1,450 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
Stress field around arbitrarily shaped cracks in two-dimensional elastic materials
The calculation of the stress field around an arbitrarily shaped crack in an
infinite two-dimensional elastic medium is a mathematically daunting problem.
With the exception of few exactly soluble crack shapes the available results
are based on either perturbative approaches or on combinations of analytic and
numerical techniques. We present here a general solution of this problem for
any arbitrary crack. Along the way we develop a method to compute the conformal
map from the exterior of a circle to the exterior of a line of arbitrary shape,
offering it as a superior alternative to the classical Schwartz-Cristoffel
transformation. Our calculation results in an accurate estimate of the full
stress field and in particular of the stress intensity factors K_I and K_{II}
and the T-stress which are essential in the theory of fracture.Comment: 7 pages, 4 figures, submitted for PR
New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps
We report a new algorithm to generate Laplacian Growth Patterns using
iterated conformal maps. The difficulty of growing a complete layer with local
width proportional to the gradient of the Laplacian field is overcome. The
resulting growth patterns are compared to those obtained by the best algorithms
of direct numerical solutions. The fractal dimension of the patterns is
discussed.Comment: Sumitted to Phys. Rev. Lett. Further details at
http://www.pik-potsdam.de/~ander
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
Ferromagnetic models for cooperative behavior: Revisiting Universality in complex phenomena
Ferromagnetic models are harmonic oscillators in statistical mechanics.
Beyond their original scope in tackling phase transition and symmetry breaking
in theoretical physics, they are nowadays experiencing a renewal applicative
interest as they capture the main features of disparate complex phenomena,
whose quantitative investigation in the past were forbidden due to data
lacking. After a streamlined introduction to these models, suitably embedded on
random graphs, aim of the present paper is to show their importance in a
plethora of widespread research fields, so to highlight the unifying framework
reached by using statistical mechanics as a tool for their investigation.
Specifically we will deal with examples stemmed from sociology, chemistry,
cybernetics (electronics) and biology (immunology).Comment: Contributing to the proceedings of the Conference "Mathematical
models and methods for Planet Heart", INdAM, Rome 201
Equilibrium statistical mechanics on correlated random graphs
Biological and social networks have recently attracted enormous attention
between physicists. Among several, two main aspects may be stressed: A non
trivial topology of the graph describing the mutual interactions between agents
exists and/or, typically, such interactions are essentially (weighted)
imitative. Despite such aspects are widely accepted and empirically confirmed,
the schemes currently exploited in order to generate the expected topology are
based on a-priori assumptions and in most cases still implement constant
intensities for links. Here we propose a simple shift in the definition of
patterns in an Hopfield model to convert frustration into dilution: By varying
the bias of the pattern distribution, the network topology -which is generated
by the reciprocal affinities among agents - crosses various well known regimes
(fully connected, linearly diverging connectivity, extreme dilution scenario,
no network), coupled with small world properties, which, in this context, are
emergent and no longer imposed a-priori. The model is investigated at first
focusing on these topological properties of the emergent network, then its
thermodynamics is analytically solved (at a replica symmetric level) by
extending the double stochastic stability technique, and presented together
with its fluctuation theory for a picture of criticality. At least at
equilibrium, dilution simply decreases the strength of the coupling felt by the
spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main
difference with respect to previous investigations and a naive picture is that
within our approach replicas do not appear: instead of (multi)-overlaps as
order parameters, we introduce a class of magnetizations on all the possible
sub-graphs belonging to the main one investigated: As a consequence, for these
objects a closure for a self-consistent relation is achieved.Comment: 30 pages, 4 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
Analogue neural networks on correlated random graphs
We consider a generalization of the Hopfield model, where the entries of
patterns are Gaussian and diluted. We focus on the high-storage regime and we
investigate analytically the topological properties of the emergent network, as
well as the thermodynamic properties of the model. We find that, by properly
tuning the dilution in the pattern entries, the network can recover different
topological regimes characterized by peculiar scalings of the average
coordination number with respect to the system size. The structure is also
shown to exhibit a large degree of cliquishness, even when very sparse.
Moreover, we obtain explicitly the replica symmetric free energy and the
self-consistency equations for the overlaps (order parameters of the theory),
which turn out to be classical weighted sums of 'sub-overlaps' defined on all
possible sub-graphs. Finally, a study of criticality is performed through a
small-overlap expansion of the self-consistencies and through a whole
fluctuation theory developed for their rescaled correlations: Both approaches
show that the net effect of dilution in pattern entries is to rescale the
critical noise level at which ergodicity breaks down.Comment: 34 pages, 3 figure
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