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

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

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

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.

Allergen-specific immunotherapy provides immediate, long-term and preventive clinical effects in children and adults: the effects of immunotherapy can be categorised by level of benefit -the centenary of allergen specific subcutaneous immunotherapy

Allergen Specific Immunotherapy (SIT) for respiratory allergic diseases is able to significantly improve symptoms as well as reduce the need for symptomatic medication, but SIT also has the capacity for long-term clinical effects and plays a protective role against the development of further allergies and symptoms. The treatment acts on basic immunological mechanisms, and has the potential to change the pathological allergic immune response. In this paper we discuss some of the most important achievements in the documentation of the benefits of immunotherapy, over the last 2 decades, which have marked a period of extensive research on the clinical effects and immunological background of the mechanisms involved. The outcome of immunotherapy is described as different levels of benefit from early reduction in symptoms over progressive clinical effects during treatment to long-term effects after discontinuation of the treatment and prevention of asthma. The efficacy of SIT increases the longer it is continued and immunological changes lead to potential long-term benefits. SIT alone and not the symptomatic treatment nor other avoidance measures has so far been documented as the therapy with long-term or preventive potential. The allergic condition is driven by a subset of T-helper lymphocytes (Th2), which are characterised by the production of cytokines like IL-4, and IL-5. Immunological changes following SIT lead to potential curative effects. One mechanism whereby immunotherapy suppresses the allergic response is through increased production of IgG4 antibodies. Induction of specific IgG4 is able to influence the allergic response in different ways and is related to immunological effector mechanisms, also responsible for the reduced late phase hyperreactivity and ongoing allergic inflammation. SIT is the only treatment which interferes with the basic pathophysiological mechanisms of the allergic disease, thereby creating the potential for changes in the long-term prognosis of respiratory allergy. SIT should not only be recognised as first-line therapeutic treatment for allergic rhinoconjunctivitis but also as secondary preventive treatment for respiratory allergic diseases

Lung clearance index: Evidence for use in clinical trials in cystic fibrosis

The ECFS-CTN Standardisation Committee has undertaken this review of lung clearance index as part of the group's work on evaluation of clinical endpoints with regard to their use in multicentre clinical trials in CF.The aims were 1) to review the literature on reliability, validity and responsiveness of LCI in patients with CF, 2) to gain consensus of the group on feasibility of LCI and 3) to gain consensus on answers to key questions regarding the promotion of LCI to surrogate endpoint status.It was concluded that LCI has an attractive feasibility and clinimetric properties profile and is particularly indicated for multicentre trials in young children with CF and patients with early or mild CF lung disease. This is the first article to collate the literature in this manner and support the use of LCI in clinical trials in CF