38 research outputs found
Spatial wave intensity correlations in quasi-one-dimensional wires
Spatial intensity correlations between waves transmitted through random media
are analyzed within the framework of the random matrix theory of transport.
Assuming that the statistical distribution of transfer matrices is isotropic,
we found that the spatial correlation function can be expressed as the sum of
three terms, with distinctive spatial dependences. This result coincides with
the one obtained in the diffusive regime from perturbative calculations, but
holds all the way from quasi-ballistic transport to localization. While
correlations are positive in the diffusive regime, we predict a transition to
negative correlations as the length of the system decreases.Comment: 10 pages, 3 figures. Submitted to Physical Review Letter
Interdependent networks with correlated degrees of mutually dependent nodes
We study a problem of failure of two interdependent networks in the case of
correlated degrees of mutually dependent nodes. We assume that both networks (A
and B) have the same number of nodes connected by the bidirectional
dependency links establishing a one-to-one correspondence between the nodes of
the two networks in a such a way that the mutually dependent nodes have the
same number of connectivity links, i.e. their degrees coincide. This implies
that both networks have the same degree distribution . We call such
networks correspondently coupled networks (CCN). We assume that the nodes in
each network are randomly connected. We define the mutually connected clusters
and the mutual giant component as in earlier works on randomly coupled
interdependent networks and assume that only the nodes which belong to the
mutual giant component remain functional. We assume that initially a
fraction of nodes are randomly removed due to an attack or failure and find
analytically, for an arbitrary , the fraction of nodes which
belong to the mutual giant component. We find that the system undergoes a
percolation transition at certain fraction which is always smaller than
the for randomly coupled networks with the same . We also find that
the system undergoes a first order transition at if has a finite
second moment. For the case of scale free networks with , the
transition becomes a second order transition. Moreover, if we find
as in percolation of a single network. For we find an exact
analytical expression for . Finally, we find that the robustness of CCN
increases with the broadness of their degree distribution.Comment: 18 pages, 3 figure
Speckle fluctuations resolve the interdistance between incoherent point sources in complex media
We study the fluctuations of the light emitted by two identical incoherent point sources in a disordered environment. The intensity-intensity correlation function and the speckle contrast, obtained after proper temporal and configurational averaging, encode the relative distance between the two sources. This suggests the intriguing possibility that intensity measurements at only one point in a speckle pattern produced by two incoherent sources can provide information about the relative distance between the sources, with a precision that is not limited by diffraction. The theory also suggests an alternative approach to the Green's-function retrieval technique, where the correlations of the isotropic ambient noise detected by two receivers are replaced by a measurement at a single point of the noise due to two fluctuating incoherent sources
The Glassy Potts Model
We introduce a Potts model with quenched, frustrated disorder, that enjoys of
a gauge symmetry that forbids spontaneous magnetization, and allows the glassy
phase to extend from down to T=0. We study numerical the 4 dimensional
model with states. We show the existence of a glassy phase, and we
characterize it by studying the probability distributions of an order
parameter, the binder cumulant and the divergence of the overlap
susceptibility. We show that the dynamical behavior of the system is
characterized by aging.Comment: 4 pages including 4 (color) ps figures (all on page 4
Evidence against a glass transition in the 10-state short range Potts glass
We present the results of Monte Carlo simulations of two different 10-state
Potts glasses with random nearest neighbor interactions on a simple cubic
lattice. In the first model the interactions come from a \pm J distribution and
in the second model from a Gaussian one, and in both cases the first two
moments of the distribution are chosen to be equal to J_0=-1 and Delta J=1. At
low temperatures the spin autocorrelation function for the \pm J model relaxes
in several steps whereas the one for the Gaussian model shows only one. In both
systems the relaxation time increases like an Arrhenius law. Unlike the
infinite range model, there are only very weak finite size effects and there is
no evidence that a dynamical or a static transition exists at a finite
temperature.Comment: 9 pages of Latex, 4 figure
Finite-size scaling at the dynamical transition of the mean-field 10-state Potts glass
We use Monte Carlo simulations to study the static and dynamical properties
of a Potts glass with infinite range Gaussian distributed exchange interactions
for a broad range of temperature and system size up to N=2560 spins. The
results are compatible with a critical divergence of the relaxation time tau at
the theoretically predicted dynamical transition temperature T_D, tau \propto
(T-T_D)^{-\Delta} with Delta \approx 2. For finite N a further power law at
T=T_D is found, tau(T=T_D) \propto N^{z^\star} with z^\star \approx 1.5 and for
T>T_D dynamical finite-size scaling seems to hold. The order parameter
distribution P(q) is qualitatively compatible with the scenario of a first
order glass transition as predicted from one-step replica symmetry breaking
schemes.Comment: 8 pages of Latex, 4 figure
One-step replica symmetry breaking solution of the quadrupolar glass model
We consider the quadrupolar glass model with infinite-range random
interaction. Introducing a simple one-step replica symmetry breaking ansatz we
investigate the para-glass continuous (discontinuous) transition which occurs
below (above) a critical value of the quadrupole dimension m*. By using a
mean-field approximation we study the stability of the one-step replica
symmetry breaking solution and show that for m>m* there are two transitions.
The thermodynamic transition is discontinuous but there is no latent heat. At a
higher temperature we find the dynamical or glass transition temperature and
the corresponding discontinuous jump of the order parameter.Comment: 10 pages, 3 figure
Inter-similarity between coupled networks
Recent studies have shown that a system composed from several randomly
interdependent networks is extremely vulnerable to random failure. However,
real interdependent networks are usually not randomly interdependent, rather a
pair of dependent nodes are coupled according to some regularity which we coin
inter-similarity. For example, we study a system composed from an
interdependent world wide port network and a world wide airport network and
show that well connected ports tend to couple with well connected airports. We
introduce two quantities for measuring the level of inter-similarity between
networks (i) Inter degree-degree correlation (IDDC) (ii) Inter-clustering
coefficient (ICC). We then show both by simulation models and by analyzing the
port-airport system that as the networks become more inter-similar the system
becomes significantly more robust to random failure.Comment: 4 pages, 3 figure