239 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
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
Large-scale proteomic analysis of human brain identifies proteins associated with cognitive trajectory in advanced age
In advanced age, some individuals maintain a stable cognitive trajectory while others experience a rapid decline. Such variation in cognitive trajectory is only partially explained by traditional neurodegenerative pathologies. Hence, to identify new processes underlying variation in cognitive trajectory, we perform an unbiased proteome-wide association study of cognitive trajectory in a discovery (n = 104) and replication cohort (n = 39) of initially cognitively unimpaired, longitudinally assessed older-adult brain donors. We find 579 proteins associated with cognitive trajectory after meta-analysis. Notably, we present evidence for increased neuronal mitochondrial activities in cognitive stability regardless of the burden of traditional neuropathologies. Furthermore, we provide additional evidence for increased synaptic abundance and decreased inflammation and apoptosis in cognitive stability. Importantly, we nominate proteins associated with cognitive trajectory, particularly the 38 proteins that act independently of neuropathologies and are also hub proteins of protein co-expression networks, as promising targets for future mechanistic studies of cognitive trajectory.Accelerating Medicine Partnership for AD [U01AG046161, U01 AG061357]; Emory Alzheimer's Disease Research Center [P50 AG025688]; NINDS Emory Neuroscience Core [P30 NS055077]; intramural program of the National Institute on Aging (NIA); Alzheimer's Association; Alzheimer's Research UK; Michael J. Fox Foundation for Parkinson's Research; Weston Brain Institute Biomarkers Across Neurodegenerative Diseases Grant [11060]; National Institute of Neurological Disorders and Stroke [U24 NS072026]; National Institute on Aging [P30 AG19610]; Arizona Department of Health Services [211002]; Arizona Biomedical Research Commission [4001, 0011, 05-901, 1001]; [R01 AG056533]; [R01 AG053960]; [U01 MH115484]; [I01 BX003853]; [IK2 BX001820]; [R01 AG061800]; [R01 AG057911]Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]
Local Persistence in the Directed Percolation Universality Class
We revisit the problem of local persistence in directed percolation,
reporting improved estimates of the persistence exponent in 1+1 dimensions,
discovering strong corrections to scaling in higher dimensions, and
investigating the mean field limit. Moreover, we introduce a graded persistence
probability that a site does not flip more than n times and demonstrate how
local persistence can be studied in seed simulations. Finally, the problem of
spatial (as opposed to temporal) persistence is investigated.Comment: LaTeX, 24 pages, 12 figures; references added and corrected, section
4.3 rewritte
- …