Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Qualitative inquiry as transformation and agency : the black sheep and workplace mobbing

This chapter discusses an action research project into the lived experience of the workplace mobbing phenomenon. The action research methodology is based on the exemplarian model (Coenen & Khonraad, 2003) from the Netherlands Group. This model requires positive outcomes for those immersed in the problem to reduce the adversity of their circumstances. The findings challenge the psychological perspective of the existing bullying literature that tends to focus on individual behaviour. This research, undertaken over a three year period with 212 participants, identified the dysfunctional nature of public sector bureaucracies and the power gained through gossip and rumour as some of the key emergent themes to explain the workplace mobbing problem. In addition, resistance, conscientisation, and agency were identified as the key to transformation for those targeted. The discussion focuses on the crystallisation phase of the exemplarian model where the participants identified themselves as the Black Sheep and adopted the motto that “a black sheep is a biting beast” (Bastard, 1565 or 6-1618, p. 90), reflecting a sense of empowerment, individual agency, and a sense of humour in dealing with the serious yet seemingly absurd reality of their situations. The identity of the Black Sheep was consolidated when the group organised a 2 day conference with over 200 attendees to discuss how best to prevent workplace mobbing. This self-affirming action was a proactive step towards metaphorically “biting back” at the problem. A number of positive outcomes were achieved including the conference with over 200 attending leading to national media coverage across Australia and additional interviews with magazines, newspapers, and radio.

Developing a framework for planning healthy communities : the Logan Beaudesert health decision support system

In the last few decades, the focus on building healthy communities has grown significantly (Ashton, 2009). There is growing evidence that new approaches to planning are required to address the challenges faced by contemporary communities. These approaches need to be based on timely access to local information and collaborative planning processes (Murray, 2006; Scotch & Parmanto, 2006; Ashton, 2009; Kazda et al., 2009). However, there is little research to inform the methods that can support this type of responsive, local, collaborative and consultative health planning (Northridge et al., 2003). Some research justifies the use of decision support systems (DSS) as a tool to support planning for healthy communities. DSS have been found to increase collaboration between stakeholders and communities, improve the accuracy and quality of the decision-making process, and improve the availability of data and information for health decision-makers (Nobre et al., 1997; Cromley & McLafferty, 2002; Waring et al., 2005). Geographic information systems (GIS) have been suggested as an innovative method by which to implement DSS because they promote new ways of thinking about evidence and facilitate a broader understanding of communities. Furthermore, literature has indicated that online environments can have a positive impact on decision-making by enabling access to information by a broader audience (Kingston et al., 2001). However, only limited research has examined the implementation and impact of online DSS in the health planning field. Previous studies have emphasised the lack of effective information management systems and an absence of frameworks to guide the way in which information is used to promote informed decisions in health planning. It has become imperative to develop innovative approaches, frameworks and methods to support health planning. Thus, to address these identified gaps in the knowledge, this study aims to develop a conceptual planning framework for creating healthy communities and examine the impact of DSS in the Logan Beaudesert area. Specifically, the study aims to identify the key elements and domains of information that are needed to develop healthy communities, to develop a conceptual planning framework for creating healthy communities, to collaboratively develop and implement an online GIS-based Health DSS (i.e., HDSS), and to examine the impact of the HDSS on local decision-making processes. The study is based on a real-world case study of a community-based initiative that was established to improve public health outcomes and promote new ways of addressing chronic disease. The study involved the development of an online GIS-based health decision support system (HDSS), which was applied in the Logan Beaudesert region of Queensland, Australia. A planning framework was developed to account for the way in which information could be organised to contribute to a healthy community. The decision support system was developed within a unique settings-based initiative Logan Beaudesert Health Coalition (LBHC) designed to plan and improve the health capacity of Logan Beaudesert area in Queensland, Australia. This setting provided a suitable platform to apply a participatory research design to the development and implementation of the HDSS. Therefore, the HDSS was a pilot study examined the impact of this collaborative process, and the subsequent implementation of the HDSS on the way decision-making was perceived across the LBHC. As for the method, based on a systematic literature review, a comprehensive planning framework for creating healthy communities has been developed. This was followed by using a mixed method design, data were collected through both qualitative and quantitative methods. Specifically, data were collected by adopting a participatory action research (PAR) approach (i.e., PAR intervention) that informed the development and conceptualisation of the HDSS. A pre- and post-design was then used to determine the impact of the HDSS on decision-making. The findings of this study revealed a meaningful framework for organising information to guide planning for healthy communities. This conceptual framework provided a comprehensive system within which to organise existing data. The PAR process was useful in engaging stakeholders and decision-making in the development and implementation of the online GIS-based DSS. Through three PAR cycles, this study resulted in heightened awareness of online GIS-based DSS and openness to its implementation. It resulted in the development of a tailored system (i.e., HDSS) that addressed the local information and planning needs of the LBHC. In addition, the implementation of the DSS resulted in improved decision- making and greater satisfaction with decisions within the LBHC. For example, the study illustrated the culture in which decisions were made before and after the PAR intervention and what improvements have been observed after the application of the HDSS. In general, the findings indicated that decision-making processes are not merely informed (consequent of using the HDSS tool), but they also enhance the overall sense of ‗collaboration‘ in the health planning practice. For example, it was found that PAR intervention had a positive impact on the way decisions were made. The study revealed important features of the HDSS development and implementation process that will contribute to future research. Thus, the overall findings suggest that the HDSS is an effective tool, which would play an important role in the future for significantly improving the health planning practice.

