1,637 research outputs found
Quasi-Static Brittle Fracture in Inhomogeneous Media and Iterated Conformal Maps: Modes I, II and III
The method of iterated conformal maps is developed for quasi-static fracture
of brittle materials, for all modes of fracture. Previous theory, that was
relevant for mode III only, is extended here to mode I and II. The latter
require solution of the bi-Laplace rather than the Laplace equation. For all
cases we can consider quenched randomness in the brittle material itself, as
well as randomness in the succession of fracture events. While mode III calls
for the advance (in time) of one analytic function, mode I and II call for the
advance of two analytic functions. This fundamental difference creates
different stress distribution around the cracks. As a result the geometric
characteristics of the cracks differ, putting mode III in a different class
compared to modes I and II.Comment: submitted to PRE For a version with qualitatively better figures see:
http://www.weizmann.ac.il/chemphys/ander
Towards an Unsupervised Speaking Style Voice Building Framework:Multi-Style Speaker Diarization
Criticality in diluted ferromagnet
We perform a detailed study of the critical behavior of the mean field
diluted Ising ferromagnet by analytical and numerical tools. We obtain
self-averaging for the magnetization and write down an expansion for the free
energy close to the critical line. The scaling of the magnetization is also
rigorously obtained and compared with extensive Monte Carlo simulations. We
explain the transition from an ergodic region to a non trivial phase by
commutativity breaking of the infinite volume limit and a suitable vanishing
field. We find full agreement among theory, simulations and previous results.Comment: 23 pages, 3 figure
Transport and dynamics on open quantum graphs
We study the classical limit of quantum mechanics on graphs by introducing a
Wigner function for graphs. The classical dynamics is compared to the quantum
dynamics obtained from the propagator. In particular we consider extended open
graphs whose classical dynamics generate a diffusion process. The transport
properties of the classical system are revealed in the scattering resonances
and in the time evolution of the quantum system.Comment: 42 pages, 13 figures, submitted to PR
The Ariel II (UK-2) International Satellite Environmental Test Program
An important new aspect of the space sciences is the associated field of reliability. The largest part of this effort on a space flight project is environmental testing. This paper presents, as an example, the successful environmental test program of the International Satellite Ariel II. Several specialized tests and unique techniques were employed to assure the quality necessary to accomplish the spacecraft mission. Valuable background information is provided on the mission, technical description, and launch of Ariel II. United Kingdom scientists have received data from more than 5000 orbits on: (a) galactic noise in the 0.75 to 3.0 Me region, (b) the vertical distribution of ozone in the earth\u27s atmosphere, and (c) micrometeoroid density
Interpolating the Sherrington-Kirkpatrick replica trick
The interpolation techniques have become, in the past decades, a powerful
approach to lighten several properties of spin glasses within a simple
mathematical framework. Intrinsically, for their construction, these schemes
were naturally implemented into the cavity field technique, or its variants as
the stochastic stability or the random overlap structures. However the first
and most famous approach to mean field statistical mechanics with quenched
disorder is the replica trick. Among the models where these methods have been
used (namely, dealing with frustration and complexity), probably the best known
is the Sherrington-Kirkpatrick spin glass: In this paper we are pleased to
apply the interpolation scheme to the replica trick framework and test it
directly to the cited paradigmatic model: interestingly this allows to obtain
easily the replica-symmetric control and, synergically with the broken replica
bounds, a description of the full RSB scenario, both coupled with several minor
theorems. Furthermore, by treating the amount of replicas as an
interpolating parameter (far from its original interpretation) this can be
though of as a quenching temperature close to the one introduce in
off-equilibrium approaches and, within this viewpoint, the proof of the
attended commutativity of the zero replica and the infinite volume limits can
be obtained.Comment: This article is dedicated to David Sherrington on the occasion of his
seventieth birthda
How glassy are neural networks?
In this paper we continue our investigation on the high storage regime of a
neural network with Gaussian patterns. Through an exact mapping between its
partition function and one of a bipartite spin glass (whose parties consist of
Ising and Gaussian spins respectively), we give a complete control of the whole
annealed region. The strategy explored is based on an interpolation between the
bipartite system and two independent spin glasses built respectively by
dichotomic and Gaussian spins: Critical line, behavior of the principal
thermodynamic observables and their fluctuations as well as overlap
fluctuations are obtained and discussed. Then, we move further, extending such
an equivalence beyond the critical line, to explore the broken ergodicity phase
under the assumption of replica symmetry and we show that the quenched free
energy of this (analogical) Hopfield model can be described as a linear
combination of the two quenched spin-glass free energies even in the replica
symmetric framework
Multitasking associative networks
We introduce a bipartite, diluted and frustrated, network as a sparse
restricted Boltzman machine and we show its thermodynamical equivalence to an
associative working memory able to retrieve multiple patterns in parallel
without falling into spurious states typical of classical neural networks. We
focus on systems processing in parallel a finite (up to logarithmic growth in
the volume) amount of patterns, mirroring the low-level storage of standard
Amit-Gutfreund-Sompolinsky theory. Results obtained trough statistical
mechanics, signal-to-noise technique and Monte Carlo simulations are overall in
perfect agreement and carry interesting biological insights. Indeed, these
associative networks pave new perspectives in the understanding of multitasking
features expressed by complex systems, e.g. neural and immune networks.Comment: to appear on Phys.Rev.Let
Conformal Dynamics of Precursors to Fracture
An exact integro-differential equation for the conformal map from the unit
circle to the boundary of an evolving cavity in a stressed 2-dimensional solid
is derived. This equation provides an accurate description of the dynamics of
precursors to fracture when surface diffusion is important. The solution
predicts the creation of sharp grooves that eventually lead to material failure
via rapid fracture. Solutions of the new equation are demonstrated for the
dynamics of an elliptical cavity and the stability of a circular cavity under
biaxial stress, including the effects of surface stress.Comment: 4 pages, 3 figure
A linear Stark shift in dressed atoms as a signal to measure a nuclear anapole moment with a cold atom fountain or interferometer
We demonstrate theoretically the existence of a linear dc Stark shift of the
individual substates of an alkali atom in its ground state, dressed by a
circularly polarized laser field. It arises from the electroweak nuclear
anapole moment violating P but not T. It is characterized by the pseudoscalar
equal to the mixed product formed with the photon angular momentum and static
electric and magnetic fields. We derive the relevant left-right asymmetry with
its complete signature in a field configuration selected for a precision
measurement with cold atom beams. The 3,3 to 4,3 Cs hyperfine-transition
frequency shift amounts to 7 Hz for a laser power of about 1 kW at 877 nm,
E=100 kV/cm and B larger than 0.5 G.Comment: Article, 4 pages, 2 figure
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