the tubular and the smooth phases are connected by a discontinuous transition. The surface in the tubular phase forms an oblong and one-dimensional object similar to a one-dimensional linear subspace in the Euclidean three-dimensional space R^3. This indicates that the rotational symmetry inherent in the model is spontaneously broken in the tubular phase, and it is restored in the smooth and the crumpled phases.Comment: 6 pages with 6 figure

Universal mean moment rate profiles of earthquake ruptures

Earthquake phenomenology exhibits a number of power law distributions including the Gutenberg-Richter frequency-size statistics and the Omori law for aftershock decay rates. In search for a basic model that renders correct predictions on long spatio-temporal scales, we discuss results associated with a heterogeneous fault with long range stress-transfer interactions. To better understand earthquake dynamics we focus on faults with Gutenberg-Richter like earthquake statistics and develop two universal scaling functions as a stronger test of the theory against observations than mere scaling exponents that have large error bars. Universal shape profiles contain crucial information on the underlying dynamics in a variety of systems. As in magnetic systems, we find that our analysis for earthquakes provides a good overall agreement between theory and observations, but with a potential discrepancy in one particular universal scaling function for moment-rates. The results reveal interesting connections between the physics of vastly different systems with avalanche noise.Comment: 13 pages, 5 figure

Neutrino Fluxes from NUHM LSP Annihilations in the Sun

We extend our previous studies of the neutrino fluxes expected from neutralino LSP annihilations inside the Sun to include variants of the minimal supersymmetric extension of the Standard Model (MSSM) with squark, slepton and gaugino masses constrained to be universal at the GUT scale, but allowing one or two non-universal supersymmetry-breaking parameters contributing to the Higgs masses (NUHM1,2). As in the constrained MSSM (CMSSM) with universal Higgs masses, there are large regions of the NUHM parameter space where the LSP density inside the Sun is not in equilibrium, so that the annihilation rate may be far below the capture rate, and there are also large regions where the capture rate is not dominated by spin-dependent LSP-proton scattering. The spectra possible in the NUHM are qualitatively similar to those in the CMSSM. We calculate neutrino-induced muon fluxes above a threshold energy of 10 GeV, appropriate for the IceCube/DeepCore detector, for points where the NUHM yields the correct cosmological relic density for representative choices of the NUHM parameters. We find that the IceCube/DeepCore detector can probe regions of the NUHM parameter space in addition to analogues of the focus-point strip and the tip of the coannihilation strip familiar from the CMSSM. These include regions with enhanced Higgsino-gaugino mixing in the LSP composition, that occurs where neutralino mass eigenstates cross over. On the other hand, rapid-annihilation funnel regions in general yield neutrino fluxes that are unobservably small.Comment: 23 pages, 11 figures. v2: expanded threshold discussion, small changes to match PRD versio

Nonlinear multidimensional scaling and visualization of earthquake clusters over space, time and feature space

International audienceWe present a novel technique based on a multi-resolutional clustering and nonlinear multi-dimensional scaling of earthquake patterns to investigate observed and synthetic seismic catalogs. The observed data represent seismic activities around the Japanese islands during 1997-2003. The synthetic data were generated by numerical simulations for various cases of a heterogeneous fault governed by 3-D elastic dislocation and power-law creep. At the highest resolution, we analyze the local cluster structures in the data space of seismic events for the two types of catalogs by using an agglomerative clustering algorithm. We demonstrate that small magnitude events produce local spatio-temporal patches delineating neighboring large events. Seismic events, quantized in space and time, generate the multi-dimensional feature space characterized by the earthquake parameters. Using a non-hierarchical clustering algorithm and nonlinear multi-dimensional scaling, we explore the multitudinous earthquakes by real-time 3-D visualization and inspection of the multivariate clusters. At the spatial resolutions characteristic of the earthquake parameters, all of the ongoing seismicity both before and after the largest events accumulates to a global structure consisting of a few separate clusters in the feature space. We show that by combining the results of clustering in both low and high resolution spaces, we can recognize precursory events more precisely and unravel vital information that cannot be discerned at a single resolution

Stochastics theory of log-periodic patterns

We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge