Distribution of the angle of rotation plane random walks

We study the probability distribution of the angle by which the tangent to the trajectory rotates in the course of a plane random walk. It is shown that the determination of this distribution function can be reduced to an integral equation, which can be rigorously transformed into a differential equation of Hill's type. We derive the asymptotic distribution for very long walks.

Carbon grazing: Managing carbon flows for resilient pasture in variable climate

Work with consultants to help graziers understand implications of carbon in their pastures.

A four-variable model for the pattern-forming mechanism in Hydra

A generalized Gierer-Meinhardt model has been used to account for the transplantation experiments in Hydra. In this model, a cross inhibition between the two organizing centres (namely, head and foot) are assumed to be the only mode of interaction in setting up a stable morphogen distribution for the pattern formation in Hydra.

Sustainable management for rangelands in a variable climate: evidence and insights from northern Australia

Inter-annual rainfall variability is a major challenge to sustainable and productive grazing management on rangelands. In Australia, rainfall variability is particularly pronounced and failure to manage appropriately leads to major economic loss and environmental degradation. Recommended strategies to manage sustainably include stocking at long-term carrying capacity (LTCC) or varying stock numbers with forage availability. These strategies are conceptually simple but difficult to implement, given the scale and spatial heterogeneity of grazing properties and the uncertainty of the climate. This paper presents learnings and insights from northern Australia gained from research and modelling on managing for rainfall variability. A method to objectively estimate LTCC in large, heterogeneous paddocks is discussed, and guidelines and tools to tactically adjust stocking rates are presented. The possible use of seasonal climate forecasts (SCF) in management is also considered. Results from a 13-year grazing trial in Queensland show that constant stocking at LTCC was far more profitable and largely maintained land condition compared with heavy stocking (HSR). Variable stocking (VAR) with or without the use of SCF was marginally more profitable, but income variability was greater and land condition poorer than constant stocking at LTCC. Two commercial scale trials in the Northern Territory with breeder cows highlighted the practical difficulties of variable stocking and provided evidence that heavier pasture utilisation rates depress reproductive performance. Simulation modelling across a range of regions in northern Australia also showed a decline in resource condition and profitability under heavy stocking rates. Modelling further suggested that the relative value of variable v. constant stocking depends on stocking rate and land condition. Importantly, variable stocking may possibly allow slightly higher stocking rates without pasture degradation. Enterprise-level simulations run for breeder herds nevertheless show that poor economic performance can occur under constant stocking and even under variable stocking in some circumstances. Modelling and research results both suggest that a form of constrained flexible stocking should be applied to manage for climate variability. Active adaptive management and research will be required as future climate changes make managing for rainfall variability increasingly challenging.

Design of single variable controllers for ammonia reactors

Abstract is not available.

A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering

We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and t tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.

Variable-number tandem repeats genotyping used to aid and inform management strategies for a bovine Johne's disease incursion in tropical and subtropical Australia

The application of variable-number tandem repeats (VNTR) genotyping of Mycobacterium avium subsp. paratuberculosis isolates to assist in investigating incidents of bovine Johne’s disease in a low-prevalence region of Australia is described in the current study. Isolates from a response to detection of bovine Johne’s disease in Queensland were compared with strains from national and international sources. The tandem application of mycobacterial interspersed repetitive unit (MIRU) and multilocus short sequence repeats (MLSSR) genotyping identified 2 strains, 1 that infected cattle on multiple properties with trace-forward histories from a common infected property, and 1 genotypically different strain recovered from a single property. The former strain showed an identical genotype to an isolate from India. Neither strain showed a genotypic link to regions of Australia with a higher prevalence of the disease. Genotyping has indicated incursions from 2 independent sources. This intelligence has informed investigations into potential routes of entry and the soundness of ongoing control measures, and supported strategy and policy decisions regarding management of Mycobacterium avium subsp. paratuberculosis incursions for Queensland.

Inelastic Postbuckling of Columns of Variable Flexural Rigidity

Effects of large deformation and inelasticity are considered in formulating the behavior of columns of variable cross section subjected to an axial compressive load. Simple, approximate methods are used to obtain numerical results. The combined effect of the nonlinearities is shown to be of a hardening type for small column deflections

A note on the effective medium theory of random resistive-reactive medium

The effective medium theory for a system with randomly distributed point conductivity and polarisability is reformulated, with attention to cross-terms involving the two disorder parameters. The treatment reveals a certain inconsistency of the conventional theory owing to the neglect of the Maxwell-Wagner effect. The results are significant for the critical resistivity and dielectric anomalies of a binary liquid mixture at the phase separation point.

Dilute Solution Properties of Methyl Methacrylate/Acrylonitrile Random Copolymers, 2a)

The Stockmayer-Fixman relation was used to evaluate the short range and long range interaction parameters for methyl methacrylate/acrylonitrile copolymers of 0,566 and 0,657 mole fraction of monomeric units of acrylonitrile in the solvents acetonitrile, 2-butanone, dimethyl formamide, and y-butyrolactone, at different temperatures (30, 45, and 60 “C). The values of KO were found to be lower than those of the parent homopolymers, and their values depend on both solvent and temperature. Even negative Ko-values were obtained, in cases in which the Mark Houwink exponent a is nearly unity. The values of the polymer-solvent interaction parameter, x, , are high and close to 0,5, indicating that these solvents are not good. The values of the excess interaction parameter, xAB, are negative and are not affected by temperature. The large extension of these copolymer chains, as exhibited by a and a;-values, can be understood in terms of unusual short range interactions only. Similar results were obtained for some cellulose derivatives.

Crop design for specific adaptation in variable dryland production environments

Climatic variability in dryland production environments (E) generates variable yield and crop production risks. Optimal combinations of genotype (G) and management (M) depend strongly on E and thus vary among sites and seasons. Traditional crop improvement seeks broadly adapted genotypes to give best average performance under a standard management regime across the entire production region, with some subsequent manipulation of management regionally in response to average local environmental conditions. This process does not search the full spectrum of potential G × M × E combinations forming the adaptation landscape. Here we examine the potential value (relative to the conventional, broad adaptation approach) of exploiting specific adaptation arising from G × M × E. We present an in-silico analysis for sorghum production in Australia using the APSIM sorghum model. Crop design (G × M) is optimised for subsets of locations within the production region (specific adaptation) and is compared with the optimum G across all environments with locally modified M (broad adaptation). We find that geographic subregions that have frequencies of major environment types substantially different from that for the entire production region show greatest advantage for specific adaptation. Although the specific adaptation approach confers yield and production risk advantages at industry scale, even greater benefits should be achievable with better predictors of environment-type likelihood than that conferred by location alone.

Non-linear bending of beams of variable cross-section

For the non-linear bending of cantilever beams of variable cross-section, the effect of large deformations, but with linear elasticity, is considered. The governing integral equation is solved by a numerical iterative procedure. Results for some typical cases are obtained and compared with some of those available in the literature.