Wideband dual sphere detector of gravitational waves

We present the concept of a sensitive and broadband resonant mass gravitational wave detector. A massive sphere is suspended inside a second hollow one. Short, high-finesse Fabry-Perot optical cavities read out the differential displacements of the two spheres as their quadrupole modes are excited. At cryogenic temperatures, one approaches the standard quantum limit for broadband operation with reasonable choices for the cavity finesses and the intracavity light power. A molybdenum detector, of overall size of 2 m, would reach spectral strain sensitivities of 2x10-23Hz-1/2 between 1000 and 3000 Hz.

Mean first-passage time for system driven by the coin-toss square wave

We study the mean-first-passage-time problem for systems driven by the coin-toss square-wave signal. Exact analytic solutions are obtained for the driftless case. We also obtain approximate solutions for the potential case. The mean-first-passage time exhibits discontinuities and a remarkable nonsmooth oscillatory behavior which, to our knowledge, has not been observed for other kinds of driving noise.

Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.

Suppression of scroll wave turbulence by noise

Rotating scroll waves are dynamical spatiotemporal structures characteristic of three-dimensional active media. It is well known that, under low excitability conditions, scroll waves develop an intrinsically unstable dynamical regime that leads to a highly disorganized pattern of wave propagation. Such a ¿turbulent¿ state bears some resemblance to fibrillation states in cardiac tissue. We show here that this unstable regime can be controlled by using a spatially distributed random forcing superimposed on a control parameter of the system. Our results are obtained from numerical simulations but an explicit analytical argument that rationalizes our observations is also presented.

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.

Evidence for oxygen-island formation on Al(111): Cluster-model theory and x-ray photoelectron spectroscopy

The O 1s x-ray photoelectron spectroscopy spectrum for Al(111)/O at 300 K shows two components whose behavior as a function of time and variation of detection angle are consistent with either (a) a surface species represented by the higher binding-energy (BE) component and a subsurface species represented by the lower BE component, or (b) small close-packed oxygen islands with the interior atoms represented by the lower BE component and the perimeter atoms by the higher BE component. We have modeled both situations using ab initio Hartree-Fock wave functions for clusters of Al and O atoms. For an O atom in a threefold site, it was found that a below-surface position gave a higher O 1s BE than an above-surface position, incompatible with interpretation (a). This change in the O 1s BE could arise because the bond for O to Al may have a more covalent character when the O is below the surface than when it is above the surface. We present evidence consistent with this view. An O adatom island with all the O atoms in threefold sites gives calculated O 1s BE's which are significantly higher for the perimeter O atoms. Further, the results for an isolated O island without the Al substrate present also give higher BE¿s for the perimeter atoms. Both these results are consistent with interpretation (b). Published scanning-tunneling-microscopy data supports the suggestion that the chemisorbed state consists of small, close-packed islands, whereas the presence of two vibrational modes in high-resolution electron-energy-loss spectroscopy data has been interpreted as representing surface and subsurface oxygen atoms. In light of the present results, we suggest that a vibrational interpretation in terms of interior and perimeter adatoms should be considered.

Measures of ionicity of alkaline-earth oxides from the analysis of ab initio cluster wave functions

We present an analysis of the M-O chemical bonding in the binary oxides MgO, CaO, SrO, BaO, and Al2O3 based on ab initio wave functions. The model used to represent the local environment of a metal cation in the bulk oxide is an MO6 cluster which also includes the effect of the lattice Madelung potential. The analysis of the wave functions for these clusters leads to the conclusion that all the alkaline-earth oxides must be regarded as highly ionic oxides; however, the ionic character of the oxides decreases as one goes from MgO, almost perfectly ionic, to BaO. In Al2O3 the ionic character is further reduced; however, even in this case, the departure from the ideal, fully ionic, model of Al3+ is not exceptionally large. These conclusions are based on three measures, a decomposition of the Mq+-Oq- interaction energy, the number of electrons associated to the oxygen ions as obtained from a projection operator technique, and the analysis of the cation core-level binding energies. The increasing covalent character along the series MgO, CaO, SrO, and BaO is discussed in view of the existing theoretical models and experimental data.

Wave propagation in a medium with disordered excitability

The effect of quenched disorder on the propagation of autowaves in excitable media is studied both experimentally and numerically in relation to the light-sensitive Belousov-Zhabotinsky reaction. The spatial disorder is introduced through a random distribution with two different levels of transmittance. In one dimension the (time-averaged) wave speed is smaller than the corresponding to a homogeneous medium with the mean excitability. Contrarily, in two dimensions the velocity increases due to the roughening of the front. Results are interpreted using kinematic and scaling arguments. In particular, for d = 2 we verify a theoretical prediction of a power-law dependence for the relative change of the propagation speed on the disorder amplitude.

Regular wave propagation out of noise in chemical active media

A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosensitive Belousov-Zhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reaction-diffusion equations for an activator-inhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noise-sustained propagation in subexcitable media.

Dynamics of turing patterns under spatiotemporal forcing

We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatiotemporal forcing in the form of a traveling-wave modulation of a control parameter. We show that from strictly spatial resonance, it is possible to induce new, generic dynamical behaviors, including temporally modulated traveling waves and localized traveling solitonlike solutions. The latter make contact with the soliton solutions of Coullet [Phys. Rev. Lett. 56, 724 (1986)] and generalize them. The stability diagram for the different propagating modes in the Lengyel-Epstein model is determined numerically. Direct observations of the predicted solutions in experiments carried out with light modulations in the photosensitive chlorine dioxide-iodine-malonic acid reaction are also reported.

Space and momentum representation analysis of Hartman's effect in wave packet transmission

The Hartman effect is analyzed in both the position and momentum representations of the problem. The importance of Wigner tunneling and deep tunneling is singled out. It is shown quantitatively how the barrier acts as a filter for low momenta (quantum speed up) as the width increases, and a detailed mechanism is proposed. Superluminal transmission is also discussed.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Frontshear and backshear instabilities of the mean longshore current

An analytical model based on Bowen and Holman [1989] is used to prove the existence of instabilities due to the presence of a second extremum of the background vorticity at the front side of the longshore current. The growth rate of the so-called frontshear waves depends primarily upon the frontshear but also upon the backshear and the maximum and the width of the current. Depending on the values of these parameters, either the frontshear or the backshear instabilities may dominate. Both types of waves have a cross-shore extension of the order of the width of the current, but the frontshear modes are localized closer to the coast than are the backshear modes. Moreover, under certain conditions both unstable waves have similar growth rates with close wave numbers and angular frequencies, leading to the possibility of having modulated shear waves in the alongshore direction. Numerical analysis performed on realistic current profiles confirm the behavior anticipated by the analytical model. The theory has been applied to a current profile fitted to data measured during the 1980 Nearshore Sediment Transport Studies experiment at Leadbetter Beach that has an extremum of background vorticity at the front side of the current. In this case and in agreement with field observations, the model predicts instability, whereas the theory based only on backshear instability fai led to do so.