Factorised Steady States in Mass Transport Models on an Arbitrary Graph

We study a general mass transport model on an arbitrary graph consisting of $L$ 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 $d$-dimensional hypercubic lattices with random sequential dynamics.Comment: 17 pages 1 figur

Conserved mass models with stickiness and chipping

We study a chipping model in one dimensional periodic lattice with continuous mass, where a fixed fraction of the mass is chipped off from a site and distributed randomly among the departure site and its neighbours; the remaining mass sticks to the site. In the asymmetric version, the chipped off mass is distributed among the site and the right neighbour, whereas in the symmetric version the redistribution occurs among the two neighbours. The steady state mass distribution of the model is obtained using a perturbation method for both parallel and random sequential updates. In most cases, this perturbation theory provides a steady state distribution with reasonable accuracy.Comment: 17 pages, 4 eps figure

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 for multi-species mass transfer models

A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and sufficient conditions on the mass transfer dynamics under which the steady state factorises. We generalise the model to mass transfer on arbitrary lattices and present sufficient conditions for factorisation. In both cases, explicit results for random sequential update and continuous time limits are given.Comment: 11 page

An exactly solvable dissipative transport model

We introduce a class of one-dimensional lattice models in which a quantity, that may be thought of as an energy, is either transported from one site to a neighbouring one, or locally dissipated. Transport is controlled by a continuous bias parameter q, which allows us to study symmetric as well as asymmetric cases. We derive sufficient conditions for the factorization of the N-body stationary distribution and give an explicit solution for the latter, before briefly discussing physically relevant situations.Comment: 7 pages, 1 figure, submitted to J. Phys.

Density functional theory for hard-sphere mixtures: the White-Bear version Mark II

In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.Comment: 16 pages, 3 figures; minor changes; J. Phys.: Condens. Matter, accepte

Modelling one-dimensional driven diffusive systems by the Zero-Range Process

The recently introduced correspondence between one-dimensional two-species driven models and the Zero-Range Process is extended to study the case where the densities of the two species need not be equal. The correspondence is formulated through the length dependence of the current emitted from a particle domain. A direct numerical method for evaluating this current is introduced, and used to test the assumptions underlying this approach. In addition, a model for isolated domain dynamics is introduced, which provides a simple way to calculate the current also for the non-equal density case. This approach is demonstrated and applied to a particular two-species model, where a phase separation transition line is calculated

An XMM-Newton observation of the young open cluster NGC 2547: coronal activity at 30 Myr

We report XMM-Newton observations of the young open cluster NGC 2547 which allow us to characterise coronal activity in solar-type stars at an age of 30 Myr. X-ray emission peaks among G-stars at luminosities (0.3-3keV) of Lx~10^{30.5} erg/s and declines to Lx<=10^{29.0} erg/s among M-stars. Coronal spectra show evidence for multi-temperature differential emission measures and low coronal metal abundances (Z~0.3). The G- and K-type stars follow the same relationship between X-ray activity and Rossby number established in older clusters and field stars, although most solar-type stars in NGC 2547 exhibit saturated/super-saturated X-ray activity levels. Median levels of Lx and Lx/Lbol in the solar-type stars of NGC 2547 are similar to T-Tauri stars of the Orion Nebula cluster (ONC), but an order of magnitude higher than in the older Pleiades. The spread in X-ray activity levels among solar-type stars in NGC 2547 is much smaller than in older or younger clusters. Coronal temperatures increase with Lx, Lx/Lbol and surface X-ray flux. Active solar-type stars in NGC 2547 have coronal temperatures between those in the ONC and the most active older ZAMS stars. A flaring rate (for total flare energies [0.3-3keV] >10^{34} erg) of 1 every 350^{+350}_{-120} ks was found for solar-type stars, similar to rates found in the ONC and Pleiades. Comparison with ROSAT HRI data taken 7 years previously reveals that only 10-15 percent of solar-type stars or stars with Lx>3x10^{29} erg/s exhibit X-ray variability by more than a factor of two. The similar levels of X-ray activity and rate of occurrence for large flares in NGC 2547 and the ONC demonstrate that the X-ray radiation environment around young solar-type stars remains relatively constant over their first 30 Myr (abridged).Comment: Accepted for publication in MNRAS. Electronic tables available from the autho