An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Address terms in turn beginnings: Managing disalignment and disaffiliation in telephone counselling

This paper examines use of address terms by counsellors on a telephone counselling service for children and young people. Drawing on conversation analytic findings and methods, we show how personal names are used in the management of structural and interpersonal aspects of counselling interaction. Focusing on address terms in turn-beginnings - where a name is used as, or as part of, a preface - the analysis shows that address terms are used in turns that are not fitted with prior talk in terms of either the activity or affective stance of the client. We discuss two environments in which this practice is observed: in beginning turns that initiate a new action sequence, and in turns that challenge the client’s position. Our focus is on the use of client names in the context of producing disaligning or disaffiliative actions. In disaligned actions, counsellors produced sequentially disjunctive turns that regularly involved a return to a counselling agenda. In disaffiliative actions counsellors presented a stance that did not fit with the affective stance of the client in the prior turn, for instance, in disagreeing with or complimenting the client. The paper discusses how such turns invoke a counselling agenda and how name use is used in the management of rapport and trust in counselling interaction.

Representative learning design and functionality of research and practice in sport

Egon Brunswik proposed the concept of “representative design” for psychological experimentation, which has historically been overlooked or confused with another of Brunswik’s terms, ecological validity. In this article, we reiterate the distinc­tion between these two important concepts and highlight the relevance of the term representative design for sports psychology, practice, and experimental design. We draw links with ideas on learning design in the constraints-led approach to motor learning and nonlinear pedagogy. We propose the adoption of a new term, repre­sentative learning design, to help sport scientists, experimental psychologists, and pedagogues recognize the potential application of Brunswik’s original concepts, and to ensure functionality and action fidelity in training and learning environments.

Using Web Search Logs to Identify Query Classification Terms

Purpose – The work presented in this paper aims to provide an approach to classifying web logs by personal properties of users. Design/methodology/approach – The authors describe an iterative system that begins with a small set of manually labeled terms, which are used to label queries from the log. A set of background knowledge related to these labeled queries is acquired by combining web search results on these queries. This background set is used to obtain many terms that are related to the classification task. The system then ranks each of the related terms, choosing those that most fit the personal properties of the users. These terms are then used to begin the next iteration. Findings – The authors identify the difficulties of classifying web logs, by approaching this problem from a machine learning perspective. By applying the approach developed, the authors are able to show that many queries in a large query log can be classified. Research limitations/implications – Testing results in this type of classification work is difficult, as the true personal properties of web users are unknown. Evaluation of the classification results in terms of the comparison of classified queries to well known age-related sites is a direction that is currently being exploring. Practical implications – This research is background work that can be incorporated in search engines or other web-based applications, to help marketing companies and advertisers. Originality/value – This research enhances the current state of knowledge in short-text classification and query log learning. Classification schemes, Computer networks, Information retrieval, Man-machine systems, User interfaces

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

A nonlinear PI and backstepping based controller for tractor-steerable trailer influenced by slip

Autonomous guidance of agricultural vehiclesis vital as mechanized farming production becomes more prevalent. It is crucial that tractor-trailers are guided with accuracy in both lateral and longitudinal directions, whilst being affected by large disturbance forces, or slips, owing to uncertain and undulating terrain. Successful research has been concentrated on trajectory control which can provide longitudinal and lateral accuracy if the vehicle moves without sliding, and the trailer is passive. In this paper, the problem of robust trajectory tracking along straight and circular paths of a tractor-steerable trailer is addressed. By utilizing a robust combination of backstepping and nonlinear PI control, a robust, nonlinear controller is proposed. For vehicles subjected to sliding, the proposed controller makes the lateral deviations and the orientation errors of the tractor and trailer converge to a neighborhood near the origin. Simulation results are presented to illustrate that the suggested controller ensures precise trajectory tracking in the presence of slip.

Practice and procedure : a recent Court of Appeal case examines the meaning of 'third party payer' in terms of Part 3.4 of the Legal Profession Act 2007.

In Legal Services Commissioner v Wright [2010] QCA 321 the Queensland Court of Appeal allowed an appeal from the first instance decision. The decision involved the construction of “third party payer” in Part 3.4 of the Legal Profession Act 2007 (Qld).

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions are reduced to convenient form, which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Design of fixed order robust power oscillation damper for TCSC

This paper illustrates robust fixed order power oscillation damper design for mitigating power systems oscillations. From implementation and tuning point of view, such low and fixed structure is common practice for most practical applications, including power systems. However, conventional techniques of optimal and robust control theory cannot handle the constraint of fixed-order as it is, in general, impossible to ensure a target closed-loop transfer function by a controller of any given order. This paper deals with the problem of synthesizing or designing a feedback controller of dynamic order for a linear time-invariant plant for a fixed plant, as well as for an uncertain family of plants containing parameter uncertainty, so that stability, robust stability and robust performance are attained. The desired closed-loop specifications considered here are given in terms of a target performance vector representing a desired closed-loop design. The performance of the designed controller is validated through non-linear simulations for a range of contingencies.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Unfair terms in residential land contracts : will the Australian consumer law improve a buyer’s bargaining position?

The prohibition on unfair contract terms in standard form consumer contracts has the potential to significantly impact on the terms of contracts for the sale of land. The definition of ‘consumer contract’ includes contracts for the sale or grant of an interest in land to an individual wholly or predominantly for personal or domestic use. Therefore, a contract for the purchase of a residence for personal occupation by the buyer, as opposed to a purchase for investment purposes, will be a consumer contract potentially attracting the application of the unfair terms provisions. Significant consumer protection mechanisms already exist in most state jurisdictions requiring disclosure of relevant matters to the buyer and providing remedies for the provision of misleading conduct. Minimal evidence of unfair terms in land contract was presented to the Productivity Commission Inquiry into the Australian Consumer Policy Framework raising the question as to whether there is an identified problem of unfair terms in real estate contracts and if so, whether the same economic and ethical rationales justify regulatory intervention. This article examines what effect if any the introduction of the unfair contract provisions will have on the enforcement of residential land contracts and the viability of previously accepted conditions if challenged as being “unfair terms”. The article concludes that despite the existence of several potentially unfair terms in some land contracts, the intervention of the rules of equity to overcome perceived hardship or unfairness to buyers from strict enforcement of terms means the unfair terms provisions are only likely to operate on terms untouched by those principles. In the authors’ view the scope for operation of the unfair terms provisions will be limited to terms untouched by the principles of equity and consumer protection legislation making it unlikely that there will be any significant realignment of the contractual obligations and rights of buyers and sellers of land.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.