Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models

We study the probability density function $P(h_m,L)$ of the maximum relative height $h_m$ in a wide class of one-dimensional solid-on-solid models of finite size $L$. For all these lattice models, in the large $L$ limit, a central limit argument shows that, for periodic boundary conditions, $P(h_m,L)$ takes a universal scaling form $P(h_m,L) \sim (\sqrt{12}w_L)^{-1}f(h_m/(\sqrt{12} w_L))$, with $w_L$ the width of the fluctuating interface and $f(x)$ the Airy distribution function. For one instance of these models, corresponding to the extremely anisotropic Ising model in two dimensions, this result is obtained by an exact computation using transfer matrix technique, valid for any $L>0$. These arguments and exact analytical calculations are supported by numerical simulations, which show in addition that the subleading scaling function is also universal, up to a non universal amplitude, and simply given by the derivative of the Airy distribution function $f'(x)$.Comment: 13 pages, 4 figure

Residence time statistics for NN blinking quantum dots and other stochastic processes

We present a study of residence time statistics for $N$ blinking quantum dots. With numerical simulations and exact calculations we show sharp transitions for a critical number of dots. In contrast to expectation the fluctuations in the limit of $N \to \infty$ are non-trivial. Besides quantum dots our work describes residence time statistics in several other many particle systems for example $N$ Brownian particles. Our work provides a natural framework to detect non-ergodic kinetics from measurements of many blinking chromophores, without the need to reach the single molecule limit

Generalized Hawking-Page Phase Transition

The issue of radiant spherical black holes being in stable thermal equilibrium with their radiation bath is reconsidered. Using a simple equilibrium statistical mechanical analysis incorporating Gaussian thermal fluctuations in a canonical ensemble of isolated horizons, the heat capacity is shown to diverge at a critical value of the classical mass of the isolated horizon, given (in Planckian units) by the {\it microcanonical} entropy calculated using Loop Quantum Gravity. The analysis reproduces the Hawking-Page phase transition discerned for anti-de Sitter black holes and generalizes it in the sense that nowhere is any classical metric made use of.Comment: 9 Pages, Latex with 2 eps figure

Statistics of Multiple Sign Changes in a Discrete Non-Markovian Sequence

We study analytically the statistics of multiple sign changes in a discrete non-Markovian sequence ,\psi_i=\phi_i+\phi_{i-1} (i=1,2....,n) where \phi_i's are independent and identically distributed random variables each drawn from a symmetric and continuous distribution \rho(\phi). We show that the probability P_m(n) of m sign changes upto n steps is universal, i.e., independent of the distribution \rho(\phi). The mean and variance of the number of sign changes are computed exactly for all n>0. We show that the generating function {\tilde P}(p,n)=\sum_{m=0}^{\infty}P_m(n)p^m\sim \exp[-\theta_d(p)n] for large n where the `discrete' partial survival exponent \theta_d(p) is given by a nontrivial formula, \theta_d(p)=\log[{{\sin}^{-1}(\sqrt{1-p^2})}/{\sqrt{1-p^2}}] for 0\le p\le 1. We also show that in the natural scaling limit when m is large, n is large but but keeping x=m/n fixed, P_m(n)\sim \exp[-n \Phi(x)] where the large deviation function \Phi(x) is computed. The implications of these results for Ising spin glasses are discussed.Comment: 4 pages revtex, 1 eps figur

Persistence in higher dimensions : a finite size scaling study

We show that the persistence probability $P(t,L)$, in a coarsening system of linear size $L$ at a time $t$, has the finite size scaling form $P(t,L)\sim L^{-z\theta}f(\frac{t}{L^{z}})$ where $\theta$ is the persistence exponent and $z$ is the coarsening exponent. The scaling function $f(x)\sim x^{-\theta}$ for $x \ll 1$ and is constant for large $x$. The scaling form implies a fractal distribution of persistent sites with power-law spatial correlations. We study the scaling numerically for Glauber-Ising model at dimension $d = 1$ to 4 and extend the study to the diffusion problem. Our finite size scaling ansatz is satisfied in all these cases providing a good estimate of the exponent $\theta$.Comment: 4 pages in RevTeX with 6 figures. To appear in Phys. Rev.

Inelastic Deformation of Metal Matrix Composites

The deformation mechanisms of a Ti 15-3/SCS6 (SiC fiber) metal matrix composite (MMC) were investigated using a combination of mechanical measurements and microstructural analysis. The objectives were to evaluate the contributions of plasticity and damage to the overall inelastic response, and to confirm the mechanisms by rigorous microstructural evaluations. The results of room temperature experiments performed on 0 degree and 90 degree systems primarily are reported in this report. Results of experiments performed on other laminate systems and at high temperatures will be provided in a forthcoming report. Inelastic deformation of the 0 degree MMC (fibers parallel to load direction) was dominated by the plasticity of the matrix. In contrast, inelastic deformations of the 90 degree composite (fibers perpendicular to loading direction) occurred by both damage and plasticity. The predictions of a continuum elastic plastic model were compared with experimental data. The model was adequate for predicting the 0 degree response; however, it was inadequate for predicting the 90 degree response largely because it neglected damage. The importance of validating constitutive models using a combination of mechanical measurements and microstructural analysis is pointed out. The deformation mechanisms, and the likely sequence of events associated with the inelastic deformation of MMCs, are indicated in this paper

Persistence and First-Passage Properties in Non-equilibrium Systems

In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.Comment: Review article submitted to Advances in Physics: 149 pages, 21 Figure