8,528 research outputs found
Desalination effluents and the establishment of the non-indigenous skeleton shrimp Paracaprella pusilla Mayer, 1890 in the south-eastern Mediterranean
A decade long monitoring programme has revealed a flourishing population of the non-indigenous skeleton shrimp Paracaprella pusilla in the vicinity of outfalls of desalination plants off the Mediterranean coast of Israel. The first specimens were collected in 2010, thus predating all previously published records of this species in the Mediterranean Sea. A decade-long disturbance regime related to the construction and operation of the plants may have had a critical role in driving the population growth
Desalination effluents and the establishment of the non-indigenous skeleton shrimp Paracaprella pusilla Mayer, 1890 in the south-eastern Mediterranean
A decade long monitoring programme has revealed a flourishing population of the non-indigenous skeleton shrimp Paracaprella pusilla in the vicinity of outfalls of desalination plants off the Mediterranean coast of Israel. The first specimens were collected in 2010, thus predating all previously published records of this species in the Mediterranean Sea. A decade-long disturbance regime related to the construction and operation of the plants may have had a critical role in driving the population growth
General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity
For a very general class of probability distributions in disordered Ising
spin systems, in the thermodynamical limit, we prove the following property for
overlaps among real replicas. Consider the overlaps among s replicas. Add one
replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas,
let us say a, and the added s+1 is either independent of the former ones, or it
is identical to one of the overlaps q(a,b), with b running among the first s
replicas, excluding a. Each of these cases has equal probability 1/s.Comment: LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical
and General. Also available at
http://rerumnatura.zool.su.se/stefano/ms/ghigu.p
On the Thermodynamic Limit in Random Resistors Networks
We study a random resistors network model on a euclidean geometry \bt{Z}^d.
We formulate the model in terms of a variational principle and show that, under
appropriate boundary conditions, the thermodynamic limit of the dissipation per
unit volume is finite almost surely and in the mean. Moreover, we show that for
a particular thermodynamic limit the result is also independent of the boundary
conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty',
revised version to appear in Journal of Physics
A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models
The aim of this paper is to discuss the main ideas of the Talagrand proof of
the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a
physicist's approach. We consider the case of the spherical -spin model,
which has the following advantages: 1) the Parisi Ansatz takes the simple ``one
step replica symmetry breaking form'', 2) the replica free-energy as a function
of the order parameters is simple enough to allow for numerical maximization
with arbitrary precision. We present the essential ideas of the proof, we
stress its connections with the theory of effective potentials for glassy
systems, and we reduce the technically more difficult part of the Talagrand's
analysis to an explicit evaluation of the solution of a variational problem.Comment: 20 pages, 5 figures. Added references and minor language correction
Replica symmetry breaking in mean field spin glasses trough Hamilton-Jacobi technique
During the last years, through the combined effort of the insight, coming
from physical intuition and computer simulation, and the exploitation of
rigorous mathematical methods, the main features of the mean field
Sherrington-Kirkpatrick spin glass model have been firmly established. In
particular, it has been possible to prove the existence and uniqueness of the
infinite volume limit for the free energy, and its Parisi expression, in terms
of a variational principle, involving a functional order parameter. Even the
expected property of ultrametricity, for the infinite volume states, seems to
be near to a complete proof. The main structural feature of this model, and
related models, is the deep phenomenon of spontaneous replica symmetry breaking
(RSB), discovered by Parisi many years ago. By expanding on our previous work,
the aim of this paper is to investigate a general frame, where replica symmetry
breaking is embedded in a kind of mechanical scheme of the Hamilton-Jacobi
type. Here, the analog of the "time" variable is a parameter characterizing the
strength of the interaction, while the "space" variables rule out
quantitatively the broken replica symmetry pattern. Starting from the simple
cases, where annealing is assumed, or replica symmetry, we build up a
progression of dynamical systems, with an increasing number of space variables,
which allow to weaken the effect of the potential in the Hamilton-Jacobi
equation, as the level of symmetry braking is increased. This new machinery
allows to work out mechanically the general K-step RSB solutions, in a
different interpretation with respect to the replica trick, and lightens easily
their properties as existence or uniqueness.Comment: 24 pages, no figure
A Statistical Interpretation of Space and Classical-Quantum duality
By defining a prepotential function for the stationary Schr\"odinger equation
we derive an inversion formula for the space variable as a function of the
wave-function . The resulting equation is a Legendre transform that
relates , the prepotential , and the probability density. We
invert the Schr\"odinger equation to a third-order differential equation for
and observe that the inversion procedure implies a -
duality. This phenomenon is related to a modular symmetry due to the
superposition of the solutions of the Schr\"odinger equation. We propose that
in quantum mechanics the space coordinate can be interpreted as a macroscopic
variable of a statistical system with playing the role of a scaling
parameter. We show that the scaling property of the space coordinate with
respect to is determined by the
``beta-function''. We propose that the quantization of the inversion formula is
a natural way to quantize geometry. The formalism is extended to higher
dimensions and to the Klein-Gordon equation.Comment: 11 pages. Standard Latex. Final version to appear in Physical Review
Letters. Revised and extended version. The formalism is extended to higher
dimensions and to the Klein-Gordon equation. A possible connection with
string theory is considered. The duality is emphasized by a minor
change in the title. The new title is: Duality of and and a
statistical interpretation of space in quantum mechanic
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
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