A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Visualization of thermal characteristics around the absorber tube of a standard parabolic trough thermal collector by 3D simulation

Three dimensional conjugate heat transfer simulation of a standard parabolic trough thermal collector receiver is performed numerically in order to visualize and analyze the surface thermal characteristics. The computational model is developed in Ansys Fluent environment based on some simplified assumptions. Three test conditions are selected from the existing literature to verify the numerical model directly, and reasonably good agreement between the model and the test results confirms the reliability of the simulation. Solar radiation flux profile around the tube is also approximated from the literature. An in house macro is written to read the input solar flux as a heat flux wall boundary condition for the tube wall. The numerical results show that there is an abrupt variation in the resultant heat flux along the circumference of the receiver. Consequently, the temperature varies throughout the tube surface. The lower half of the horizontal receiver enjoys the maximum solar flux, and therefore, experiences the maximum temperature rise compared to the upper part with almost leveled temperature. Reasonable attributions and suggestions are made on this particular type of conjugate thermal system. The knowledge that gained so far from this study will be used to further the analysis and to design an efficient concentrator photovoltaic collector in near future.

Three dimensional simulation of a parabolic trough concentrator thermal collector

Parabolic Trough Concentrators (PTC) are the most proven solar collectors for solar thermal power plants, and are suitable for concentrating photovoltaic (CPV) applications. PV cells are sensitive to spatial uniformity of incident light and the cell operating temperature. This requires the design of CPV-PTCs to be optimised both optically and thermally. Optical modelling can be performed using Monte Carlo Ray Tracing (MCRT), with conjugate heat transfer (CHT) modelling using the computational fluid dynamics (CFD) to analyse the overall designs. This paper develops and evaluates a CHT simulation for a concentrating solar thermal PTC collector. It uses the ray tracing work by Cheng et al. (2010) and thermal performance data for LS-2 parabolic trough used in the SEGS III-VII plants from Dudley et al. (1994). This is a preliminary step to developing models to compare heat transfer performances of faceted absorbers for concentrating photovoltaic (CPV) applications. Reasonable agreement between the simulation results and the experimental data confirms the reliability of the numerical model. The model explores different physical issues as well as computational issues for this particular kind of system modeling. The physical issues include the resultant non-uniformity of the boundary heat flux profile and the temperature profile around the tube, and uneven heating of the HTF. The numerical issues include, most importantly, the design of the computational domain/s, and the solution techniques of the turbulence quantities and the near-wall physics. This simulation confirmed that optical simulation and the computational CHT simulation of the collector can be accomplished independently.

Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.

Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Trends in the Australian gender wage differential over the 1980s : some evidence on the effectiveness of legislative reform

The article examines the legislative reforms incorporating the Sex Discrimination Act and the Affirmative Action Act introduced during the 1980s. We utilise the Australian Bureau of Statistics Income Distribution Surveys 1981–82 and 1989–90 to reflect pre- and post-legislative reform. The article adopts the Brown, Moon and Zoloth (1980) methodology which treats both the wage and occupational status of the individual as endogenously determined. In the current context this is a particularly flexible framework allowing one to capture both the direct and indirect effects of the legislative reforms. The indirect effect refers to the narrowing of the gender wage gap associated with legislative manipulation of the male-female occupational distributions. The results contrast the slow convergence in the gender wage gap during the 1980s with the much faster pace of the 1970s. The article concludes that despite the focus of the 1980s legislation on employment equity, changes in the male-female occupational distribution over the period are small and the associated impact on gender wage convergence is also small.

The use of a Riesz fractional differential-based approach for texture enhancement in image processing

Abstract: Texture enhancement is an important component of image processing, with extensive application in science and engineering. The quality of medical images, quantified using the texture of the images, plays a significant role in the routine diagnosis performed by medical practitioners. Previously, image texture enhancement was performed using classical integral order differential mask operators. Recently, first order fractional differential operators were implemented to enhance images. Experiments conclude that the use of the fractional differential not only maintains the low frequency contour features in the smooth areas of the image, but also nonlinearly enhances edges and textures corresponding to high-frequency image components. However, whilst these methods perform well in particular cases, they are not routinely useful across all applications. To this end, we applied the second order Riesz fractional differential operator to improve upon existing approaches of texture enhancement. Compared with the classical integral order differential mask operators and other fractional differential operators, our new algorithms provide higher signal to noise values, which leads to superior image quality.

