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.

The applicability of aesthetic knowledge in organizational decision making processes

We argue that aesthetic knowledge, which is a form of tacit knowledge of beauty and related concepts, is an important, yet under-researched, topic in the study of organizational decision making processes. The significance of aesthetic knowledge for decision making processes is derived from its universal application by humans to commonplace practices; its use as the basis of decision criteria in complex situations to which the effective application of logic and reason is difficult; and its role both in assisting cognition in general and in enabling the choice of solutions generated from rational decision making processes. Despite its importance, the empirical research examining the application of aesthetic knowledge in organizational decision making processes is limited. Further detailed study of aesthetic knowledge in the context of organizational decision making processes is required to extend the recent movement in the field aimed at examining the role that extrarational, human-centered factors play in organizational decisions.

Modeling and Analyzing the Carbon Footprint of Business Processes

Many corporations and individuals realize that environmental sustainability is an urgent problem to address. In this chapter, we contribute to the emerging academic discussion by proposing two innovative approaches for engaging in the development of environmentally sustainable business processes. Specifically, we describe an extended process modeling approach for capturing and documenting the dioxide emissions produced during the execution of a business process. For illustration, we apply this approach to the case of a governmental Shared Services provider. Second, we then introduce an analysis method for measuring the carbon dioxide emissions produced during the execution of a business process. To illustrative this approach, we apply it in the real-life case of an European airport and show how this information can be leveraged in the re-design of “green” busi-ness processes.

Understanding hydrochemical processes using 3D models and hydrochemical facies in Wairau Plain groundwater, Marlborough

Three dimensional models and groundwater quality are combined to better understand and conceptualise groundwater systems in complex geological settings in the Wairau Plain, Marlborough. Hydrochemical facies, which are characteristic of distinct evolutionary pathways and a common hydrologic history of groundwaters, are identified within geological formations to assess natural water-rock interactions, redox potential and human agricultural impact on groundwater quality in the Wairau Plain.

An analysis of the differences in audit processes used in the audit of nonprofit and profit organisations

Nonprofits constitute a large part of collective behaviour in society. Presently there is little formal research addressing the role of audits in nonprofit organisations. Before models can be developed for the production of nonprofit auditing information, it is necessary to examine the present conduct of nonprofit audits. The Australian Accounting Research Foundation - Legislation Review Board has released a position paper on the Association Incorporation Acts in Australia - the most frequently used legal form for nonprofit organisations. The Board is addressing the issue of financial statement reporting including audit. This is coinciding with the investigations resulting from the collapse of the National Safety Council (Victorian Division), (NSC). The NSC, a nonprofit organisation formed as a company limited by guarantee, is in liquidation and the auditors are being sued for damages resulting from their alleged failure to perform their duties adequately.

Determination of coastal ground and surface water processes and character by use of hydrochemistry and stable isotopes, Fraser Coast, Queensland

This study was part of an integrated project developed in response to concerns regarding current and future land practices affecting water quality within coastal catchments and adjacent marine environments. Two forested coastal catchments on the Fraser Coast, Australia, were chosen as examples of low-modification areas with similar geomorphological and land-use characteristics to many other coastal zones in southeast Queensland. For this component of the overall project, organic , physico-chemical (Eh, pH and DO), ionic (Fe2+, Fe3+), and isotopic (ä13CDIC, ä15NDIN ä34SSO4) data were used to characterise waters and identify sources and processes contributing to concentrations and form of dissolved Fe, C, N and S within the ground and surface waters of these coastal catchments. Three sites with elevated Fe concentrations are discussed in detail. These included a shallow pool with intermittent interaction with the surface water drainage system, a monitoring well within a semi-confined alluvial aquifer, and a monitoring well within the fresh/saline water mixing zone adjacent to an estuary. Conceptual models of processes occurring in these environments are presented. The primary factors influencing Fe transport were; microbial reduction of Fe3+ oxyhydroxides in groundwaters and in the hyporheic zone of surface drainage systems, organic input available for microbial reduction and Fe3+ complexation, bacterial activity for reduction and oxidation, iron curtain effects where saline/fresh water mixing occurs, and variation in redox conditions with depth in ground and surface water columns. Data indicated that groundwater seepage appears a more likely source of Fe to coastal waters (during periods of low rainfall) via tidal flux. The drainage system is ephemeral and contributes little discharge to marine waters. However, data collected during a high rainfall event indicated considerable Fe loads can be transported to the estuary mouth from the catchment.

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Creating new possibilities : using design processes to overcome constraints

This paper describes how a team from a large company, when faced with a challenge to develop new customers in fast growing international markets, carried out the exploration of the needs of new clients in the largely unexplored market space of a developing country. This team used design methods and processes to identify the latent needs of new customers in situations of major economic, geographical, cultural and financial constraints. This encapsulation of the life experiences of potential customers is used extensively in some new product development, but is largely novel to business practices and in processes of developing new services. This research links with the sub-theme of discovering creativity in necessity and highlights the potential benefits of design methodologies to create new possibilities for better accessibility of the company’s products to new clients, with future implications for organizational strategy. The overall theme of Design for the Colloquium encourages exploration of the ways and means of developing new ideas for new business with better outcomes, using design concepts and design technologies.

