278 research outputs found
Directed percolation with incubation times
We introduce a model for directed percolation with a long-range temporal
diffusion, while the spatial diffusion is kept short ranged. In an
interpretation of directed percolation as an epidemic process, this
non-Markovian modification can be understood as incubation times, which are
distributed accordingly to a Levy distribution. We argue that the best approach
to find the effective action for this problem is through a generalization of
the Cardy-Sugar method, adding the non-Markovian features into the geometrical
properties of the lattice. We formulate a field theory for this problem and
renormalize it up to one loop in a perturbative expansion. We solve the various
technical difficulties that the integrations possess by means of an asymptotic
analysis of the divergences. We show the absence of field renormalization at
one-loop order, and we argue that this would be the case to all orders in
perturbation theory. Consequently, in addition to the characteristic scaling
relations of directed percolation, we find a scaling relation valid for the
critical exponents of this theory. In this universality class, the critical
exponents vary continuously with the Levy parameter.Comment: 17 pages, 7 figures. v.2: minor correction
Gas Enrichment at Liquid-Wall Interfaces
Molecular dynamics simulations of Lennard-Jones systems are performed to
study the effects of dissolved gas on liquid-wall and liquid-gas interfaces.
Gas enrichment at walls is observed which for hydrophobic walls can exceed more
than two orders of magnitude when compared to the gas density in the bulk
liquid. As a consequence, the liquid structure close to the wall is
considerably modified, leading to an enhanced wall slip. At liquid-gas
interfaces gas enrichment is found which reduces the surface tension.Comment: main changes compared to version 1: flow simulations are included as
well as different types of gase
Spreading with immunization in high dimensions
We investigate a model of epidemic spreading with partial immunization which
is controlled by two probabilities, namely, for first infections, , and
reinfections, . When the two probabilities are equal, the model reduces to
directed percolation, while for perfect immunization one obtains the general
epidemic process belonging to the universality class of dynamical percolation.
We focus on the critical behavior in the vicinity of the directed percolation
point, especially in high dimensions . It is argued that the clusters of
immune sites are compact for . This observation implies that a
recently introduced scaling argument, suggesting a stretched exponential decay
of the survival probability for , in one spatial dimension,
where denotes the critical threshold for directed percolation, should
apply in any dimension and maybe for as well. Moreover, we
show that the phase transition line, connecting the critical points of directed
percolation and of dynamical percolation, terminates in the critical point of
directed percolation with vanishing slope for and with finite slope for
. Furthermore, an exponent is identified for the temporal correlation
length for the case of and , , which
is different from the exponent of directed percolation. We also
improve numerical estimates of several critical parameters and exponents,
especially for dynamical percolation in .Comment: LaTeX, IOP-style, 18 pages, 9 eps figures, minor changes, additional
reference
Yang-Lee zeros for a nonequilibrium phase transition
Equilibrium systems which exhibit a phase transition can be studied by
investigating the complex zeros of the partition function. This method,
pioneered by Yang and Lee, has been widely used in equilibrium statistical
physics. We show that an analogous treatment is possible for a nonequilibrium
phase transition into an absorbing state. By investigating the complex zeros of
the survival probability of directed percolation processes we demonstrate that
the zeros provide information about universal properties. Moreover we identify
certain non-trivial points where the survival probability for bond percolation
can be computed exactly.Comment: LaTeX, IOP-style, 13 pages, 10 eps 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
Proteomic Analysis of Hippocampal Dentate Granule Cells in Frontotemporal Lobar Degeneration: Application of Laser Capture Technology
Frontotemporal lobar degeneration (FTLD) is the most common cause of dementia with pre-senile onset, accounting for as many as 20% of cases. A common subset of FTLD cases is characterized by the presence of ubiquitinated inclusions in vulnerable neurons (FTLD-U). While the pathophysiological mechanisms underlying neurodegeneration in FTLD-U have not yet been elucidated, the presence of inclusions in this disease indicates enhanced aggregation of one or several proteins. Moreover, these inclusions suggest altered expression, processing, or degradation of proteins during FTLD-U pathogenesis. Thus, one approach to understanding disease mechanisms is to delineate the molecular changes in protein composition in FTLD-U brain. Using a combined approach consisting of laser capture microdissection (LCM) and high-resolution liquid chromatography-tandem mass spectrometry (LCāMS/MS), we identified 1252 proteins in hippocampal dentate granule cells excised from three post-mortem FTLD-U and three unaffected control cases processed in parallel. Additionally, we employed a labeling-free quantification technique to compare the abundance of the identified proteins between FTLD-U and control cases. Quantification revealed 54 proteins with selective enrichment in FTLD-U, including TARāDNA binding protein 43 (TDP-43), a recently identified component of ubiquitinated inclusions. Moreover, 19 proteins were selectively decreased in FTLD-U. Subsequent immunohistochemical analysis of TDP-43 and three additional protein candidates suggests that our proteomic profiling of FTLD-U dentate granule cells reveals both inclusion-associated proteins and non-aggregated disease-specific proteins. Application of LCM is a valuable tool in the molecular analysis of complex tissues, and its application in the proteomic characterization of neurodegenerative disorders such as FTLD-U may be used to identify proteins altered in disease
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
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