The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Timber frame construction

SIGLEAvailable from British Library Document Supply Centre- DSC:8850.55V(TRADA-TBL--58) / BLDSC - British Library Document Supply CentreGBUnited Kingdo

How to weigh coastal hazard against economic consequence (poster)

It is well recognised that sea level change over the coming century will have an extraordinary economic impact on coastal communities. To overcome the uncertainty that still surrounds the mechanics of shoreline recession and stochastic forcing, landuse planning and management decisions will require a robust and quantitative risk-based approach. A new approach is presented, which has been evaluated using field measurements and assessed in economic terms. The paper discusses a framework for coastal risk analysis which combines four main components 1) the effects of non-stationary climate, including decade scale variability and anthropogenic change; 2) a full probabilistic assessment of incident wave and surge conditions; 3) determination of storm erosion extents; and 4) the economic impact of combined coastal erosion and recession. The framework is illustrated in Figure 1. The operation of this framework has been demonstrated, building upon previous work (Callaghan et al., 2008; Jongejan et al., 2011; Ranasinghe et al., 2011). The first three components relate to physical hazards. Using stochastic simulation, we quantify the ‘likelihood’ side of risk. That likelihood is typically represented by lines indicating a projected extreme landward shoreline condition and an associated quantitative probability. For the first time, the effects of non-stationary climate (e.g. sea level rise) have been included. This can be extended to include decadal scale climate variation effects such as beach rotation. The fourth component requires the determination of values associated with land threatened by coastal erosion during the time frame being considered. We assign a spatially varying value density relationship. The exceedance probability of erosion is combined with the value density to calculate the expected value of damage at a given point in time. In a non-stationary climate scenario, the exceedance probabilities change with time, and this is also considered. Given a known rate of return on investment, the differentials in the rates of return (between coastal and inland property investments) are subsequently used to determine the efficient position of the setback line. The results are presented within a GIS framework to effectively feed into the coastal land use planning process. We demonstrate the framework by applying it to using real data (both physical and economic) for our subject site, Narrabeen Beach in Sydney.Hydraulic EngineeringCivil Engineering and Geoscience

Incidental phosphorus and nitrogen loss from grassland plots receiving chemically amended dairy cattle slurry

peer-reviewedChemical amendment of dairy cattle slurry has been shown to effectively reduce incidental phosphorus (P) losses in runoff; however, the effects of amendments on incidental nitrogen (N) losses are not as well documented. This study examined P and N losses in runoff during three simulated rainfall events 2, 10 and 28 days after a single application of unamended/chemically amended dairy cattle slurry. Twenty-five hydraulically isolated plots, each measuring 0.9 m by 0.4 m and instrumented with runoff collection channels, were randomly assigned the following treatments: (i) grass-only, (ii) slurry-only (the study-control), (iii) slurry amended with industrial grade liquid alum comprising 8% Al2O3, (iv) slurry amended with industrial grade liquid poly-aluminum chloride (PAC) comprising 10% Al2O3, and (v) slurry amended with lime. During the first rainfall event, lime was ineffective but alum and PAC effectively reduced dissolved reactive P (DRP) (by 95 and 98%, respectively) and total P (TP) flow-weighted-mean-concentrations (by 82 and 93%, respectively) in runoff compared to the study-control. However, flow-weighted-mean-concentrations of ammonium–N (NH4–N) in runoff were increased with alum- (81%) and lime-treated (11%) slurry compared to the study-control whereas PAC reduced the NH4–N by 82%. Amendments were not observed to have a significant effect on NO3–N losses during this study. Slurry amendments reduced P losses for the duration of the study, whereas the effect of amendments on N losses was not significant following the first event. Antecedent volumetric water content of the soil or slope of the plots did not appear to affect runoff volume. However, runoff volumes (and consequently loads of P and N) were observed to increase for the chemically amended plots compared to the control and soil-only plots. This work highlights the importance of considering both P and N losses when implementing a specific nutrient mitigation measure.Teagasc Walsh Fellowship Schem

A continuous max-flow approach to Potts model

Abstract. We address the continuous problem of assigning multiple (unordered) labels with the minimum perimeter. The corresponding discrete Potts model is typically addressed with a-expansion which can generate metrication artifacts. Existing convex continuous formulations of the Potts model use TV-based functionals directly encoding perimeter costs. Such formulations are analogous to ’min-cut ’ problems on graphs. We propose a novel convex formulation with a continous ’max-flow ’ functional. This approach is dual to the standard TV-based formulations of the Potts model. Our continous max-flow approach has significant numerical advantages; it avoids extra computational load in enforcing the simplex constraints and naturally allows parallel computations over different labels. Numerical experiments show competitive performance in terms of quality and significantly reduced number of iterations compared to the previous state of the art convex methods for the continuous Potts model.