A study of ionic liquids for dissolution of sugarcane bagasse

Over the last decade, Ionic Liquids (ILs) have been used for the dissolution and derivatization of isolated cellulose. This ability of ILs is now sought for their application in the selective dissolution of cellulose from lignocellulosic biomass, for the manufacture of cellulosic ethanol. However, there are significant knowledge gaps in the understanding of the chemistry of the interaction of biomass and ILs. While imidazolium ILs have been used successfully to dissolve both isolated crystalline cellulose and components of lignocellulosic biomass, phosphonium ILs have not been sufficiently explored for the use in dissolution of lignocellulosic biomass. This thesis reports on the study of the chemistry of sugarcane bagasse with phosphonium ILs. Qualitative and quantitative measurements of biomass components dissolved in the phosphonium ionic liquids (ILs), trihexyltetradecylphosphonium chloride ([P66614]Cl) and tributylmethylphosphonium methylsulphate ([P4441]MeSO4) are obtained using attenuated total reflectance-Fourier Transform Infra Red (FTIR). Absorption bands related to cellulose, hemicelluloses and lignin dissolution monitored in situ in biomass-IL mixtures indicate lignin dissolution in both ILs and some holocellulose dissolution in the hydrophilic [P4441]MeSO4. The kinetics of lignin dissolution reported here indicate that while dissolution in the hydrophobic IL [P66614]Cl appears to follow an accepted mechanism of acid catalysed β-aryl ether cleavage, dissolution in the hydrophilic IL [P4441]MeSO4 does not appear to follow this mechanism and may not be followed by condensation reactions (initiated by reactive ketones). The quantitative measurement of lignin dissolution in phosphonium ILs based on absorbance at 1510 cm-1 has demonstrated utility and greater precision than the conventional Klason lignin method. The cleavage of lignin β-aryl ether bonds in sugarcane bagasse by the ionic liquid [P66614]Cl, in the presence of catalytic amounts of mineral acid. (ca. 0.4 %). The delignification process of bagasse is studied over a range of temperatures (120 °C to 150 °C) by monitoring the production of β-ketones (indicative of cleavage of β-aryl ethers) using FTIR spectroscopy and by compositional analysis of the undissolved fractions. Maximum delignification is obtained at 150 °C, with 52 % of lignin removed from the original lignin content of bagasse. No delignification is observed in the absence of acid which suggests that the reaction is acid catalysed with the IL solubilising the lignin fragments. The rate of delignification was significantly higher at 150 °C, suggesting that crossing the glass transition temperature of lignin effects greater freedom of rotation about the propanoid carbon-carbon bonds and leads to increased cleavage of β-aryl ethers. An attempt has been made to propose a probable mechanism of delignifcation of bagasse with the phosphonuim IL. All polymeric components of bagasse, a lignocellulosic biomass, dissolve in the hydrophilic ionic liquid (IL) tributylmethylphosphonium methylsulfate ([P4441]MeSO4) with and without a catalytic amount of acid (H2SO4, ca. 0.4 %). The presence of acid significantly increases the extent of dissolution of bagasse in [P4441]MeSO4 (by ca. 2.5 times under conditions used here). The dissolved fractions can be partially recovered by the addition of an antisolvent (water) and are significantly enriched in lignin. Unlike acid catalysed dissolution in the hydrophobic IL tetradecyltrihexylphosphonium chloride there is little evidence of cleavage of β-aryl ether bonds of lignin dissolving in [P4441]MeSO4 (with and without acid), but this mechanism may play some role in the acid catalysed dissolution. The XRD of the undissolved fractions suggests that the IL may selectively dissolve the amorphous cellulose component, leaving behind crystalline material.

