A model for anomalous directed percolation

We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability distribution for long-range infections which decays in $d$ spatial dimensions as $1/r^{d+\sigma}$. Extensive numerical simulations are performed in order to determine the density exponent $\beta$ and the correlation length exponents $\nu_{||}$ and $\nu_\perp$ for various values of $\sigma$. We observe that these exponents vary continuously with $\sigma$, in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with algebraically distributed long-range interactions.Comment: RevTeX, 9 pages, including 6 eps-figure

Pattern formation inside bacteria: fluctuations due to low copy number of proteins

We examine fluctuation effects due to the low copy number of proteins involved in pattern-forming dynamics within a bacterium. We focus on a stochastic model of the oscillating MinCDE protein system regulating accurate cell division in E. coli. We find that, for some parameter regions, the protein concentrations are low enough that fluctuations are essential for the generation of patterns. We also examine the role of fluctuations in constraining protein concentration levels.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev. Let

`Real' vs `Imaginary' Noise in Diffusion-Limited Reactions

Reaction-diffusion systems which include processes of the form A+A->A or A+A->0 are characterised by the appearance of `imaginary' multiplicative noise terms in an effective Langevin-type description. However, if `real' as well as `imaginary' noise is present, then competition between the two could potentially lead to novel behaviour. We thus investigate the asymptotic properties of the following two `mixed noise' reaction-diffusion systems. The first is a combination of the annihilation and scattering processes 2A->0, 2A->2B, 2B->2A, and 2B->0. We demonstrate (to all orders in perturbation theory) that this system belongs to the same universality class as the single species annihilation reaction 2A->0. Our second system consists of competing annihilation and fission processes, 2A->0 and 2A->(n+2)A, a model which exhibits a transition between active and absorbing phases. However, this transition and the active phase are not accessible to perturbative methods, as the field theory describing these reactions is shown to be non-renormalisable. This corresponds to the fact that there is no stationary state in the active phase, where the particle density diverges at finite times. We discuss the implications of our analysis for a recent study of another active / absorbing transition in a system with multiplicative noise.Comment: 22 pages, LaTex, 2 figures included as eps-files; submitted to J. Phys. A: Math. Gen.; considerably enlarged reincarnatio

Hole-defect chaos in the one-dimensional complex Ginzburg-Landau equation

We study the spatiotemporally chaotic dynamics of holes and defects in the 1D complex Ginzburg--Landau equation (CGLE). We focus particularly on the self--disordering dynamics of holes and on the variation in defect profiles. By enforcing identical defect profiles and/or smooth plane wave backgrounds, we are able to sensitively probe the causes of the spatiotemporal chaos. We show that the coupling of the holes to a self--disordered background is the dominant mechanism. We analyze a lattice model for the 1D CGLE, incorporating this self--disordering. Despite its simplicity, we show that the model retains the essential spatiotemporally chaotic behavior of the full CGLE.Comment: 8 pages, 10 figures; revised and shortened; extra discussion of self-disordering dynamic

The end of the map?

Martin Smith and Andy Howard* explain why moving away from the printed map to a digital 3D National Geological Model is a ‘coming of age’ for William Smith’s great visio

L'acquisition de la morphologie verbale chez des apprenants guidés en milieu naturel : une comparaison préliminaire des temps du passé en français langue seconde

This article presents a quantitative comparison of the development of past time verbal morphological forms in the case of a group of Anglophone L2 learners of French in a study abroad context. While previous studies call into question the potential of study abroad to have a more positive impact on grammatical development than classroom instruction, we firstly offer a critique of those studies in relation to a number of hypotheses which may constitute constraints on the potential of study abroad to impact grammatical development. We then present the results of a longitudinal study over a full year which attempts to control for some of these factors with a view to comparing development at three data collection times across the past time verbal morphological forms in L2 French. Results point to the complexity of identifying a uniform trajectory of development across the morphological forms, with some evidencing minimal change, while others point to relative stability. The results are discussed in relation to the hypotheses outlined and directions for future research