A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

Numerical simulation of anomalous infiltration in porous media

Nonlinear time-fractional diffusion equations have been used to describe the liquid infiltration for both subdiffusion and superdiffusion in porous media. In this paper, some problems of anomalous infiltration with a variable-order timefractional derivative in porous media are considered. The time-fractional Boussinesq equation is also considered. Two computationally efficient implicit numerical schemes for the diffusion and wave-diffusion equations are proposed. Numerical examples are provided to show that the numerical methods are computationally efficient.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

Towards Self-improving School Systems: Lessons from a City Challenge

This important new book draws lessons from a large-scale initiative to bring about the improvement of an urban education system. Written from an insider perspective by an internationally recognized researcher, it presents a new way of thinking about system change. This builds on the idea that there are untapped resources within schools and the communities they serve that can be mobilized in order to transform schools from places that do well for some children so that they can do well for many more. Towards Self-improving School Systems presents a strategic framework that can help to foster new, more fruitful working relationships: between national and local government; within and between schools; and between schools and their local communities. What is distinctive in the approach is that this is mainly led from within schools, with senior staff having a central role as system leaders. The book will be relevant to a wide range of readers throughout the world who are concerned with the strengthening of their national educational systems, including teachers, school leaders, policy makers and researchers. The argument it presents is particularly important for the growing number of countries where increased emphasis on school autonomy, competition and choice is leading to fragmentation within education provision.

Fuzzy-DL perception for multi-robot systems

For future planetary robot missions, multi-robot-systems can be considered as a suitable platform to perform space mission faster and more reliable. In heterogeneous robot teams, each robot can have different abilities and sensor equipment. In this paper we describe a lunar demonstration scenario where a team of mobile robots explores an unknown area and identifies a set of objects belonging to a lunar infrastructure. Our robot team consists of two exploring scout robots and a mobile manipulator. The mission goal is to locate the objects within a certain area, to identify the objects, and to transport the objects to a base station. The robots have a different sensor setup and different capabilities. In order to classify parts of the lunar infrastructure, the robots have to share the knowledge about the objects. Based on the different sensing capabilities, several information modalities have to be shared and combined by the robots. In this work we propose an approach using spatial features and a fuzzy logic based reasoning for distributed object classification.

Fractional models in space for diffusive processes in heterogeneous media with applications in cell motility and electrical signal propagation

This work addresses fundamental issues in the mathematical modelling of the diffusive motion of particles in biological and physiological settings. New mathematical results are proved and implemented in computer models for the colonisation of the embryonic gut by neural cells and the propagation of electrical waves in the heart, offering new insights into the relationships between structure and function. In particular, the thesis focuses on the use of non-local differential operators of non-integer order to capture the main features of diffusion processes occurring in complex spatial structures characterised by high levels of heterogeneity.

Cultural factors: Understanding culture to design organisation structures and systems to optimise safety

Safety culture is a term with numerous definitions in the literature. Many authors advocate a prescriptive approach to safety culture in which if an organisation has certain levels of externally prescribed systems and structures in place it has a “good safety culture”. Conversely, other researchers suggest an anthropological approach of exploring deep meanings and understandings present within an organisation’s workforce. In a recent published review, the authors presented an alternative view to safety culture, in which the anthropological aspects of safety culture interact with the structures and systems in place within an organisation to result in behavioural patterns. This can be viewed as a human factors approach to safety culture in which, through understanding the specific interactions between the culture of a workforce and external organisational elements, organisational structures and systems can be optimised in order to shape worker behaviour and improve safety. This paper presents findings from a recent investigation of safety culture in the Australian heavy vehicle (transport) industry. Selected results are discussed to explore how understanding culture can provide direction to the optimisation of organisational structures and systems to match worker culture and thus improve safety. Specifically the value placed on personal experience and stories, as well as on both time and money are discussed, and interventions that are suited to these aspects of the culture are discussed. These findings demonstrate the importance of shifting beyond mere prescriptive and interpretive approaches to safety culture and instead to focus on the interaction between cultural and contextual elements to optimise organisational structures and systems.

A dynamic navigation model for unmanned aircraft systems and an application to autonomous front-on environmental sensing and photography using low-cost sensor systems

This paper presents an unmanned aircraft system (UAS) that uses a probabilistic model for autonomous front-on environmental sensing or photography of a target. The system is based on low-cost and readily-available sensor systems in dynamic environments and with the general intent of improving the capabilities of dynamic waypoint-based navigation systems for a low-cost UAS. The behavioural dynamics of target movement for the design of a Kalman filter and Markov model-based prediction algorithm are included. Geometrical concepts and the Haversine formula are applied to the maximum likelihood case in order to make a prediction regarding a future state of a target, thus delivering a new waypoint for autonomous navigation. The results of the application to aerial filming with low-cost UAS are presented, achieving the desired goal of maintained front-on perspective without significant constraint to the route or pace of target movement.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

The design and implementation of an Information Accountability Framework for eHealth systems

This tutorial primarily focuses on the implementation of Information Accountability (IA) protocols defined in an Information Accountability Framework (IAF) in eHealth systems. Concerns over the security and privacy of patient information are one of the biggest hindrances to sharing health information and the wide adoption of eHealth systems. At present, there are competing requirements between healthcare consumers' (i.e. patients) requirements and healthcare professionals' (HCP) requirements. While consumers want control over their information, healthcare professionals want access to as much information as required in order to make well-informed decisions and provide quality care. This conflict is evident in the review of Australia's PCEHR system and in recent studies of patient control of access to their eHealth information. In order to balance these requirements, the use of an Information Accountability Framework devised for eHealth systems has been proposed. Through the use of IA protocols, so-called Accountable-eHealth systems (AeH) create an eHealth environment where health information is available to the right person at the right time without rigid barriers whilst empowering the consumers with information control and transparency. In this half-day tutorial, we will discuss and describe the technical challenges surrounding the implementation of the IAF protocols into existing eHealth systems and demonstrate their use. The functionality of the protocols and AeH systems will be demonstrated, and an example of the implementation of the IAF protocols into an existing eHealth system will be presented and discussed.

A strong lightweight authentication protocol for low-cost RFID systems

RFID is an important technology that can be used to create the ubiquitous society. But an RFID system uses open radio frequency signal to transfer information and this leads to pose many serious threats to its privacy and security. In general, the computing and storage resources in an RFID tag are very limited and this makes it difficult to solve its secure and private problems, especially for low-cost RFID tags. In order to ensure the security and privacy of low-cost RFID systems we propose a lightweight authentication protocol based on Hash function. This protocol can ensure forward security and prevent information leakage, location tracing, eavesdropping, replay attack and spoofing. This protocol completes the strong authentication of the reader to the tag by twice authenticating and it only transfers part information of the encrypted tag’s identifier for each session so it is difficult for an adversary to intercept the whole identifier of a tag. This protocol is simple and it takes less computing and storage resources, it is very suitable to some low-cost RFID systems.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Thermopower and nature of the hole-doped states in LaMnO3 and related systems showing giant magnetoresistance

We have measured the thermopower (S) of hole-doped LaMnO3 systems in order to see its dependence on the Mn4+ content as well as to investigate other crucial factors that determine S. We have carried out hole doping (creation of Mn4+ by two distinct means, namely, by the substitution of La by divalent cations such as Ca and Sr and by self-doping without aliovalent substitution). The thermopower is sensitive not only to the hole concentration but also to the process employed for hole doping, which we explain as arising from the differences in the nature of the hole-doped states. We also point out a general trend in the dependence of S on hole concentration at high temperatures (T> T-c), similar to that found in the normal-state thermopower of the cuprates.

Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.