Oscillatory processes in the theory of particulate formation in supersaturated chemical solutions

We study a nonlinear problem which occurs in the theory of particulate formation in supersaturated chemical solutions. Mathematically, the problem involves the bifurcation of time-periodic solutions in an initial-boundary value problem involving a nonlinear integro-differential equation. The mechanism controlling the oscillatory states is revealed by combining the theory of characteristics for first order partial differential equations with the multi-time scale perturbation analysis of a certain third order system of nonlinear ordinary differential equations

An evaluation of two grassland-based systems of mid-season prime lamb production using prolific ewes of two genotypes

peer-reviewedA 4-year study was undertaken to evaluate the effects of two contrasting management systems [year-round grazing (YRG) and normal seasonal grazing followed by indoor feeding during winter (GWF)] on performance of mid-season lambing ewes. On the GWF system, the annual stocking rate was 14.4 ewes/ha, grass silage was conserved for winter feeding indoors, and the ewes were lambed indoors and were then turned out to pasture. The YRG system was stocked at 10.5 ewes/ha, was grazed during the winter, had outdoor lambing and the animals had access to all the farmlet for summer grazing. The ewes were Belclare and Cheviot × Belclare which were balanced across systems. Mean lambing dates and fertiliser N application rates were 20 and 30 March, and 85 and 92 kg/ha, for the GWF and YRG systems, respectively. Concentrate supplementation during late pregnancy was similar on both systems. For the GWF and YRG systems, litter size, lamb mortality, number of lambs reared, birth weight (kg), weaning weight (kg) and lamb carcass output (kg/ha) were 2.17 and 2.24 (s.e. 0.038), 10.1 and 13.8% (P = 0.05), 1.77 and 1.78 (s.e. 0.042), 4.0 and 4.7 (s.e. 0.05, P < 0.001), 27.9 and 30.8 (s.e. 0.25, P < 0.001) and 469 and 348, respectively. Belclare ewes had a higher litter size (2.34 v 2.07; s.e. 0.038, P < 0.001) and number of lambs reared per ewe joined (1.86 v 1.69; s.e. 0.048, P < 0.01) than the Cheviot × Belclare ewes. There were no significant interactions between system and ewe breed type. It is concluded that the YRG system of prime lamb production was sustainable using prolific ewes but at a reduced stocking rate (−26%) and with greater lamb mortality relative to the GWF system. Ewe genotypes with a mean litter size of up to 2.34 lambs are suitable for both systems. Lamb carcass output of 501 kg/ha was achieved from a primarily grass-based system of mid-season prime lamb production using prolific ewes (Belclare)

Resilience of Hierarchical Critical Infrastructure Networks

Concern over the resilience of critical infrastructure networks has increased dramatically over the last decade due to a number of well documented failures and the significant disruption associated with these. This has led to a large body of research that has adopted graph-theoretic based analysis in order to try and improve our understanding of infrastructure network resilience. Many studies have asserted that infrastructure networks possess a scale-free topology which is robust to random failures but sensitive to targeted attacks at highly connected hubs. However, many studies have ignored that many networks in addition to their topological connectivity may be organised either logically or spatially in a hierarchical system which may significantly change their response to perturbations. In this paper we explore if hierarchical network models exhibit significantly different higher-order topological characteristics compared to other network structures and how this impacts on their resilience to a number of different failure types. This is achieved by investigating a suite of synthetic networks as well as a suite of ‘real world’ spatial infrastructure networks