Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Visual support for work assignment in process-aware information systems : framework formalisation and implementation

Process-aware information systems, ranging from generic workflow systems to dedicated enterprise information systems, use work-lists to offer so-called work items to users. In real scenarios, users can be confronted with a very large number of work items that stem from multiple cases of different processes. In this jungle of work items, users may find it hard to choose the right item to work on next. The system cannot autonomously decide which is the right work item, since the decision is also dependent on conditions that are somehow outside the system. For instance, what is “best” for an organisation should be mediated with what is “best” for its employees. Current work-list handlers show work items as a simple sorted list and therefore do not provide much decision support for choosing the right work item. Since the work-list handler is the dominant interface between the system and its users, it is worthwhile to provide an intuitive graphical interface that uses contextual information about work items and users to provide suggestions about prioritisation of work items. This paper uses the so-called map metaphor to visualise work items and resources (e.g., users) in a sophisticated manner. Moreover, based on distance notions, the work-list handler can suggest the next work item by considering different perspectives. For example, urgent work items of a type that suits the user may be highlighted. The underlying map and distance notions may be of a geographical nature (e.g., a map of a city or office building), but may also be based on process designs, organisational structures, social networks, due dates, calendars, etc. The framework proposed in this paper is generic and can be applied to any process-aware information system. Moreover, in order to show its practical feasibility, the paper discusses a full-fledged implementation developed in the context of the open-source workflow environment YAWL, together with two real examples stemming from two very different scenarios. The results of an initial usability evaluation of the implementation are also presented, which provide a first indication of the validity of the approach.

Cyclic imides and an open-chain amide carboxylic acid from the facile reaction of cis-cyclohexane-1,2-dicarboxylic anhydride with the isomeric monofluoroanilines

The structures of the cyclic imides cis-2-(2-fluorophenyl)-3a,4,5,6,7,7a-hexahydroisoindole-1,3-dione, C14H14FNO2, (I), and cis-2-(4-fluorophenyl)-3a,4,5,6,7,7a-hexahydroisoindoline-1,3-dione, C14H14FNO2, (III), and the open-chain amide acid rac-cis-2-[(3-fluorophenyl)carbamoyl]cyclohexane-1-carboxylic acid, C14H16FNO3, (II), are reported. Cyclic imides (I) and (III) are conformationally similar, with comparable ring rotations about the imide N-Car bond [the dihedral angles between the benzene ring and the five-membered isoindole ring are 55.40 (8)° for (I) and 51.83 (7)° for (III)]. There are no formal intermolecular hydrogen bonds involved in the crystal packing of either (I) or (III). With the acid (II), in which the meta-related F-atom substituent is rotationally disordered (0.784:0.216), the amide group lies slightly out of the benzene plane [the interplanar dihedral angle is 39.7 (1)°]. Intermolecular amide-carboxyl N-HO hydrogen-bonding interactions between centrosymmetrically related molecules form stacks extending down b, and these are linked across c by carboxyl-amide O-HO hydrogen bonds, giving two-dimensional layered structures which lie in the (011) plane. The structures reported here represent examples of compounds analogous to the phthalimides or phthalanilic acids and have little precedence in the crystallographic literature.

Reclaiming the art of teaching

This paper explores the art and craft of teaching in higher education. It presents a model of the relationship between art and craft drawn from the author’s theoretical and empirical work, and provides examples from the higher education context to illustrate the model. It discusses the characteristics of teaching as art and craft and critiques the move towards standardisation and conformity in favour of originality, creativity and innovation. It suggests that to see teaching as art is more holistic, satisfying and transformative than to see it as craft. It argues for reclaiming the art of teaching and provides strategies for encouraging and supporting artistic teaching.

Leveraging innovation for sustainable construction, proceedings of the CIB Task Group 58: Clients and Construction Innovation Workshop

This publication consists of a volume of papers presented at the workshop of the CIB Task Group 58: Clients and Construction Innovation, held on May 18- 19, 2009 at the University of Alberta in Edmonton, Canada. The workshop theme, “Leveraging Innovation for Sustainable Construction”, reflects a growing concern among clients for perspectives, approaches, and tools that will secure the practice of construction economically, socially, and environmentally. This collection encompasses some of the most incisive assessments of the challenges facing the construction industry today from a range of researchers and industry practitioners who are leading the way for tomorrow’s innovations. It provides a useful documentation of the ongoing conversation regarding innovation and sustainability issues and a foundation of knowledge for future research and development. The papers contained in this volume explore the workshop’s overarching theme of how to leverage innovation to increase the sustainability of the construction process and product. Participants sought to generate discussion on the topics of innovation and sustainability within the construction field, to share international examples of innovation from the research community and from industry, and to establish a point of reference for ongoing enquiry. In particular, our contributors have noted the value of learning through practice in order to orient research based on real-world industry experience. Chapters two and three present complementary models of sustainable research programs through the three parts collaboration of government, industry, and academia. Chapters four and five explore new tools and forms of technological innovation as they are deployed to improve construction project management and set the direction for advances in research. Chapters six, seven, and eight closely study practical examples of innovation in large-scale construction projects, showing with concrete results the impact of applying creative methods and best practices to the field. Innovation and sustainability in construction are truly global efforts; these papers illustrate how we can draw on international examples and cooperative organizations to address these important issues for long-term benefit of the industry.

Anomalous subdiffusion equations by the meshless collocation method

This paper aims to develop an implicit meshless collocation technique based on the moving least squares approximation for numerical simulation of the anomalous subdiffusion equation(ASDE). The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach related to the time discretization are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling of ASDEs.

Building and construction industries supply chain project (domestic) : report for Commonwealth Department of Industry, Science and Resources

The Commonwealth Department of Industry, Science and Resources is identifying best practice case study examples of supply chain management within the building and construction industry to illustrate the concepts, innovations and initiatives that are at work. The projects provide individual enterprises with examples of how to improve their performance, and the competitiveness of the industry as a whole.

In vitro breeding strategies in the development of Australian native plants

Plant tissue culture is a technique that exploits the ability of many plant cells to revert to a meristematic state. Although originally developed for botanical research, plant tissue culture has now evolved into important commercial practices and has become a significant research tool in agriculture, horticulture and in many other areas of plant sciences. Plant tissue culture is the sterile culture of plant cells, tissues, or organs under aseptic conditions leading to cell multiplication or regeneration or organs and whole plants. The steps required to develop reliable systems for plant regeneration and their application in plant biotechnology are reviewed in countless books. Some of the major landmarks in the evolution of in vitro techniques are summarised in Table 5.1. In this chapter the current applications of this technology to agriculture, horticulture, forestry and plant breeding are briefly described with specific examples from Australian plants when applicable.

Aspect oriented business process modeling with precedence

Complexity is a major concern which is aimed to be overcome by people through modeling. One way of reducing complexity is separation of concerns, e.g. separation of business process from applications. One sort of concerns are cross-cutting concerns i.e. concerns which are scattered and tangled through one of several models. In business process management, examples of such concerns are security and privacy policies. To deal with these cross-cutting concerns, the aspect orientated approach was introduced in the software development area and recently also in the business process management area. The work presented in this paper elaborates on aspect oriented process modelling. It extends earlier work by defining a mechanism for capturing multiple concerns and specifying a precedence order according to which they should be handled in a process. A formal syntax of the notation is presented precisely capturing the extended concepts and mechanisms. Finally, the relevant of the approach is demonstrated through a case study.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

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.

Sensitivity of the NMR density matrix to pulse sequence parameters : a simplified analytic approach

We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.