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

Matrix product approach for the asymmetric random average process

We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called beta densities, of all local interactions leading to steady states of product measure form are rigorously derived. This also completes an outstanding proof given in a previous publication. Then, we present an alternative solution for the processes with factorized stationary states by using a matrix product ansatz. Due to continuous state variables we obtain a matrix algebra in form of a functional equation which can be solved exactly.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

Breakdown and recovery in traffic flow models

Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the laminar into the congested phase. In stochastic models, it may be assumed that the size of this amplitude gets translated into a waiting time, i.e.\ until fluctuations sufficiently add up to trigger the transition. A recently introduced model of traffic flow however does not show this behavior: in the density regime where the jam solution co-exists with the high-flow state, the intrinsic stochasticity of the model is not sufficient to cause a transition into the jammed regime, at least not within relevant time scales. In addition, models can be differentiated by the stability of the outflow interface. We demonstrate that this additional criterion is not related to the stability of the flow. The combination of these criteria makes it possible to characterize commonalities and differences between many existing models for traffic in a new way

Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process

We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the continuous-time limit the process turns into the totally asymmetric simple exclusion process (only pieces of size 1 break off a given cluster). We express the exact solution of master equation for the process in terms of a determinant which can be derived using the Bethe ansatz. From this determinant we compute the distribution of the current across an arbitrary bond which after appropriate scaling is given by the distribution of the largest eigenvalue of the Gaussian unitary ensemble of random matrices. This result confirms universality of the scaling form of the current distribution in the KPZ universality class and suggests that there is a link between integrable particle systems and random matrix ensembles.Comment: 11 page

ERS statement on the multidisciplinary respiratory management of ataxia telangiectasia

ERR articles are open access and distributed under the terms of the Creative Commons Attribution Non-Commercial Licence 4.0.Peer reviewedPublisher PD

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

Exhaled Aerosols in SARS-CoV-2 Polymerase Chain Reaction-Positive Children and Age-Matched-Negative Controls

BackgroundChildren and adolescents seem to be less affected by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) disease in terms of severity, especially until the increasing spread of the omicron variant in December 2021. Anatomical structures and lower number of exhaled aerosols may in part explain this phenomenon. In a cohort of healthy and SARS-CoV-2 infected children, we compared exhaled particle counts to gain further insights about the spreading of SARS-CoV-2.Materials and MethodsIn this single-center prospective observational trial, a total of 162 children and adolescents (age 6–17 years), of whom 39 were polymerase chain reaction (PCR)-positive for SARS-CoV-2 and 123 PCR-negative, were included. The 39 PCR-positive children were compared to 39 PCR-negative age-matched controls. The data of all PCR-negative children were analyzed to determine baseline exhaled particle counts in children. In addition, medical and clinical history was obtained and spirometry was measured.ResultsBaseline exhaled particle counts were low in healthy children. Exhaled particle counts were significantly increased in SARS-CoV-2 PCR-positive children (median 355.0/L; range 81–6955/L), compared to age-matched -negative children (median 157.0/L; range 1–533/L; p < 0.001).ConclusionSARS-CoV-2 PCR-positive children exhaled significantly higher levels of aerosols than healthy children. Overall children had low levels of exhaled particle counts, possibly indicating that children are not the major driver of the SARS-CoV-2 pandemic.Trial Registration[ClinicalTrials.gov], Identifier [NCT04739020]

Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles

Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence in nonequilibrium steady states, even if translational invariance is not broken by defects or open boundaries. If both particle species are conserved, the temporal behaviour is largely unexplored, but first results of current work on the transition from the microscopic to the macroscopic scale yield exact coupled nonlinear hydrodynamic equations and indicate the emergence of novel types of shock waves which are collective excitations stabilized by the flow of microscopic fluctuations. We review the basic stationary and dynamic properties of these systems, highlighting the role of conservation laws and kinetic constraints for the hydrodynamic behaviour, the microscopic origin of domain wall (shock) stability and the coarsening dynamics of domains during phase separation.Comment: 72 pages, 6 figures, 201 references (topical review for J. Phys. A: Math. Gen.