Energy bursts in fiber bundle models of composite materials

As a model of composite materials, a bundle of many fibers with stochastically distributed breaking thresholds for the individual fibers is considered. The bundle is loaded until complete failure to capture the failure scenario of composite materials under external load. The fibers are assumed to share the load equally, and to obey Hookean elasticity right up to the breaking point. We determine the distribution of bursts in which an amount of energy $E$ is released. The energy distribution follows asymptotically a universal power law $E^{-5/2}$, for any statistical distribution of fiber strengths. A similar power law dependence is found in some experimental acoustic emission studies of loaded composite materials.Comment: 5 pages, 4 fig

The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius--Perron operator $U$ of the cusp map $F:[-1,1]\to[-1,1]$, $F(x)=1-2\sqrt{|x|}$ (which is an approximation of the Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in(0,1)$ the spectrum of $U$ in the Hardy space in the disk \{z\in\C:|z-q|<1+q\} is the union of the segment $[0,1]$ and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy spaces is adde

Resonances of the cusp family

We study a family of chaotic maps with limit cases the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius--Perron operator in different function spaces including spaces of analytic functions. A numerical study of the eigenvalues and eigenfunctions is performed.Comment: 14 pages, 3 figures. Submitted to J.Phys.

The Casimir Problem of Spherical Dielectrics: Quantum Statistical and Field Theoretical Approaches

The Casimir free energy for a system of two dielectric concentric nonmagnetic spherical bodies is calculated with use of a quantum statistical mechanical method, at arbitrary temperature. By means of this rather novel method, which turns out to be quite powerful (we have shown this to be true in other situations also), we consider first an explicit evaluation of the free energy for the static case, corresponding to zero Matsubara frequency ($n=0$). Thereafter, the time-dependent case is examined. For comparison we consider the calculation of the free energy with use of the more commonly known field theoretical method, assuming for simplicity metallic boundary surfaces.Comment: 31 pages, LaTeX, one new reference; version to appear in Phys. Rev.

On the unique possibility to increase significantly the contrast of dark resonances on D1 line of 87^{87}Rb

We propose and study, theoretically and experimentally, a new scheme of excitation of a coherent population trapping resonance for D1 line of alakli atoms with nuclear spin $I=3/2$ by bichromatic linearly polarized light ({\em lin}$||${\em lin} field) at the conditions of spectral resolution of the excited state. The unique properties of this scheme result in a high contrast of dark resonance for D1 line of $^{87}$Rb.Comment: 9 pages, 7 figures. This material has been partially presented on ICONO-2005, 14 May 2005, St. Petersburg, Russia. v2 references added; text is changed a bi

Failure Processes in Elastic Fiber Bundles

The fiber bundle model describes a collection of elastic fibers under load. the fibers fail successively and for each failure, the load distribution among the surviving fibers change. Even though very simple, the model captures the essentials of failure processes in a large number of materials and settings. We present here a review of fiber bundle model with different load redistribution mechanism from the point of view of statistics and statistical physics rather than materials science, with a focus on concepts such as criticality, universality and fluctuations. We discuss the fiber bundle model as a tool for understanding phenomena such as creep, and fatigue, how it is used to describe the behavior of fiber reinforced composites as well as modelling e.g. network failure, traffic jams and earthquake dynamics.Comment: This article has been Editorially approved for publication in Reviews of Modern Physic

Failure due to fatigue in fiber bundles and solids

We consider first a homogeneous fiber bundle model where all the fibers have got the same stress threshold beyond which all fail simultaneously in absence of noise. At finite noise, the bundle acquires a fatigue behavior due to the noise-induced failure probability at any stress. We solve this dynamics of failure analytically and show that the average failure time of the bundle decreases exponentially as the stress increases. We also determine the avalanche size distribution during such failure and find a power law decay. We compare this fatigue behavior with that obtained phenomenologically for the nucleation of Griffith cracks. Next we study numerically the fatigue behavior of random fiber bundles having simple distributions of individual fiber strengths, at stress less than the bundle's strength (beyond which it fails instantly). The average failure time is again seen to decrease exponentially as the stress increases and the avalanche size distribution shows similar power law decay. These results are also in broad agreement with experimental observations on fatigue in solids. We believe, these observations regarding the failure time are useful for quantum breakdown phenomena in disordered systems.Comment: 13 pages, 4 figures, figures added and the text is revise