A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Towards a potential model to enhance language learner autonomy in the Vietnamese higher education context

This constructivist theory-led case study explored how the term language learner autonomy (LLA) is interpreted and the appropriate pedagogy to foster LLA in the Vietnamese higher education context. Evidence through the exploration of the government policies and the cases of three EFL classes confirms the interpretation that learner autonomy and language acquisition are mutually supported. The study has proposed project work as a potential model while demonstrating the role of the teacher and the use of target language as mediators to enhance LLA in the local context. Findings of the study contribute a theoretical and pedagogical justification for encouraging LLA in Vietnam and other similar contexts.

Developing countries and the potential of mandatory reporting laws to identify severe child abuse and neglect

This chapter considers the key characteristics of different types of child abuse and neglect, and outlines the nature and justifiability of mandatory reporting laws. The issue of whether these laws may be useful for child protection in developing countries with emerging economies is an important one. ‘Developing country’ is a term used by various institutions to describe a nation which has a lower living standard, industrial base, and human development index (HDI) compared to other countries (World Bank 2012; United Nations Development Programme 2013). In the context of developing countries, the chapter addresses two questions: first, might some forms of maltreatment be more suited to mandatory reporting than others? Second, what options for child protection may be considered by developing countries, taking into account children’s needs, cultural conditions and practices, economic imperatives, and the different levels of preparedness to implement child protection strategies?

Transitioning to energy efficient vehicles: An analysis of the potential rebound effects and subsequent impact upon emissions

Given the shift toward energy efficient vehicles (EEVs) in recent years, it is important that the effects of this transition are properly examined. This paper investigates some of these effects by analyzing annual kilometers traveled (AKT) of private vehicle owners in Stockholm in 2008. The difference in emissions associated with EEV adoption is estimated, along with the effect of a congestion-pricing exemption for EEVs on vehicle usage. Propensity score matching is used to compare AKT rates of different vehicle owner groups based on the treatments of: EEV ownership and commuting across the cordon, controlling for confounding factors such as demographics. Through this procedure, rebound effects are identified, with some EEV owners found to have driven up to 12.2% further than non-EEV owners. Although some of these differences could be attributed to the congestion-pricing exemption, the results were not statistically significant. Overall, taking into account lifecycle emissions of each fuel type, average EEV emissions were 50.5% less than average non-EEV emissions, with this reduction in emissions offset by 2.0% due to rebound effects. Although it is important for policy-makers to consider the potential for unexpected negative effects in similar transitions, the overall benefit of greatly reduced emissions appears to outweigh any rebound effects present in this case study.

The potential impact of climate change and ultraviolet radiation on vaccine preventable infectious diseases and immunisation service delivery system

Climate change and solar ultraviolet radiation may affect vaccine-preventable infectious diseases (VPID), the human immune response process and the immunization service delivery system. We systematically reviewed the scientific literature and identified 37 relevant publications. Our study shows that climate variability and ultraviolet radiation may potentially affect VPID and the immunization delivery system through modulating vector reproduction and vaccination effectiveness, possibly influencing human immune response systems to the vaccination, and disturbing immunization service delivery. Further research is needed to determine these affects on climate-sensitive VPID and on human immune response to common vaccines. Such research will facilitate the development and delivery of optimal vaccination programs for target populations, to meet the goal of disease control and elimination.

A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Secondly, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Thirdly, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional Fitzhugh-Nagumo model on both an approximate circular and an approximate irregular domain.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

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.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

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.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Transdisciplinary approaches to urban computing

The research field of urban computing – defined as “the integration of computing, sensing, and actuation technologies into everyday urban settings and lifestyles” – considers the design and use of ubiquitous computing technology in public and shared urban environments. Its impact on cities, buildings, and spaces evokes innumerable kinds of change. Embedded into our everyday lived environments, urban computing technologies have the potential to alter the meaning of physical space, and affect the activities performed in those spaces. This paper starts a multi-themed discussion of various aspects that make up the, at times, messy and certainly transdisciplinary field of urban computing and urban informatics.

The potential for utilising the collaborative learning spaces approach in the delivery of résumé development education

This study investigated the potential for using collaborative learning spaces for the development of résumé writing knowledge and skills in higher education students. Utilising a collaborative learning environment, 227 students from a mix of programmes and year levels participated in one of 24 workshops centering on a technology supported, shared review and reflection approach to résumé construction. It was concluded that use of technology supported collaborative learning spaces has the potential to be a valuable, innovative approach for the delivery of career management related skills in higher education.

"Doing” social justice in early childhood: The potential of leadership

Early childhood education and care (ECEC) has long been connected with objectives related to social justice. ECEC in Australia has its roots in philanthropic and educational reform movements, and more recently with the National Early Childhood Reform Agenda, ECEC has once more been linked to the redressing inequality and disadvantage. Drawing on extant literature, including data from two previously reported Australian studies in which leadership emerged as having a transformational impact on service delivery, this paper examines the potential of early childhood leadership to generate ‘socially just’ educational communities. With reference to critical theory, we argue that critically informed, intentional and strategic organisational leadership can play a pivotal role in creating changed circumstances and opportunities for children and families.