A finite element model of seat cushion indentation with a soft tissue human occupant model

Effective digital human model (DHM) simulation of automotive driver packaging ergonomics, safety and comfort depends on accurate modelling of occupant posture, which is strongly related to the mechanical interaction between human body soft tissue and flexible seat components. This paper presents a finite-element study simulating the deflection of seat cushion foam and supportive seat structures, as well as human buttock and thigh soft tissue when seated. The three-dimensional data used for modelling thigh and buttock geometry were taken on one 95th percentile male subject, representing the bivariate percentiles of the combined hip breadth (seated) and buttock-to-knee length distributions of a selected Australian and US population. A thigh-buttock surface shell based on this data was generated for the analytic model. A 6mm neoprene layer was offset from the shell to account for the compression of body tissue expected through sitting in a seat. The thigh-buttock model is therefore made of two layers, covering thin to moderate thigh and buttock proportions, but not more fleshy sizes. To replicate the effects of skin and fat, the neoprene rubber layer was modelled as a hyperelastic material with viscoelastic behaviour in a Neo-Hookean material model. Finite element (FE) analysis was performed in ANSYS V13 WB (Canonsburg, USA). It is hypothesized that the presented FE simulation delivers a valid result, compared to a standard SAE physical test and the real phenomenon of human-seat indentation. The analytical model is based on the CAD assembly of a Ford Territory seat. The optimized seat frame, suspension and foam pad CAD data were transformed and meshed into FE models and indented by the two layer, soft surface human FE model. Converging results with the least computational effort were achieved for a bonded connection between cushion and seat base as well as cushion and suspension, no separation between neoprene and indenter shell and a frictional connection between cushion pad and neoprene. The result is compared to a previous simulation of an indentation with a hard shell human finite-element model of equal geometry, and to the physical indentation result, which is approached with very high fidelity. We conclude that (a) SAE composite buttock form indentation of a suspended seat cushion can be validly simulated in a FE model of merely similar geometry, but using a two-layer hard/soft structure. (b) Human-seat indentation of a suspended seat cushion can be validly simulated with a simplified human buttock-thigh model for a selected anthropomorphism.

A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions

A quasi-maximum likelihood procedure for estimating the parameters of multi-dimensional diffusions is developed in which the transitional density is a multivariate Gaussian density with first and second moments approximating the true moments of the unknown density. For affine drift and diffusion functions, the moments are exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good and is as effective as alternative methods based on likelihood approximations. The estimation procedure generalises to models with latent factors. A conditioning procedure is developed that allows parameter estimation in the absence of proxies.

The N550K/H mutations in FGFR2 confer differential resistance to PD173074, dovitinib and ponatinib ATP-competitive inhibitors

We sought to identify fibroblast growth factor receptor 2 (FGFR2) kinase domain mutations that confer resistance to the pan-FGFR inhibitor, dovitinib, and explore the mechanism of action of the drug-resistant mutations. We cultured BaF3 cells overexpressing FGFR2 in high concentrations of dovitinib and identified fourteen dovitinib-resistant mutations, including the N550K mutation observed in 25% of FGFR2mutant endometrial cancers (EC). Structural and biochemical in vitro kinase analyses, together with BaF3 proliferation assays, showed that the resistance mutations elevate the intrinsic kinase activity of FGFR2. BaF3 lines were used to assess the ability of each mutation to confer cross-resistance to PD173074 and ponatinib. Unlike PD173074, ponatinib effectively inhibited all the dovitinib-resistant FGFR2 mutants except the V565I gatekeeper mutation, suggesting ponatinib but not dovitinib targets the active conformation of FGFR2 kinase. EC cell lines expressing wild-type FGFR2 were relatively resistant to all inhibitors. Whereas EC cell lines expressing mutated FGFR2 showed differential sensitivity. Within the FGFR2mutant cell lines, 3/7 showed marked resistance to PD173074 and relative resistance to dovitinib and ponatinib. This suggests that alternative mechanisms distinct from kinase domain mutations are responsible for intrinsic resistance in these three EC lines. Finally, overexpression of FGFR2N550K in JHUEM-2 cells (FGFR2C383R) conferred resistance (~5 fold) to PD173074, providing independent data that FGFR2N550K can be associated with drug resistance. Biochemical in vitro kinase analyses also shows ponatinib is more effective than dovitinib at inhibiting FGFR2N550K. We propose tumors harboring mutationally activated FGFRs should be treated with FGFR inhibitors that specifically bind the active kinase.

