1,073 research outputs found
Spatial fluctuations of a surviving particle in the trapping reaction
We consider the trapping reaction, , where and particles
have a diffusive dynamics characterized by diffusion constants and .
The interaction with particles can be formally incorporated in an effective
dynamics for one particle as was recently shown by Bray {\it et al}. [Phys.
Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space
dimension , the asymptotic behaviour of the spatial fluctuation,
, for a surviving particle in the perturbative regime,
, for the case of an initially uniform distribution of
particles. We show that, for , with
. By contrast, the fluctuations of paths constrained to return to
their starting point at time grow with the larger exponent 1/3. Numerical
tests are consistent with these predictions.Comment: 10 pages, 5 figure
Dyck Paths, Motzkin Paths and Traffic Jams
It has recently been observed that the normalization of a one-dimensional
out-of-equilibrium model, the Asymmetric Exclusion Process (ASEP) with random
sequential dynamics, is exactly equivalent to the partition function of a
two-dimensional lattice path model of one-transit walks, or equivalently Dyck
paths. This explains the applicability of the Lee-Yang theory of partition
function zeros to the ASEP normalization.
In this paper we consider the exact solution of the parallel-update ASEP, a
special case of the Nagel-Schreckenberg model for traffic flow, in which the
ASEP phase transitions can be intepreted as jamming transitions, and find that
Lee-Yang theory still applies. We show that the parallel-update ASEP
normalization can be expressed as one of several equivalent two-dimensional
lattice path problems involving weighted Dyck or Motzkin paths. We introduce
the notion of thermodynamic equivalence for such paths and show that the
robustness of the general form of the ASEP phase diagram under various update
dynamics is a consequence of this thermodynamic equivalence.Comment: Version accepted for publicatio
Reports Of Conferences, Institutes, And Seminars
This quarter\u27s column offers coverage of multiple sessions from the 2016 Electronic Resources & Libraries (ER&L) Conference, held April 3–6, 2016, in Austin, Texas. Topics in serials acquisitions dominate the column, including reports on altmetrics, cost per use, demand-driven acquisitions, and scholarly communications and the use of subscriptions agents; ERMS, access, and knowledgebases are also featured
Lee-Yang zeros and phase transitions in nonequilibrium steady states
We consider how the Lee-Yang description of phase transitions in terms of
partition function zeros applies to nonequilibrium systems. Here one does not
have a partition function, instead we consider the zeros of a steady-state
normalization factor in the complex plane of the transition rates. We obtain
the exact distribution of zeros in the thermodynamic limit for a specific
model, the boundary-driven asymmetric simple exclusion process. We show that
the distributions of zeros at the first and second order nonequilibrium phase
transitions of this model follow the patterns known in the Lee-Yang equilibrium
theory.Comment: 4 pages RevTeX4 with 4 figures; revised version to appear in Phys.
Rev. Let
When is a bottleneck a bottleneck?
Bottlenecks, i.e. local reductions of capacity, are one of the most relevant
scenarios of traffic systems. The asymmetric simple exclusion process (ASEP)
with a defect is a minimal model for such a bottleneck scenario. One crucial
question is "What is the critical strength of the defect that is required to
create global effects, i.e. traffic jams localized at the defect position".
Intuitively one would expect that already an arbitrarily small bottleneck
strength leads to global effects in the system, e.g. a reduction of the maximal
current. Therefore it came as a surprise when, based on computer simulations,
it was claimed that the reaction of the system depends in non-continuous way on
the defect strength and weak defects do not have a global influence on the
system. Here we reconcile intuition and simulations by showing that indeed the
critical defect strength is zero. We discuss the implications for the analysis
of empirical and numerical data.Comment: 8 pages, to appear in the proceedings of Traffic and Granular Flow
'1
Modelling of quasi-optical arrays
A model for analyzing quasi-optical grid amplifiers based on a finite-element electromagnetic simulator is presented. This model is deduced from the simulation of the whole unit cell and takes into account mutual coupling effects. By using this model, the gain of a 10×10 grid amplifier has been accurately predicted. To further test the validity of the model three passive structures with different loads have been fabricated and tested using a new focused-beam network analyzer that we developed
Perceived Hearing Loss and Availability of Audiologists in Appalachia
Introduction: There is a high demand for audiologists throughout the United States. Previous research has supported an additional demand for these providers within Appalachia.
Purpose: The purpose of the study was to determine if Appalachia has a disproportionally high demand for audiologists compared to the rest of the United States.
Methods: A cross-sectional retrospective study was performed with population data from the Appalachian Regional Commission, the American Academy of Audiology, and the United States Census Bureau. County-level population-weighted averages of individuals with perceived hearing loss and number of audiologists per capita were compared between Appalachian and non-Appalachian counties.
Results: A mean weighted 5.76 % of individuals reported hearing loss within Appalachia, which was 1.1% higher than the rest of the United States. The 1.14 audiologists per 100,000 individuals in Appalachian counties was not significantly lower than the 1.32 audiologists per 100,000 individuals found in non-Appalachian counties. Audiologists per capita decreased with increases in Beale code and percent reporting hearing loss.
Conclusion: The high number of individuals reporting hearing loss supports an increased demand for audiologists in rural Appalachia. More research is needed to determine how to meet this demand or improve the efficacy of the limited number of providers
Exact joint density-current probability function for the asymmetric exclusion process
We study the asymmetric exclusion process with open boundaries and derive the
exact form of the joint probability function for the occupation number and the
current through the system. We further consider the thermodynamic limit,
showing that the resulting distribution is non-Gaussian and that the density
fluctuations have a discontinuity at the continuous phase transition, while the
current fluctuations are continuous. The derivations are performed by using the
standard operator algebraic approach, and by the introduction of new operators
satisfying a modified version of the original algebra.Comment: 4 pages, 3 figure
Nonequilibrium stationary states and equilibrium models with long range interactions
It was recently suggested by Blythe and Evans that a properly defined steady
state normalisation factor can be seen as a partition function of a fictitious
statistical ensemble in which the transition rates of the stochastic process
play the role of fugacities. In analogy with the Lee-Yang description of phase
transition of equilibrium systems, they studied the zeroes in the complex plane
of the normalisation factor in order to find phase transitions in
nonequilibrium steady states. We show that like for equilibrium systems, the
``densities'' associated to the rates are non-decreasing functions of the rates
and therefore one can obtain the location and nature of phase transitions
directly from the analytical properties of the ``densities''. We illustrate
this phenomenon for the asymmetric exclusion process. We actually show that its
normalisation factor coincides with an equilibrium partition function of a walk
model in which the ``densities'' have a simple physical interpretation.Comment: LaTeX, 23 pages, 3 EPS figure
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