6,625 research outputs found
Shape-dependence of transmission, reflection and absorption eigenvalue densities in disordered waveguides with dissipation
The universal bimodal distribution of transmission eigenvalues in lossless
diffusive systems un- derpins such celebrated phenomena as universal
conductance fluctuations, quantum shot noise in condensed matter physics and
enhanced transmission in optics and acoustics. Here, we show that in the
presence of absorption, density of the transmission eigenvalues depends on the
confinement geometry of scattering media. Furthermore, in an asymmetric
waveguide, densities of the reflection and absorption eigenvalues also depend
of the side from which the waves are incident. With increas- ing absorpotion,
the density of absorption eigenvalues transforms from single-peak to
double-peak function. Our findings open a new avenue for coherent control of
wave transmission, reflection and absorption in random media.Comment: 9 pages 8 figure
First passages in bounded domains: When is the mean first passage time meaningful?
We study the first passage statistics to adsorbing boundaries of a Brownian
motion in bounded two-dimensional domains of different shapes and
configurations of the adsorbing and reflecting boundaries. From extensive
numerical analysis we obtain the probability P(\omega) distribution of the
random variable \omega=\tau_1/(\tau_1+\tau_2), which is a measure for how
similar the first passage times \tau_1 and \tau_2 are of two independent
realisations of a Brownian walk starting at the same location. We construct a
chart for each domain, determining whether P(\omega) represents a unimodal,
bell-shaped form, or a bimodal, M-shaped behaviour. While in the former case
the mean first passage time (MFPT) is a valid characteristic of the first
passage behaviour, in the latter case it is an insufficient measure for the
process. Strikingly we find a distinct turnover between the two modes of
P(\omega), characteristic for the domain shape and the respective location of
absorbing and reflective boundaries. Our results demonstrate that large
fluctuations of the first passage times may occur frequently in two-dimensional
domains, rendering quite vague the general use of the MFPT as a robust measure
of the actual behaviour even in bounded domains, in which all moments of the
first passage distribution exist.Comment: 9 pages, 6 figure
Dynamics at barriers in bidirectional two-lane exclusion processes
A two-lane exclusion process is studied where particles move in the two lanes
in opposite directions and are able to change lanes. The focus is on the steady
state behavior in situations where a positive current is constrained to an
extended subsystem (either by appropriate boundary conditions or by the
embedding environment) where, in the absence of the constraint, the current
would be negative. We have found two qualitatively different types of steady
states and formulated the conditions of them in terms of the transition rates.
In the first type of steady state, a localized cluster of particles forms with
an anti-shock located in the subsystem and the current vanishes exponentially
with the extension of the subsystem. This behavior is analogous to that of the
one-lane partially asymmetric simple exclusion process, and can be realized
e.g. when the local drive is induced by making the jump rates in two lanes
unequal. In the second type of steady state, which is realized e.g. if the
local drive is induced purely by the bias in the lane change rates, and which
has thus no counterpart in the one-lane model, a delocalized cluster of
particles forms which performs a diffusive motion as a whole and, as a
consequence, the current vanishes inversely proportionally to the extension of
the subsystem. The model is also studied in the presence of quenched
disordered, where, in case of delocalization, phenomenological considerations
predict anomalously slow, logarithmic decay of the current with the system size
in contrast with the usual power-law.Comment: 24 pages, 13 figure
The Cavity Approach to Parallel Dynamics of Ising Spins on a Graph
We use the cavity method to study parallel dynamics of disordered Ising
models on a graph. In particular, we derive a set of recursive equations in
single site probabilities of paths propagating along the edges of the graph.
These equations are analogous to the cavity equations for equilibrium models
and are exact on a tree. On graphs with exclusively directed edges we find an
exact expression for the stationary distribution of the spins. We present the
phase diagrams for an Ising model on an asymmetric Bethe lattice and for a
neural network with Hebbian interactions on an asymmetric scale-free graph. For
graphs with a nonzero fraction of symmetric edges the equations can be solved
for a finite number of time steps. Theoretical predictions are confirmed by
simulation results. Using a heuristic method, the cavity equations are extended
to a set of equations that determine the marginals of the stationary
distribution of Ising models on graphs with a nonzero fraction of symmetric
edges. The results of this method are discussed and compared with simulations
Symmetric and Asymmetric Distributions
In recent years, the advances and abilities of computer software have substantially increased the number of scientific publications that seek to introduce new probabilistic modelling frameworks, including continuous and discrete approaches, and univariate and multivariate models. Many of these theoretical and applied statistical works are related to distributions that try to break the symmetry of the normal distribution and other similar symmetric models, mainly using Azzalini's scheme. This strategy uses a symmetric distribution as a baseline case, then an extra parameter is added to the parent model to control the skewness of the new family of probability distributions. The most widespread and popular model is the one based on the normal distribution that produces the skewed normal distribution. In this Special Issue on symmetric and asymmetric distributions, works related to this topic are presented, as well as theoretical and applied proposals that have connections with and implications for this topic. Immediate applications of this line of work include different scenarios such as economics, environmental sciences, biometrics, engineering, health, etc. This Special Issue comprises nine works that follow this methodology derived using a simple process while retaining the rigor that the subject deserves. Readers of this Issue will surely find future lines of work that will enable them to achieve fruitful research results
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