Wind-energy based path planning for unmanned aerial vehicles using Markov decision processes

Exploiting wind-energy is one possible way to extend flight duration for Unmanned Arial Vehicles. Wind-energy can also be used to minimise energy consumption for a planned path. In this paper, we consider uncertain time-varying wind fields and plan a path through them. A Gaussian distribution is used to determine uncertainty in the Time-varying wind fields. We use Markov Decision Process to plan a path based upon the uncertainty of Gaussian distribution. Simulation results that compare the direct line of flight between start and target point and our planned path for energy consumption and time of travel are presented. The result is a robust path using the most visited cell while sampling the Gaussian distribution of the wind field in each cell.

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0◦ to 90◦. The corresponding diffusion ellipsoids are prolate for θ < θMA, spherical for θ ≈ θMA, and oblate for θ > θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.

Engagement, persistence, progress and success as theoretically distinct aspects of business creation processes

Starting from the vantage point that explaining success at creating a venture should be the unique contribution—or at least one unique contribution—of entrepreneurship research, we argue that this success construct has not yet been adequately defined an operationalized. We thus offer suggestions for more precise conceptualization and measurement of this central construct. Rather than regarding various success proxies used in prior research as poor operationalizations of success we argue that they represent other important aspects of the venture creation process: engagement, persistence and progress. We hold that in order to attain a better understanding of venture creation these constructs also need to be theoretically defined. Further, their respective drivers need to be theorized and tested separately. We suggest theoretical definitions of each. We then develop and test hypotheses concerning how human capital, venture idea novelty and business planning has different impact on the different assessments of the process represented by engagement, persistence, progress and success. The results largely confirm the stated hypotheses, suggesting that the conceptual and empirical approach we are suggesting is a path towards improved understanding of the central entrepreneurship phenomenon of new venture creation.

Measurements of particle emissions from nanotechnology processes, with assessment of measuring techniques and workplace controls

The overall aim of this project was to contribute to existing knowledge regarding methods for measuring characteristics of airborne nanoparticles and controlling occupational exposure to airborne nanoparticles, and to gather data on nanoparticle emission and transport in various workplaces. The scope of this study involved investigating the characteristics and behaviour of particles arising from the operation of six nanotechnology processes, subdivided into nine processes for measurement purposes. It did not include the toxicological evaluation of the aerosol and therefore, no direct conclusion was made regarding the health effects of exposure to these particles. Our research included real-time measurement of sub, and supermicrometre particle number and mass concentration, count median diameter, and alveolar deposited surface area using condensation particle counters, an optical particle counter, DustTrak photometer, scanning mobility particle sizer, and nanoparticle surface area monitor, respectively. Off-line particle analysis included scanning and transmission electron microscopy, energy-dispersive x-ray spectrometry, and thermal optical analysis of elemental carbon. Sources of fibrous and non-fibrous particles were included.

Unstructured processes of strategic decision-making

The author aims at developing a better understanding of unstructured strategic decision making processes and the conditions for achieving successful decision outcomes. Specifically he investigates the processes used to make CRE (Corporate Real Estate) decisions. To reveal the fundamental differences between CRE decision-making in practice and the prescriptive ‘best practice’ advocated in the CRE literature, a study of seven leading Italian management consulting firms is undertaken addressing the aspects of content and process of decisions. This research makes its primary contribution by identifying the importance and difficulty of finding the right balance between problem complexity, process richness and cohesion to ensure a decision-making process that is sufficiently rich and yet quick enough to deliver a prompt outcome. While doing so, the study also provides more empirical evidence to some of the most established theories of decision-making, while reinterpreting their mono-dimensional arguments in a multi-dimensional model of successful decision-making.

Building envelope : performance optimisation processes for a daylight responsive architecture

Traditional shading design principles guide the vertical and horizontal orientation of fins, louvres and awnings being applied to orthogonal planar façades. Due to doubly curved envelopes characterising many contemporary designs, these rules of thumb are now not always applicable. Operable blinds attempt to regulate the fluctuating luminance of daylight and aid in shading direct sunlight. Mostly they remain closed, as workers are commonly too preoccupied to continually adjust them so a reliance on electrically powered lights remains a preference. To remedy these problems, the idea of what it is to sustainable enclose space is reconsidered through the geometric and kinetic optimisation of a parametric skin, with sunlight responsive modules that regulate interior light levels. This research concludes with an optimised design and also defines some unique metrics to gauge the design’s performance in terms of, the amount of exterior unobstructed view, its ability to shade direct sunlight and, its daylight glare probability.

Modelling processes and the question of impact

In this Column, I have teamed up with a colleague, Eike Bernhard, a doctoral student who is studying the impact of process modelling on organizational practices. Together, we want to shed light on an age-old question of Business Process Management: What is the value proposition of process modelling?