The longest excursion of stochastic processes in nonequilibrium systems

We consider the excursions, i.e. the intervals between consecutive zeros, of stochastic processes that arise in a variety of nonequilibrium systems and study the temporal growth of the longest one l_{\max}(t) up to time t. For smooth processes, we find a universal linear growth \simeq Q_{\infty} t with a model dependent amplitude Q_\infty. In contrast, for non-smooth processes with a persistence exponent \theta, we show that < l_{\max}(t) > has a linear growth if \theta \sim t^{1-\psi} if \theta > \theta_c. The amplitude Q_{\infty} and the exponent \psi are novel quantities associated to nonequilibrium dynamics. These behaviors are obtained by exact analytical calculations for renewal and multiplicative processes and numerical simulations for other systems such as the coarsening dynamics in Ising model as well as the diffusion equation with random initial conditions.Comment: 4 pages,2 figure

Reconstruction of deglacial sea surface temperatures in the tropical Pacific from selective analysis of a fossil coral

The Sr/Ca of coral skeletons demonstrates potential as an indicator of sea surface temperatures (SSTs). However, the glacial-interglacial SST ranges predicted from Sr/Ca of fossil corals are usually higher than from other marine proxies. We observed infilling of secondary aragonite, characterised by high Sr/Ca ratios, along intraskeletal pores of a fossil coral from Papua New Guinea that grew during the penultimate deglaciation (130 +/- 2 ka). Selective microanalysis of unaltered areas of the fossil coral indicates that SSTs at similar to 130 ka were &lt;= 1 degrees C cooler than at present in contrast with bulk measurements ( combining infilled and unaltered areas) which indicate a difference of 6-7 degrees C. The analysis of unaltered areas of fossil skeletons by microprobe techniques may offer a route to more accurate reconstruction of past SSTs.</p

Evidence of Variable Zn/Fe in Zinc-Ferrites Produced From Roasting of Zinc Sulphide Concentrate

Zn-Fe-O phases formed during roasting of concentrates from zinc sulfide ores produce soluble zinc oxide, oxy-sulfates and insoluble ferrite compounds. The ferrites have a general formula ZnOFe2O3. However, these ferrites have a range of magnetic properties, suggesting variable stoichiometry. Scanning electron microscopy has been used to obtain the general relationship between the Zn/Fe ratio of the ferrites and their magnetic susceptibility

Grothendieck's constant and local models for noisy entangled quantum states

We relate the nonlocal properties of noisy entangled states to Grothendieck's constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states \rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}, we show that there is a local model for projective measurements if and only if $p \le 1/K_G(3)$, where $K_G(3)$ is Grothendieck's constant of order 3. Known bounds on $K_G(3)$ prove the existence of this model at least for $p \lesssim 0.66$, quite close to the current region of Bell violation, $p \sim 0.71$. We generalize this result to arbitrary quantum states.Comment: 6 pages, 1 figur

The spectrum of large powers of the Laplacian in bounded domains

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.Comment: 13 pages, 2 figure

Statistical Properties of the Final State in One-dimensional Ballistic Aggregation

We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final `fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Frechet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of N-body dissipative dynamics.Comment: 19 pages, 5 figures include

Charged anisotropic matter with linear equation of state

We consider the general situation of a compact relativistic body with anisotropic pressures in the presence of the electromagnetic field. The equation of state for the matter distribution is linear and may be applied to strange stars with quark matter. Three classes of new exact solutions are found to the Einstein-Maxwell system. This is achieved by specifying a particular form for one of the gravitational potentials and the electric field intensity. We can regain anisotropic and isotropic models from our general class of solution. A physical analysis indicates that the charged solutions describe realistic compact spheres with anisotropic matter distribution. The equation of state is consistent with dark energy stars and charged quark matter distributions. The masses and central densities correspond to realistic stellar objects in the general case when anisotropy and charge are present.Comment: 17 pages, To appear in Class. Quantum Gra