Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t) of spins not flipped by time t decays to zero like t^[-theta(d)] for low d; for high d, p(t) may decay to p(infinity)>0, because of ``blocking'' (but perhaps still like a power). What are the effects of disorder or changes of lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples --- one disordered and one homogeneous --- where p(t) decays exponentially to p(infinity).Comment: 8 pages (LaTeX); to appear in Physical Review Letter

Convex hull of a Brownian motion in confinement

We study the effect of confinement on the mean perimeter of the convex hull of a planar Brownian motion, defined as the minimum convex polygon enclosing the trajectory. We use a minimal model where an infinite reflecting wall confines the walk to its one side. We show that the mean perimeter displays a surprising minimum with respect to the starting distance to the wall and exhibits a non-analyticity for small distances. In addition, the mean span of the trajectory in a fixed direction {$\theta \in ]0,\pi/2[$}, which can be shown to yield the mean perimeter by integration over $\theta$, presents these same two characteristics. This is in striking contrast with the one dimensional case, where the mean span is an increasing analytical function. The non-monotonicity in the 2D case originates from the competition between two antagonistic effects due to the presence of the wall: reduction of the space accessible to the Brownian motion and effective repulsion

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

Inelastic deformation of metal matrix composites: Plasticity and damage mechanisms, part 2

The inelastic deformation mechanisms for the SiC (SCS-6)/Ti-15-3 system were studied at 538 C (1000 F) using a combination of mechanical measurements and detailed microstructural examinations. The objectives were to evaluate the contributions of plasticity and damage to the overall MMC response, and to compare the room temperature and elevated temperature deformation behaviors. Four different laminates were studied: (0)8, (90)8,(+ or -45)2s, and (0/90)2s, with the primary emphasis on the unidirectional (0)8, and (90)8 systems. The elevated temperature responses were similar to those at room temperature, involving a two-stage elastic-plastic type of response for the (0)8 system, and a characteristic three-stage deformation response for the (90)8 and (+ or -45)2s systems. The primary effects of elevated temperatures included: (1) reduction in the 'yield' and failure strengths; (2) plasticity through diffused slip rather than concentrated planar slip (which occurred at room temperature); and (3) time-dependent deformation. The inelastic deformation mechanism for the (0)8 MMC was dominated by plasticity at both temperatures. For the (90)8 and (+ or -45)2s MMCs, a combination of damage and plasticity contributed to the deformation at both temperatures

Area Distribution of Elastic Brownian Motion

We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion bridge on the real line with the origin removed. We will stress on the power of self adjoint extension to investigate different possible boundary conditions for the stochastic processes.Comment: 18 pages, published versio

Two Cases of Primary Ectopic Ovarian Pregnancy

Primary ovarian pregnancy is one of the rarest varieties of ectopic pregnancies. Patients frequently present with abdominal pain and menstrual irregularities. Intrauterine devices have evolved as probable risk factors. Preoperative diagnosis is challenging but transvaginal sonography has often been helpful. A diagnostic delay may lead to rupture, secondary implantation or operative difficulties. Therefore, awareness of this rare condition is important in reducing the associated risks. Here, we report two cases of primary ovarian pregnancies presenting with acute abdominal pain. Transabdominal ultrasonography failed to hint at ovarian pregnancy in one, while transvaginal sonography aided in the correct diagnosis of the other. Both cases were confirmed by histopathological examinations and were successfully managed by surgery

Spatial survival probability for one-dimensional fluctuating interfaces in the steady state

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the `sampling interval' used in the measurement for both `steady-state' and `finite' initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A `deterministic approximation' is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.Comment: RevTeX4, 21 pages, 8 .eps figures, changes in sections IIIB and IIIC and in Figs 7 and 8, version to be published in Physical Review

Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation

We consider a class of real random polynomials, indexed by an integer d, of large degree n and focus on the number of real roots of such random polynomials. The probability that such polynomials have no real root in the interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)>0 is the exponent associated to the decay of the persistence probability for the diffusion equation with random initial conditions in space dimension d. For n even, the probability that such polynomials have no root on the full real axis decays as n^{-2(\theta(d) + \theta(2))}. For d=1, this connection allows for a physical realization of real random polynomials. We further show that the probability that such polynomials have exactly k real roots in [0,1] has an unusual scaling form given by n^{-\tilde \phi(k/\log n)} where \tilde \phi(x) is a universal large deviation function.Comment: 4 pages, 3 figures. Minor changes. Accepted version in Phys. Rev. Let