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.

An analytical and experimental study of the vibration response of a clamped ribbed plate

An analytical solution is presented in this paper for the vibration response of a ribbed plate clamped on all its boundary edges by employing a travelling wave solution. A clamped ribbed plate test rig is also assembled in this study for the experimental investigation of the ribbed plate response and to provide verification results to the analytical solution. The dynamic characteristics and mode shapes of the ribbed plate are measured and compared to those obtained from the analytical solution and from finite element analysis (FEA). General good agreements are found between the results. Discrepancies between the computational and experimental results at low and high frequencies are also discussed. Explanations are offered in the study to disclose the mechanism causing the discrepancies. The dependency of the dynamic response of the ribbed plate on the distance between the excitation force and the rib is also investigated experimentally. It confirms the findings disclosed in a previous analytical study [T. R. Lin and J. Pan, A closed form solution for the dynamic response of finite ribbed plates. Journal of the Acoustical Society of America 119 (2006) 917-925] that the vibration response of a clamped ribbed plate due to a point force excitation is controlled by the plate stiffness when the source is more than a quarter plate bending wavelength away from the rib and from the plate boundary. The response is largely affected by the rib stiffness when the source location is less than a quarter bending wavelength away from the rib.

Analysis of productive performance of crop and animal production systems : an integrated analytical framework

This article presents a two-stage analytical framework that integrates ecological crop (animal) growth and economic frontier production models to analyse the productive efficiency of crop (animal) production systems. The ecological crop (animal) growth model estimates "potential" output levels given the genetic characteristics of crops (animals) and the physical conditions of locations where the crops (animals) are grown (reared). The economic frontier production model estimates "best practice" production levels, taking into account economic, institutional and social factors that cause farm and spatial heterogeneity. In the first stage, both ecological crop growth and economic frontier production models are estimated to calculate three measures of productive efficiency: (1) technical efficiency, as the ratio of actual to "best practice" output levels; (2) agronomic efficiency, as the ratio of actual to "potential" output levels; and (3) agro-economic efficiency, as the ratio of "best practice" to "potential" output levels. Also in the first stage, the economic frontier production model identifies factors that determine technical efficiency. In the second stage, agro-economic efficiency is analysed econometrically in relation to economic, institutional and social factors that cause farm and spatial heterogeneity. The proposed framework has several important advantages in comparison with existing proposals. Firstly, it allows the systematic incorporation of all physical, economic, institutional and social factors that cause farm and spatial heterogeneity in analysing the productive performance of crop and animal production systems. Secondly, the location-specific physical factors are not modelled symmetrically as other economic inputs of production. Thirdly, climate change and technological advancements in crop and animal sciences can be modelled in a "forward-looking" manner. Fourthly, knowledge in agronomy and data from experimental studies can be utilised for socio-economic policy analysis. The proposed framework can be easily applied in empirical studies due to the current availability of ecological crop (animal) growth models, farm or secondary data, and econometric software packages. The article highlights several directions of empirical studies that researchers may pursue in the future.

Ethical decision making and health care managers : developing managerial profiles based on ethical frameworks and other influencing factors

Whether the community is looking for “scapegoats” to blame, or seeking more radical and deeper causes, health care managers are in the firing line whenever there are woes in the health care sector. The public has a right to question whether ethics have much influence on the everyday decision making of health care managers. This thesis explores, through a series of published papers, the influence of ethics and other factors on the decision making of health care managers in Australia. Critical review of over 40 years of research on ethical decision making has revealed a large number of influencing factors, but there is a demonstrable lack of a multidimensional approach that measures the combined influences of these factors on managers. This thesis has developed an instrument, the Managerial Ethical Profile (MEP) scale, based on a multidimensional model combining a large number of influencing factors. The MEP scale measures the range of influences on individual managers, and describes the major tendencies by developing a number of empirical profiles derived from a hierarchical cluster analysis. The instrument was developed and refined through a process of pilot studies on academics and students (n=41) and small-business managers (n=41), and then was administered to the larger sample of health care managers (n=441). Results from this study indicate that Australian health care managers draw on a range of ethical frameworks in their everyday decision making, forming the basis of five MEPs (Knights, Guardian Angels, Duty Followers, Defenders, and Chameleons). Results from the study also indicate that the range of individual, organisational, and external factors that influence decision making can be grouped into three major clusters or functions. Cross referencing these functions and other demographic data to the MEPs provides analytical insight into the characteristics of the MEPs. These five profiles summarise existing strengths and weaknesses in managerial ethical decision making. Therefore identifying these profiles not only can contribute to increasing organisational knowledge and self-awareness, but also has clear implications for the design and implementation of ethics education and training in large scale organisations in the health care industry.

