885 research outputs found
Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process
As a solvable and broadly applicable model system, the totally asymmetric
exclusion process enjoys iconic status in the theory of non-equilibrium phase
transitions. Here, we focus on the time dependence of the total number of
particles on a 1-dimensional open lattice, and its power spectrum. Using both
Monte Carlo simulations and analytic methods, we explore its behavior in
different characteristic regimes. In the maximal current phase and on the
coexistence line (between high/low density phases), the power spectrum displays
algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the
high/low density phases, we find pronounced \emph{oscillations}, which damp
into power laws. This behavior can be understood in terms of driven biased
diffusion with conserved noise in the bulk.Comment: 4 pages, 4 figure
Far-from-equilibrium transport with constrained resources
The totally asymmetric simple exclusion process (TASEP) is a well studied
example of far-from-equilibrium dynamics. Here, we consider a TASEP with open
boundaries but impose a global constraint on the total number of particles. In
other words, the boundary reservoirs and the system must share a finite supply
of particles. Using simulations and analytic arguments, we obtain the average
particle density and current of the system, as a function of the boundary rates
and the total number of particles. Our findings are relevant to biological
transport problems if the availability of molecular motors becomes a
rate-limiting factor.Comment: 14 pages, 7 figures, uses iopart12.clo and iopart.cl
Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources
We revisit a totally asymmetric simple exclusion process (TASEP) with open
boundaries and a global constraint on the total number of particles [Adams, et.
al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles
into the lattice depends on the number available in the reservoir. Thus, the
total occupation on the lattice feeds back into its filling process. Although a
simple domain wall theory provided reasonably good predictions for Monte Carlo
simulation results for certain quantities, it did not account for the
fluctuations of this feedback. We generalize the previous study and find
dramatically improved predictions for, e.g., the density profile on the lattice
and provide a better understanding of the phenomenon of "shock localization."Comment: 11 pages, 3 figures, v2: Minor change
On the Zero-Slope Limit of the Compactified Closed Bosonic String
In the framework of the compactified closed bosonic string theory with the
extra spatial coordinates being circular with radius , we perform both the
zero-slope limit and the limit of the tree scattering
amplitude of four massless scalar particles. We explicitly show that this
double limit leads to amplitudes involving scalars which interact through the
exchange of a scalar, spin 1 and spin 2 particle. In particular, this latter
case reproduces the same result obtained in linearized quantum gravity.Comment: 10 pages, LaTex file, DSF-T-43/9
Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
We show in the example of a one-dimensional asymmetric exclusion process that
stationary states of models with parallel dynamics may be written in a matrix
product form. The corresponding algebra is quadratic and involves three
different matrices. Using this formalism we prove previous conjectures for the
equal-time correlation functions of the model.Comment: LaTeX, 8 pages, one postscript figur
Power Spectra of a Constrained Totally Asymmetric Simple Exclusion Process
To synthesize proteins in a cell, an mRNA has to work with a finite pool of
ribosomes. When this constraint is included in the modeling by a totally
asymmetric simple exclusion process (TASEP), non-trivial consequences emerge.
Here, we consider its effects on the power spectrum of the total occupancy,
through Monte Carlo simulations and analytical methods. New features, such as
dramatic suppressions at low frequencies, are discovered. We formulate a theory
based on a linearized Langevin equation with discrete space and time. The good
agreement between its predictions and simulation results provides some insight
into the effects of finite resoures on a TASEP.Comment: 4 pages, 2 figures v2: formatting change
Gas permeation through a polymer network
We study the diffusion of gas molecules through a two-dimensional network of
polymers with the help of Monte Carlo simulations. The polymers are modeled as
non-interacting random walks on the bonds of a two-dimensional square lattice,
while the gas particles occupy the lattice cells. When a particle attempts to
jump to a nearest-neighbor empty cell, it has to overcome an energy barrier
which is determined by the number of polymer segments on the bond separating
the two cells. We investigate the gas current as a function of the mean
segment density , the polymer length and the probability
for hopping across segments. Whereas decreases monotonically with
for fixed , its behavior for fixed and increasing
depends strongly on . For small, non-zero , appears to increase
slowly with . In contrast, for , it is dominated by the underlying
percolation problem and can be non-monotonic. We provide heuristic arguments to
put these interesting phenomena into context.Comment: Dedicated to Lothar Schaefer on the occasion of his 60th birthday. 11
pages, 3 figure
Clinical, Radiological, and Molecular Findings of Acute Encephalitis in a COVID-19 Patient: A Rare Case Report.
We report a case of encephalitis in a young male patient with severe coronavirus disease 2019 (COVID-19) who initially presented with typical symptoms of fever, dry cough, and shortness of breath but later on developed acute respiratory distress syndrome and required mechanical ventilation. Two days post-extubation, the patient developed new-onset generalized tonic-clonic seizures and confusion. MRI of the brain was done and it showed an abnormal signal in the bilateral medial cortical frontal region. His cerebral spinal fluid (CSF) analysis revealed a characteristic picture of a viral infection with a high white blood cell count and normal glucose and protein levels. After ruling out all common causes of viral encephalitis such as herpes simplex virus (HSV) and based on the review of available literature regarding the neurological manifestations of COVID-19, this case was labeled as acute viral encephalitis secondary to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection
Zero-range process with long-range interactions at a T-junction
A generalized zero-range process with a limited number of long-range
interactions is studied as an example of a transport process in which particles
at a T-junction make a choice of which branch to take based on traffic levels
on each branch. The system is analysed with a self-consistent mean-field
approximation which allows phase diagrams to be constructed. Agreement between
the analysis and simulations is found to be very good.Comment: 21 pages, 6 figure
Periodic One-Dimensional Hopping Model with one Mobile Directional Impurity
Analytic solution is given in the steady state limit for the system of Master
equations describing a random walk on one-dimensional periodic lattices with
arbitrary hopping rates containing one mobile, directional impurity (defect
bond). Due to the defect, translational invariance is broken, even if all other
rates are identical. The structure of Master equations lead naturally to the
introduction of a new entity, associated with the walker-impurity pair which we
call the quasi-walker. The velocities and diffusion constants for both the
random walker and impurity are given, being simply related to that of the
quasi-particle through physically meaningful equations. Applications in driven
diffusive systems are shown, and connections with the Duke-Rubinstein reptation
models for gel electrophoresis are discussed.Comment: 31 LaTex pages, 5 Postscript figures included, to appear in Journal
of Statistical Physic
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