Multi-method, multi-theoretical, multi-level research in the learning sciences

We examine methodologies and methods that apply to multi-level research in the learning sciences. In so doing we describe how multiple theoretical frameworks informs the use of different methods that apply to social levels involving space-time relationships that are not accessible consciously as social life is enacted. Most of the methods involve analyses of video and audio files. Within a framework of interpretive research we present a methodology of event-oriented social science, which employs video ethnography, narrative, conversation analysis, prosody analysis, and facial expression analysis. We illustrate multi-method research in an examination of the role of emotions in teaching and learning. Conversation and prosody analyses augment facial expression analysis and ethnography. We conclude with an exploration of ways in which multi-level studies can be complemented with neural level analyses.

ATR-FTIR measurement of biomass components in phosphonium ionic liquids

Qualitative and quantitative measurements of biomass components dissolved in the phosphonium ionic liquids (ILs), trihexyltetradecylphosphonium chloride ([P66614]Cl) and tributylmethylphosphonium methylsulphate ([P4441]MeSO 4), are obtained using attenuated total reflectance-FTIR. Absorption bands related to cellulose, hemicelluloses, and lignin dissolution monitored in situ in biomass-IL mixtures indicate lignin dissolution in both ILs and some holocellulose dissolution in the hydrophilic [P4441]MeSO 4. The kinetics of lignin dissolution reported here indicate that while dissolution in the hydrophobic IL [P66614]Cl appears to follow an accepted mechanism of acid catalyzed -aryl ether cleavage, dissolution in the hydrophilic IL [P4441]MeSO 4 does not appear to follow this mechanism and may not be followed by condensation reactions (initiated by reactive ketones). The measurement of lignin dissolution in phosphonium ILs based on absorbance at 1510 cm 1 has demonstrated utility. When coupled with the gravimetric Klason lignin method, ATR-FTIR study of reaction mixtures can lead to a better understanding of the delignification process. © 2012 Copyright Taylor and Francis Group, LLC.

Experiences of a walking intervention in a University community : Qualitative perspectives

Background: This study explored the experiences of university employees that participated in a walking intervention that encouraged individuals to walk more throughout their workday. The 10-week program was comprised of 5 phases (i.e. baseline, anticipating barriers, short planned walks, longer planned walks and maintenance) and utilized a pedometer diary and an online website for logging steps. The pedometer diary included “action plans” for addressing barriers and planning walking and the online dashboard provided graphical outputs that allowed participants to visualize whether they were reaching or exceeding their step targets. Methods: A subsample of 12 academic and administrative employees from the study completed open ended questionnaires at the end of the study. The questions focused on capturing the major themes of benefits/mediators and problems/moderators of the program and were assessed using phenomenological approaches. Results: Participants found a raised consciousness of physical inactivity throughout the work day. They also found it useful to have a graphical display of physical activity patterns, but found time constraints and lack of managerial support to be the primary barriers/moderators of the program. Those most likely to withdraw from the program experienced technical difficulties with objective monitors and the online website. Conclusions: Findings highlight the value in being involved in a group forum and provide insights into the challenges of supporting such programs within the workplace.

