11 research outputs found
Factorised Steady States in Mass Transport Models on an Arbitrary Graph
We study a general mass transport model on an arbitrary graph consisting of
nodes each carrying a continuous mass. The graph also has a set of directed
links between pairs of nodes through which a stochastic portion of mass, chosen
from a site-dependent distribution, is transported between the nodes at each
time step. The dynamics conserves the total mass and the system eventually
reaches a steady state. This general model includes as special cases various
previously studied models such as the Zero-range process and the Asymmetric
random average process. We derive a general condition on the stochastic mass
transport rules, valid for arbitrary graph and for both parallel and random
sequential dynamics, that is sufficient to guarantee that the steady state is
factorisable. We demonstrate how this condition can be achieved in several
examples. We show that our generalized result contains as a special case the
recent results derived by Greenblatt and Lebowitz for -dimensional
hypercubic lattices with random sequential dynamics.Comment: 17 pages 1 figur
Construction of the factorized steady state distribution in models of mass transport
For a class of one-dimensional mass transport models we present a simple and
direct test on the chipping functions, which define the probabilities for mass
to be transferred to neighbouring sites, to determine whether the stationary
distribution is factorized. In cases where the answer is affirmative, we
provide an explicit method for constructing the single-site weight function. As
an illustration of the power of this approach, previously known results on the
Zero-range process and Asymmetric random average process are recovered in a few
lines. We also construct new models, namely a generalized Zero-range process
and a binomial chipping model, which have factorized steady states.Comment: 6 pages, no figure
Factorised Steady States in Mass Transport Models
We study a class of mass transport models where mass is transported in a
preferred direction around a one-dimensional periodic lattice and is globally
conserved. The model encompasses both discrete and continuous masses and
parallel and random sequential dynamics and includes models such as the
Zero-range process and Asymmetric random average process as special cases. We
derive a necessary and sufficient condition for the steady state to factorise,
which takes a rather simple form.Comment: 6 page
Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
We review recent progress on the zero-range process, a model of interacting
particles which hop between the sites of a lattice with rates that depend on
the occupancy of the departure site. We discuss several applications which have
stimulated interest in the model such as shaken granular gases and network
dynamics, also we discuss how the model may be used as a coarse-grained
description of driven phase-separating systems. A useful property of the
zero-range process is that the steady state has a factorised form. We show how
this form enables one to analyse in detail condensation transitions, wherein a
finite fraction of particles accumulate at a single site. We review
condensation transitions in homogeneous and heterogeneous systems and also
summarise recent progress in understanding the dynamics of condensation. We
then turn to several generalisations which also, under certain specified
conditions, share the property of a factorised steady state. These include
several species of particles; hop rates which depend on both the departure and
the destination sites; continuous masses; parallel discrete-time updating;
non-conservation of particles and sites.Comment: 54 pages, 9 figures, review articl
A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
These notes are based on lectures delivered by the authors at a Langeoog
seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a
mixed audience of mathematicians and theoretical physicists. After a brief
outline of the basic physical concepts of equilibrium and nonequilibrium
states, the one-dimensional simple exclusion process is introduced as a
paradigmatic nonequilibrium interacting particle system. The stationary measure
on the ring is derived and the idea of the hydrodynamic limit is sketched. We
then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and
explain the associated universality conjecture for surface fluctuations in
growth models. This is followed by a detailed exposition of a seminal paper of
Johansson that relates the current fluctuations of the totally asymmetric
simple exclusion process (TASEP) to the Tracy-Widom distribution of random
matrix theory. The implications of this result are discussed within the
framework of the KPZ conjecture.Comment: 52 pages, 4 figures; to appear in J. Phys. A: Math. Theo
Dimethyl fumarate in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial
Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome
Dimethyl fumarate in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial
Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome