Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

'You're not fit to wear the shirt': towards a cultural sociology of the football shirt

The world of football is a matter of life and death for many of its fans, and has also attracted much sociological attention. Much of this scholarly work focuses on issues such as deviance, identity, globalisation and commodification (Elias and Dunning 1986; Giulianotti and Robertson 2009). More recently, there has been some evidence of a cultural approach to football and to the football shirt (Benzecry 2008). In this paper, we seek to develop this trend by examining the football shirt as a totem, and by understanding it as inserted into circuits of the sacred and the profane, and the authentic and the inauthentic. Through examples such as shirt throwing, badge kissing, shirt swapping and supporters‟ efforts to construct alternative, protest strips, we show that the football shirt is deeply embedded in narratives of authenticity, sacredness and profaneness. In doing so, we aim to represent football as a rich cultural practice, which involves secular rituals and performances.

Electro-cortical implicit race bias does not vary with participants' race or sex

Earlier research found evidence for electro-cortical race bias towards black target faces in white American participants irrespective of the task relevance of race. The present study investigated whether an implicit race bias generalizes across cultural contexts and racial in- and out-groups. An Australian sample of 56 Chinese and Caucasian males and females completed four oddball tasks that required sex judgements for pictures of male and female Chinese and Caucasian posers. The nature of the background (across task) and of the deviant stimuli (within task) was fully counterbalanced. Event-related potentials (ERPs) to deviant stimuli recorded from three midline sites were quantified in terms of mean amplitude for four components: N1, P2, N2 and a late positive complex (LPC; 350–700 ms). Deviants that differed from the backgrounds in sex or race elicited enhanced LPC activity. These differences were not modulated by participant race or sex. The current results replicate earlier reports of effects of poser race relative to background race on the LPC component of the ERP waveform. In addition, they indicate that an implicit race bias occurs regardless of participant's or poser's race and is not confined to a particular cultural context.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Explorations into the Sociology of Criminal Justice and Punishment. Leaving the Modernist Project Behind

Law has been a close partner to sociology from its very beginning, and the partnership often has proven to be extremely prolific for sociology. Grand theories as well as vital conceptual tools can be counted among its offspring. Both disciplines share the common ground of socio-legal studies, which has developed into a nearly independent interdisciplinary enterprise where legal scholars and sociologists happily meander between the normative and the analytical. From the vast array of topics in the field of socio-legal studies I select the sociology of criminal justice and punishment in order to demonstrate the characteristics of this relationship. The partnership between sociology and law emerged as part of the modernization project in the 19th and 20th centuries, and the sociology of punishment was part of this endeavour. Rooted in a strong tradition of old (Durkheim) and new (Elias, Foucault) classics, recent developments in this field are leaving the idea of an `unproblematically modern punishment' (Whitman, 2005a) behind, and new fields of inquiry for comparative lawyers and sociologists are opening up.

Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

Capitalising on Bourdieu : how useful is his sociology?

Research questions: How Chinese Australians capitalise on resources (Capital) and negotiate Chineseness (habitus) through learning Chinese as a Heritage Language (CHL practice) in the lived world (field)? Are Chinese Australians’ Chineseness and their CHL learning co-constructed? What does ‘looking Chinese’ mean in Chinese Australians’ CHL learning? How do Chinese Australians learn CHL within the family milieu?

Making the implicit explicit : successful student skills for commencing cohorts

Making institutional expectations explicit using clear and common language engages commencing students and promotes help-seeking behaviour. When first year students enter university they cross the threshold into an unfamiliar environment (Devlin, Kift, Nelson, Smith & McKay, 2012). Universities endeavour to provide appropriate learning support services and resources; however research suggests that there is limited up take of these services, particularly in high risk students (Nelson-Field & Goodman, 2005). The Successful Student Skills Checklist is a tool which will be trialled during the 2013 Orientation period at the QUT Caboolture campus. The new tool is a response to the university’s commitment to provide “an environment where [students] are supported to take responsibility for their own learning, and to embrace an active role in succeeding to their full potential” (QUT, 2012, 6.2.1). This paper will outline the design of the support tool implemented during Orientation, as well as discuss the anticipated outcomes of the trial.

A social matching system : using implicit and explicit information for personalized recommendation in online dating service

Online dating websites enable a specific form of social networking and their efficiency can be increased by supporting proactive recommendations based on participants' preferences with the use of data mining. This research develops two-way recommendation methods for people-to-people recommendation for large online social networks such as online dating networks. This research discovers the characteristics of the online dating networks and utilises these characteristics in developing efficient people-to-people recommendation methods. Methods developed support improved recommendation accuracy, can handle data sparsity that often comes with large data sets and are scalable for handling online networks with a large number of users.

Teaching sociology within teacher education : revisiting, realigning and re-embedding

This paper uses theoretical resources from the sociology of education to consider the teaching of sociology in teacher education programs in Australia. Once a disciplinary ‘pillar’ of teacher education, sociology’s contribution has become less explicit while more integrated, with consequences for disciplinary identity. Here we explore how sociology is taught in teacher education curricula on two fronts. Firstly we outline how sociology is embedded as one of a number of competing perspectives in foundational studies, and its pedagogic consequences. Then we consider the powerful contribution of sociology in literacy studies, amidst public debate about literacy performance. The analysis draws on Bernstein’s (2000) distinction between singular disciplinary curriculum design and practically-oriented regional curriculum design. We seek to trouble the commonsense binary between theory and practice that structures debates around professional education in higher education more broadly, and to dignify service sociology as a valuable, generative site for the discipline’s future.