Non-invasive method for detecting changes in soil moisture using wireless sensor networks

There are several popular soil moisture measurement methods today such as time domain reflectometry, electromagnetic (EM) wave, electrical and acoustic methods. Significant studies have been dedicated in developing method of measurements using those concepts, especially to achieve the characteristics of noninvasiveness. EM wave method provides an advantage because it is non-invasive to the soil and does not need to utilise probes to penetrate or bury in the soil. But some EM methods are also too complex, expensive, and not portable for the application of Wireless Sensor Networks; for example satellites or UAV (Unmanned Aerial Vehicle) based sensors. This research proposes a method in detecting changes in soil moisture using soil-reflected electromagnetic (SREM) wave from Wireless Sensor Networks (WSNs). Studies have shown that different levels of soil moisture will affects soil’s dielectric properties, such as relative permittivity and conductivity, and in turns change its reflection coefficients. The SREM wave method uses a transmitter adjacent to a WSNs node with purpose exclusively to transmit wireless signals that will be reflected by the soil. The strength from the reflected signal that is determined by the soil’s reflection coefficients is used to differentiate the level of soil moisture. The novel nature of this method comes from using WSNs communication signals to perform soil moisture estimation without the need of external sensors or invasive equipment. This innovative method is non-invasive, low cost and simple to set up. There are three locations at Brisbane, Australia chosen as the experiment’s location. The soil type in these locations contains 10–20% clay according to the Australian Soil Resource Information System. Six approximate levels of soil moisture (8, 10, 13, 15, 18 and 20%) are measured at each location; with each measurement consisting of 200 data. In total 3600 measurements are completed in this research, which is sufficient to achieve the research objective, assessing and proving the concept of SREM wave method. These results are compared with reference data from similar soil type to prove the concept. A fourth degree polynomial analysis is used to generate an equation to estimate soil moisture from received signal strength as recorded by using the SREM wave method.

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.

RCA method for fault diagnosis in digital substations of power systems

The authors present a Cause-Effect fault diagnosis model, which utilises the Root Cause Analysis approach and takes into account the technical features of a digital substation. The Dempster/Shafer evidence theory is used to integrate different types of fault information in the diagnosis model so as to implement a hierarchical, systematic and comprehensive diagnosis based on the logic relationship between the parent and child nodes such as transformer/circuit-breaker/transmission-line, and between the root and child causes. A real fault scenario is investigated in the case study to demonstrate the developed approach in diagnosing malfunction of protective relays and/or circuit breakers, miss or false alarms, and other commonly encountered faults at a modern digital substation.

Investigating the potential value of individual parameters of histological grading systems in a sheep model of cartilage damage : the modified Mankin method

A total histological grade does not necessarily distinguish between different manifestations of cartilage damage or degeneration. An accurate and reliable histological assessment method is required to separate normal and pathological tissue within a joint during treatment of degenerative joint conditions and to sub-classify the latter in meaningful ways. The Modified Mankin method may be adaptable for this purpose. We investigated how much detail may be lost by assigning one composite score/grade to represent different degenerative components of the osteoarthritic condition. We used four ovine injury models (sham surgery, anterior cruciate ligament/medial collateral ligament instability, simulated anatomic anterior cruciate ligament reconstruction and meniscal removal) to induce different degrees and potentially 'types' (mechanisms) of osteoarthritis. Articular cartilage was systematically harvested, prepared for histological examination and graded in a blinded fashion using a Modified Mankin grading method. Results showed that the possible permutations of cartilage damage were significant and far more varied than the current intended use that histological grading systems allow. Of 1352 cartilage specimens graded, 234 different manifestations of potential histological damage were observed across 23 potential individual grades of the Modified Mankin grading method. The results presented here show that current composite histological grading may contain additional information that could potentially discern different stages or mechanisms of cartilage damage and degeneration in a sheep model. This approach may be applicable to other grading systems.

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.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

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.