A multi-layered approach for site detection in UAS emergency landing scenarios using geometry-based image segmentation

This paper presents an alternative approach to image segmentation by using the spatial distribution of edge pixels as opposed to pixel intensities. The segmentation is achieved by a multi-layered approach and is intended to find suitable landing areas for an aircraft emergency landing. We combine standard techniques (edge detectors) with novel developed algorithms (line expansion and geometry test) to design an original segmentation algorithm. Our approach removes the dependency on environmental factors that traditionally influence lighting conditions, which in turn have negative impact on pixel-based segmentation techniques. We present test outcomes on realistic visual data collected from an aircraft, reporting on preliminary feedback about the performance of the detection. We demonstrate consistent performances over 97% detection rate.

Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions...

Analysing the Sri Lankan conflict using Michael Mann's four-dimensional model of social power

This thesis provides an overview of the Sri Lankan civil war with a view to identifying some of the factors that contributed to the dispute between the Sri Lankan government and the Liberation Tigers of Tamil Eelam. It adopts a multi-causal explanation of the conflict by reference to the theories of social power developed by Michael Mann. The conflict has been variously described as an ethnic or political conflict, or has been characterised as a determined by a number of interacting factors (including colonialism, ethnicity, religion, economy, politics and globalisation). Mann’s four-dimensional model of social power is deployed to analyse the causal relationships, together with their inter-connections, which clarify the origins of the dispute. It argues that Mann’s theoretical framework helps to highlight some of the interconnected elements that contributed to the conflict.

Is quality more important if you’re quirky? A review of the literature on differential susceptibility to childcare environments

Evidence concerning the impact of child care on child development suggests that higher-quality environments, particularly those that are more responsive, predict more favourable social and behavioural outcomes. However, the extent of this effect is not as great as might be expected. Impacts on child outcomes are, at best, modest. One recent explanation emerging from a new theoretical perspective of development, differential susceptibility theory, is that a minority of children are more reactive to both positive and negative environments, while the majority are relatively unaffected. These 'quirky' children have temperamental traits that are more extreme, and are often described in research studies as having 'difficult temperaments'. This paper reviews the literature on such children and argues for the need for further research to identify components of childcare environments that optimise the potential of these more sensitive, quirky individuals.

Dosimetric effects of a high-density spinal implant

In this study, a treatment plan for a spinal lesion, with all beams transmitted though a titanium vertebral reconstruction implant, was used to investigate the potential effect of a high-density implant on a three-dimensional dose distribution for a radiotherapy treatment. The BEAMnrc/DOSXYZnrc and MCDTK Monte Carlo codes were used to simulate the treatment using both a simplified, recltilinear model and a detailed model incorporating the full complexity of the patient anatomy and treatment plan. The resulting Monte Carlo dose distributions showed that the commercial treatment planning system failed to accurately predict both the depletion of dose downstream of the implant and the increase in scattered dose adjacent to the implant. Overall, the dosimetric effect of the implant was underestimated by the commercial treatment planning system and overestimated by the simplified Monte Carlo model. The value of performing detailed Monte Carlo calculations, using the full patient and treatment geometry, was demonstrated.