A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

The Not for Profit Sector in Australia : Fact Sheet

This fact sheet outlines aspects of the nonprofit sector in Australia, under the following headings: size; economic contribution; employment; volunteering; income; expenses; and philanthropy; and provides international comparisons on aspects including size, growth, economic contribution, giving, and workforce.

Computation of Mathematical Models for Complex Industrial Processes

Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes and thus provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios.

The geography of the UK’s creative and high–tech economies

This report is the first systematic analysis of employment in the UK’s creative and high-tech economies. It analyses their size, growth and distribution across the country. Key Findings • The UK’s creative economy had 2.6 million jobs in 2013, consisting of 1.7 million jobs in the creative industries (890,000 in creative occupations and 818,000 working in other roles) and 907,000 jobs in creative occupations outside of the creative industries. • The UK’s high–tech economy had 3.2 million jobs in 2013, 2.4 million of which were jobs in high–tech industries (825,000 in Science Technology Engineering and Mathematics (STEM) occupations and 1.6 million in other roles) and 806,000 jobs in STEM occupations outside of the high–tech industries. • Employment in the creative economy grew on average over three times faster than the workforce as a whole (4.3 per cent per annum (p.a.) vs 1.2 per cent p.a.) between 2011 and 2013. • Employment in the high–tech economy also grew faster than the workforce over this period (2.1 per cent p.a. vs 1.2 per cent p.a.). • The creative economy is particularly concentrated in London and the South East which together account for 43 per cent of the UK’s creative economy workforce. By contrast, 31 per cent of high-tech economy employment and 28 per cent of the UK’s workforce is located in this area.

A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Existence of complementary pairs of proportionally balanced designs

Proportionally balanced designs (pi BDs) were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Subsequent papers extended the theoretical results relating to such designs and provided further instances and general constructions. This work focused on designs comprising blocks of precisely two sizes, and when each variety occurs with one of precisely two possible frequencies. Two designs based on the set V of varieties are complementary if, whenever B is a block of one, then its complement with regard to the set V is a block of the other. Here we present necessary conditions for the existence of complementary pairs of such pi BDs and provide lists of some restricted parameter sets satisfying these necessary conditions. The lists are arranged according to the number of blocks. We demonstrate that not all of these parameter sets give rise to designs. However we establish by construction of the sets of blocks that, for every feasible number of blocks less than or equal to 100, with the possible exception of 63, there exists at least one pair of complementary pi BDs. We also investigate the conditions under which the complementary design can be isomorphic to the original design, and again provide a list of feasible parameters for pairs of such designs with at most 400 blocks.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

A flaw in the use of minimal defining sets for secret sharing schemes

It is shown that in some cases it is possible to reconstruct a block design D uniquely from incomplete knowledge of a minimal defining set for D. This surprising result has implications for the use of minimal defining sets in secret sharing schemes.

Fibre slippage in cyclically perturbed fibrous assemblies

The dynamics of fibre slippage within general non-bonded fibrous assemblies is studied in the situation where the assembly is subjected to general small cyclic loads. Two models are proposed. The first is applicable when the general cyclic loading is complemented by an occasional tugging force on one end of a fibre, which causes it to gradually withdraw from the assembly, such as might occur during the pilling of a textile. The second considers the situation in which the cyclic perturbations act around a constant background load applied to the assembly. The dynamics is reminiscent of self-organized critical behaviour. This model is applied to predict the progressive elongation of a single yarn during weaving.

Endangerment and Likeability of Wildlife Species: How Important are they for Payments Proposed for Conservation?

This paper examines empirically the relative influence of the degree of endangerment of wildlife species and their stated likeability on individuals' allocation of funds for their conservation. To do this, it utilises data obtained from the IUCN Red List, and likeability and fund allocation data obtained from two serial surveys of a sample of the Australian public who were requested to assess 24 Australian wildlife species from three animal classes: mammals, birds and reptiles. Between the first and second survey, respondents were provided with extra information about the focal species. This information resulted in the dominance of endangerment as the major influence on the allocation of funding of respondents for the conservation of the focal wildlife species. Our results throw doubts on the proposition in the literature that the likeability of species is the dominant influence on willingness to pay for conservation of wildlife species. Furthermore, because the public's allocation of fund for conserving wildlife species seems to be more sensitive to information about the conservation status of species than to factors influencing their likeability, greater attention to providing accurate information about the former than the latter seems justified. Keywords: Conservation of wildlife species; Contingent valuation; Endangerment of species; Likeability of species; Willingness to pay