The Becker-Döring equations with exponentially size-dependent rate coefficients

This paper is concerned with an analysis of the Becker-Döring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Döring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years. Here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size. These choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in, for example, simulations of simple fluids. New similarity solutions for the constant monomer Becker-Döring system are identified, and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size.

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored.

Stromule formation is dependent upon plastid size, plastid differentiation status and the density of plastids within the cell

Stromules are motile extensions of the plastid envelope membrane, whose roles are not fully understood. They are present on all plastid types but are more common and extensive on non-green plastids that are sparsely distributed within the cell. During tomato fruit ripening, chloroplasts in the mesocarp tissue differentiate into chromoplasts and undergo major shifts in morphology. In order to understand what factors regulate stromule formation, we analysed stromule biogenesis in tobacco hypocotyls and in two distinct plastid populations in tomato mesocarp. We show that increases in stromule length and frequency are correlated with chromoplast differentiation, but only in one plastid population where the plastids are larger and less numerous. We used tobacco hypocotyls to confirm that stromule length increases as plastids become further apart, suggesting that stromules optimise the plastid-cytoplasm contact area. Furthermore, we demonstrate that ectopic chloroplast components decrease stromule formation on tomato fruit chromoplasts, whereas preventing chloroplast development leads to increased numbers of stromules. Inhibition of fruit ripening has a dramatic impact on plastid and stromule morphology, underlining that plastid differentiation status, and not cell type, is a significant factor in determining the extent of plastid stromules. By modifying the plastid surface area, we propose that stromules enhance the specific metabolic activities of plastids. This is an electronic version of an Article published in The Plant Journal, August 2004, Volume 39, pp. 655-667. Copyright 2004 Blackwell Publishing Ltd and The Society for Experimental Biology.