Philosophy, behaviour disorders, and the school

The recent exponential rise in the number of behaviour disorders has been the focus of a wide range of commentaries, ranging from the pedagogic and the administrative, to the sociological, and even the legal. This book will be the first to apply, in a systematic and thorough manner, the ideas of the foundational discipline of philosophy. A number of philosophical tools are applied here, tools arising through the medium of the traditional philosophical debates, such as those concerning governance, truth, logic, ethics, free-will, law and language. Each forms a separate chapter, but together they constitute a comprehensive, rigorous and original insight into what is now an important set of concerns for all those interested in the governance of children. The intention is threefold: first, to demonstrate the utility, accessibility and effectiveness of philosophical ideas within this important academic area. Philosophy does not have to be regarded an arcane and esoteric discipline, with only limited contemporary application, far from it. Second, the book offers a new set of approaches and ideas for both researchers and practitioners within education, a field is in danger of continually using the same ideas, to endlessly repeat the same conclusions. Third, the book offers a viable alternative to the dominant psychological model which increasingly employs pathology as its central rationale for conduct. The book would not only be of interest to mainstream educators, and to those students and academics interested in philosophy, and more specifically, the application of philosophical ideas to educational issues, it would also be an appropriate text for courses on education and difference, and due to the breadth of the philosophical issues addressed, courses on applied philosophy.

Tracking employees' twists and turns : describing a mixed methods approach to assessing change in the psychological contract

The psychological contract is a key analytical device utilised by both academics and practitioners to conceptualise and explore the dynamics of the employment relationship. However, despite the recognised import of the construct, some authors suggest that its empirical investigation has fallen into a 'methodological rut' [Conway & Briner, 2005, p. 89] and is neglecting to assess key tenets of the concept, such as its temporal and dynamic nature. This paper describes the research design of a longitudinal, mixed methods study which draws upon the strengths of both qualitative and quantitative modes of inquiry in order to explore the development of, and changes in, the psychological contract. Underpinned by a critical realist philosophy, the paper seeks to offer a research design suitable for exploring the process of change not only within the psychological contract domain, but also for similar constructs in the human resource management and broader organisational behaviour fields.

The philosophy and practice of water sensitive urban design : is it consistent with a whole system approach

This paper provides a critique of the Water Sensitive Urban Design (WSUD) paradigm by discussing its congruence with an established sustainable design principle called 'whole system design'. It was found that WSUD is congruent with the whole system design approach as a philosophy, but not in practice. Future improvement of WSUD practice may depend on the adoption of a front-loaded, teamwork-based design and planning process that is embedded in the principle of whole system design.

Power in legal education : a (new) critical and analytical approach

This article explores power within legal education scholarship. It suggests that power relations are not effectively reflected on within this scholarship, and it provokes legal educators to consider power more explicitly and effectively. It then outlines in-depth a conceptual and methodological approach based on Michel Foucault’s concept of ‘governmentality’ to assist in such an analysis. By detailing the conceptual moves required in order to research power in legal education more effectively, this article seeks to stimulate new reflection and thought about the practice and scholarship of legal education, and allow for political interventions to become more ethically sensitive and potentially more effective.

Leveraging social network data for analytical CRM strategies : the introduction of social BI

The skyrocketing trend for social media on the Internet greatly alters analytical Customer Relationship Management (CRM). Against this backdrop, the purpose of this paper is to advance the conceptual design of Business Intelligence (BI) systems with data identified from social networks. We develop an integrated social network data model, based on an in-depth analysis of Facebook. The data model can inform the design of data warehouses in order to offer new opportunities for CRM analyses, leading to a more consistent and richer picture of customers? characteristics, needs, wants, and demands. Four major contributions are offered. First, Social CRM and Social BI are introduced as emerging fields of research. Second, we develop a conceptual data model to identify and systematize the data available on online social networks. Third, based on the identified data, we design a multidimensional data model as an early contribution to the conceptual design of Social BI systems and demonstrate its application by developing management reports in a retail scenario. Fourth, intellectual challenges for advancing Social CRM and Social BI are discussed.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.