67,291 research outputs found
Material independent crack arrest statistics
The propagation of (planar) cracks in a heterogeneous brittle material
characterized by a random field of toughness is considered, taking into account
explicitly the effect of the crack front roughness on the local stress
intensity factor. In the so-called strong-pinning regime, the onset of crack
propagation appears to map onto a second-order phase transition characterized
by universal critical exponents which are independent of the local
characteristics of the medium. Propagation over large distances can be
described by using a simple one-dimensional description, with a correlation
length and an effective macroscopic toughness distribution that scale in a
non-trivial fashion with the crack front length. As an application of the above
concepts, the arrest of indentation cracks is addressed, and the analytical
expression for the statistical distribution of the crack radius at arrest is
derived. The analysis of indentation crack radii on alumina is shown to obey
the predicted algebraic expression for the radius distribution and its
dependence on the indentation load
Infinite Volume Relaxation in the Sherrington-Kirkpatrick Model
In a recent work (Eissfeller and Opper, 1992) a numerical method has been
proposed to simulate off-equilibrium zero-temperature parallel dynamics for the
SK model without finite size effects. We study the extension of the method to
non-zero temperature and sequential dynamics, and analyze more carefully the
involved computational problems. We find evidence, in the glassy phase, for an
algebraic relaxation of the energy density to its equilibrium value, at least
at large enough temperatures, and for an algebraic relaxation of the
magnetization to zero at non-zero temperatures, with an exponent directly
proportional to the temperature.Comment: 20 pages, Plain TeX with macros included, 11 PostScript figures in a
separate file, included via EPSF and ROTATE macro packages for DVIPS driver,
internal report n. 1039 Dipartimento di Fisica dell'Univ. di Roma La Sapienza
e INFN sezione di Rom
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example
We propose a generalisation of Gibbs' statistical mechanics into the domain
of non-negligible phase space correlations. Derived are the probability
distribution and entropy as a generalised ensemble average, replacing
Gibbs-Boltzmann-Shannon's entropy definition enabling construction of new forms
of statistical mechanics. The general entropy may also be of importance in
information theory and data analysis. Application to generalised Lorentzian
phase space elements yields the Gibbs-Lorentzian power law probability
distribution and statistical mechanics. Details can be found in arXiv:1406.6639Comment: 6 pages, no figures, paper appeared in slightly different form in.
For details on application see arXiv:1406.663
Google matrix analysis of DNA sequences
For DNA sequences of various species we construct the Google matrix G of
Markov transitions between nearby words composed of several letters. The
statistical distribution of matrix elements of this matrix is shown to be
described by a power law with the exponent being close to those of outgoing
links in such scale-free networks as the World Wide Web (WWW). At the same time
the sum of ingoing matrix elements is characterized by the exponent being
significantly larger than those typical for WWW networks. This results in a
slow algebraic decay of the PageRank probability determined by the distribution
of ingoing elements. The spectrum of G is characterized by a large gap leading
to a rapid relaxation process on the DNA sequence networks. We introduce the
PageRank proximity correlator between different species which determines their
statistical similarity from the view point of Markov chains. The properties of
other eigenstates of the Google matrix are also discussed. Our results
establish scale-free features of DNA sequence networks showing their
similarities and distinctions with the WWW and linguistic networks.Comment: latex, 11 fig
Noncommutative Bayesian Statistical Inference from a wedge of a Bifurcate Killing Horizon
Expanding a remark of my PHD-thesis the noncommutative bayesian statistical
inference from one wedge of a bifurcate Killing horizon is analyzed looking at
its inter-relation with the Unruh effectComment: some correction performed; to appear in "International Journal of
Theoretical Physics
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