Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

How does ‘Newstainment’ actually work? : ethnographic research methods and contemporary popular news

Much debate has taken place recently over the potential for entertainment genres and unorthodox forms of news to provide legitimate – indeed democratized – in-roads into the public sphere. Amidst these discussions, however, little thought has been paid to the audiences for programs of this sort, and (even when viewers are considered) the research can too easily treat audiences in homogenous terms and therefore replicate the very dichotomies these television shows directly challenge. This paper is a critical reflection on an audience study into the Australian morning “newstainment” program Sunrise. After examining the show and exploring how it is ‘used’ as a news source, this paper will promote the use of ethnographic study to better conceptualize how citizens integrate and connect the increasingly fragmented and multifarious forms of postmodern political communication available in their everyday lives.

Fungal spore fragmentation as a function of airflow rates and fungal generation methods

The aim of this study was to characterise and quantify the fungal fragment propagules derived and released from several fungal species (Penicillium, Aspergillus niger and Cladosporium cladosporioides) using different generation methods and different air velocities over the colonies. Real time fungal spore fragmentation was investigated using an Ultraviolet Aerodynamic Particle Sizer (UVASP) and a Scanning Mobility Particle Sizer (SMPS). The study showed that there were significant differences (p < 0.01) in the fragmentation percentage between different air velocities for the three generation methods, namely the direct, the fan and the fungal spore source strength tester (FSSST) methods. The percentage of fragmentation also proved to be dependant on fungal species. The study found that there was no fragmentation for any of the fungal species at an air velocity ≤ 0.4 m/s for any method of generation. Fluorescent signals, as well as mathematical determination also showed that the fungal fragments were derived from spores. Correlation analysis showed that the number of released fragments measured by the UVAPS under controlled conditions can be predicted on the basis of the number of spores, for Penicillium and Aspergillus niger, but not for Cladosporium cladosporioides. The fluorescence percentage of fragment samples was found to be significantly different to that of non-fragment samples (p < 0.0001) and the fragment sample fluorescence was always less than that of the non-fragment samples. Size distribution and concentration of fungal fragment particles were investigated qualitatively and quantitatively, by both UVAPS and SMPS, and it was found that the UVAPS was more sensitive than the SMPS for measuring small sample concentrations, and the results obtained from the UVAPS and SMAS were not identical for the same samples.

Flow of a micropolar fluid bounded by a stretching sheet

We consider boundary layer flow of a micropolar fluid driven by a porous stretching sheet. A similarity solution is defined, and numerical solutions using Runge-Kutta and quasilinearisation schemes are obtained. A perturbation analysis is also used to derive analytic solutions to first order in the perturbing parameter. The resulting closed form solutions involve relatively complex expressions, and the analysis is made more tractable by a combination of offline and online work using a computational algebra system (CAS). For this combined numerical and analytic approach, the perturbation analysis yields a number of benefits with regard to the numerical work. The existence of a closed form solution helps to discriminate between acceptable and spurious numerical solutions. Also, the expressions obtained from the perturbation work can provide an accurate description of the solution for ranges of parameters where the numerical approaches considered here prove computationally more difficult.

A bridging transition technique for the combination of meshfree method with finite element method in 2D solids and structures

For certain continuum problems, it is desirable and beneficial to combine two different methods together in order to exploit their advantages while evading their disadvantages. In this paper, a bridging transition algorithm is developed for the combination of the meshfree method (MM) with the finite element method (FEM). In this coupled method, the meshfree method is used in the sub-domain where the MM is required to obtain high accuracy, and the finite element method is employed in other sub-domains where FEM is required to improve the computational efficiency. The MM domain and the FEM domain are connected by a transition (bridging) region. A modified variational formulation and the Lagrange multiplier method are used to ensure the compatibility of displacements and their gradients. To improve the computational efficiency and reduce the meshing cost in the transition region, regularly distributed transition particles, which are independent of either the meshfree nodes or the FE nodes, can be inserted into the transition region. The newly developed coupled method is applied to the stress analysis of 2D solids and structures in order to investigate its’ performance and study parameters. Numerical results show that the present coupled method is convergent, accurate and stable. The coupled method has a promising potential for practical applications, because it can take advantages of both the meshfree method and FEM when overcome their shortcomings.