1,246 research outputs found
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
is released. The energy distribution follows asymptotically a universal power
law , 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 of the cusp map
, (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
the spectrum of in the Hardy space in the disk
\{z\in\C:|z-q|<1+q\} is the union of the segment 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 ().
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 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 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 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
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