Renormalized field theory of collapsing directed randomly branched polymers

We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with $\varepsilon$-expansion that this transition belongs to the same universality class as directed percolation.Comment: 18 pages, 7 figure

Resistance, epidemiology and sustainable management of Rhynchosporium secalis populations on barley

The definitive version can be found at: http://onlinelibrary.wiley.com/ Copyright Wiley-Blackwell [Full text of this article is not available in the UHRA]Rhynchosporium secalis is one of the most destructive pathogens of barley worldwide, causing yield decreases of up to 40% and reduced grain quality. Rhynchosporium is a polycyclic disease. Primary inoculum includes conidia produced on crop debris, infected seeds and possibly ascospores, although these have not yet been identified. Secondary disease spread is primarily by splash dispersal of conidia produced on infected leaves, which may be symptomless early in the growing season. Host resistance to R. secalis is mediated by both 'major' or host-specific genes (complete resistance) and 'minor' genes of smaller, generally additive effects (partial resistance). Crop growth stage and plant or canopy architecture can modify the expression of resistance. Resistance genes are distributed unevenly across the barley genome, with most being clustered on the short arms of chromosomes 1H, 3H, 6H and 7H, or in the centromeric region or on the long arm of chromosome 3H. Strategies used to manage rhynchosporium epidemics include cultivar resistance and fungicides, and also cultural practices such as crop rotation, cultivar mixtures and manipulation of sowing date, sowing rate or fertiliser rate. However, the high genetic variability of R. secalis can result in rapid adaptation of pathogen populations to render some of these control strategies ineffective when they are used alone. Sustainable control of rhynchosporium needs to integrate major-gene-mediated resistance, partial resistance and other strategies such as customized fungicide programmes, species or cultivar rotation, resistance gene deployment, clean seed and cultivar mixtures.Peer reviewe