Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Evolutionary optimisation methods with uncertainty for modern multidisciplinary design in aeronautical engineering

One of the new challenges in aeronautics is combining and accounting for multiple disciplines while considering uncertainties or variability in the design parameters or operating conditions. This paper describes a methodology for robust multidisciplinary design optimisation when there is uncertainty in the operating conditions. The methodology, which is based on canonical evolution algorithms, is enhanced by its coupling with an uncertainty analysis technique. The paper illustrates the use of this methodology on two practical test cases related to Unmanned Aerial Systems (UAS). These are the ideal candidates due to the multi-physics involved and the variability of missions to be performed. Results obtained from the optimisation show that the method is effective to find useful Pareto non-dominated solutions and demonstrate the use of robust design techniques.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Linkage and heritability analysis of migraine symptom groupings: A comparison of three different clustering methods on twin data

Migraine is a painful disorder for which the etiology remains obscure. Diagnosis is largely based on International Headache Society criteria. However, no feature occurs in all patients who meet these criteria, and no single symptom is required for diagnosis. Consequently, this definition may not accurately reflect the phenotypic heterogeneity or genetic basis of the disorder. Such phenotypic uncertainty is typical for complex genetic disorders and has encouraged interest in multivariate statistical methods for classifying disease phenotypes. We applied three popular statistical phenotyping methods—latent class analysis, grade of membership and grade of membership “fuzzy” clustering (Fanny)—to migraine symptom data, and compared heritability and genome-wide linkage results obtained using each approach. Our results demonstrate that different methodologies produce different clustering structures and non-negligible differences in subsequent analyses. We therefore urge caution in the use of any single approach and suggest that multiple phenotyping methods be used.

Industrial playwriting : forms, strategies, and methods for creative production

This study, in its exploration of the attached play scripts and their method of development, evaluates the forms, strategies, and methods of an organised model of formalised playwriting. Through the examination, reflection and reaction to a perceived crisis in playwriting in the Australian theatre sector, the notion of Industrial Playwriting is arrived at: a practice whereby plays are designed and constructed, and where the process of writing becomes central to the efficient creation of new work and the improvement of the writer’s skill and knowledge base. Using a practice-led methodology and action research the study examines a system of play construction appropriate to and addressing the challenges of the contemporary Australian theatre sector. Specifically, using the action research methodology known as design-based research a conceptual framework was constructed to form the basis of the notion of Industrial Playwriting. From this two plays were constructed using a case study method and the process recorded and used to create a practical, step-by-step system of Industrial Playwriting. In the creative practice of manufacturing a single authored play, and then a group-devised play, Industrial Playwriting was tested and found to also offer a valid alternative approach to playwriting in the training of new and even emerging playwrights. Finally, it offered insight into how Industrial Playwriting could be used to greatly facilitate theatre companies’ ongoing need to have access to new writers and new Australian works, and how it might form the basis of a cost effective writer development model. This study of the methods of formalised writing as a means to confront some of the challenges of the Australian theatre sector, the practice of playwriting and the history associated with it, makes an original and important contribution to contemporary playwriting practice.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Multivariate methods to identify cancer-related symptom clusters

Multivariate methods are required to assess the interrelationships among multiple, concurrent symptoms. We examined the conceptual and contextual appropriateness of commonly used multivariate methods for cancer symptom cluster identification. From 178 publications identified in an online database search of Medline, CINAHL, and PsycINFO, limited to articles published in English, 10 years prior to March 2007, 13 cross-sectional studies met the inclusion criteria. Conceptually, common factor analysis (FA) and hierarchical cluster analysis (HCA) are appropriate for symptom cluster identification, not principal component analysis. As a basis for new directions in symptom management, FA methods are more appropriate than HCA. Principal axis factoring or maximum likelihood factoring, the scree plot, oblique rotation, and clinical interpretation are recommended approaches to symptom cluster identification.

Comparison of three expert elicitation methods for logistic regression on predicting the presence of the threatened brush-tailed rock-wallaby petrogale penicillata

Numerous expert elicitation methods have been suggested for generalised linear models (GLMs). This paper compares three relatively new approaches to eliciting expert knowledge in a form suitable for Bayesian logistic regression. These methods were trialled on two experts in order to model the habitat suitability of the threatened Australian brush-tailed rock-wallaby (Petrogale penicillata). The first elicitation approach is a geographically assisted indirect predictive method with a geographic information system (GIS) interface. The second approach is a predictive indirect method which uses an interactive graphical tool. The third method uses a questionnaire to elicit expert knowledge directly about the impact of a habitat variable on the response. Two variables (slope and aspect) are used to examine prior and posterior distributions of the three methods. The results indicate that there are some similarities and dissimilarities between the expert informed priors of the two experts formulated from the different approaches. The choice of elicitation method depends on the statistical knowledge of the expert, their mapping skills, time constraints, accessibility to experts and funding available. This trial reveals that expert knowledge can be important when modelling rare event data, such as threatened species, because experts can provide additional information that may not be represented in the dataset. However care must be taken with the way in which this information is elicited and formulated.

A comparison of different methods to determine diffusion length in dye-sensitized solar cells

A new steady state method for determination of the electron diffusion length in dye-sensitized solar cells (DSCs) is described and illustrated with data obtained using cells containing three different types of electrolyte. The method is based on using near-IR absorbance methods to establish pairs of illumination intensity for which the total number of trapped electrons is the same at open circuit (where all electrons are lost by interfacial electron transfer) as at short circuit (where the majority of electrons are collected at the contact). Electron diffusion length values obtained by this method are compared with values derived by intensity modulated methods and by impedance measurements under illumination. The results indicate that the values of electron diffusion length derived from the steady state measurements are consistently lower than the values obtained by the non steady-state methods. For all three electrolytes used in the study, the electron diffusion length was sufficiently high to guarantee electron collection efficiencies greater than 90%. Measurement of the trap distributions by near-IR absorption confirmed earlier observations of much higher electron trap densities for electrolytes containing Li+ ions. It is suggested that the electron trap distributions may not be intrinsic properties of the TiO2 nanoparticles, but may be associated with electron-ion interactions.