Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Pretreatment of sugarcane bagasse by acid-catalysed process in aqueous ionic liquid solutions

A biomass pretreatment process was developed using acidified ionic liquid (IL) solutions containing 10-30% water. Pretreatment of sugarcane bagasse at 130°C for 30min by aqueous 1-butyl-3-methylimidazolium chloride (BMIMCl) solution containing 1.2% HCl resulted in a glucan digestibility of 94-100% after 72h of enzymatic hydrolysis. HCl was found to be a more effective catalyst than H(2)SO(4) or FeCl(3). Increasing acid concentration (from 0.4% to 1.2%) and reaction temperature (from 90 to 130°C) increased glucan digestibility. The glucan digestibility of solid residue obtained with the acidified BMIMCl solution that was re-used for three times was >97%. The addition of water to ILs for pretreatment could significantly reduce IL solvent costs and allow for increased biomass loadings, making the pretreatment by ILs a more economic proposition.

Literacy in Early Childhood and Primary Education : Issues, Challenges and Solutions

Literacy in Early Childhood and Primary Education provides a comprehensive introduction to literacy teaching and learning. The book explores the continuum of literacy learning and children’s transitions from early childhood settings to junior primary classrooms, and then to senior primary and beyond. Reader-friendly and accessible, this book equips pre-service teachers with the theoretical underpinnings and practical strategies and skills needed to teach literacy. It places the ‘reading wars’ firmly in the past as it examines contemporary research and practices. The book covers important topics such as literacy acquisition, family literacies and multiliteracies, foundation skills for literacy learning, reading difficulties, assessment, and supporting diverse literacy learners in early childhood and primary classrooms. It also addresses some of the challenges that teachers may face in the classroom and provides solutions to these. Each chapter includes learning objectives, reflective questions and definitions to key terms to engage and assist readers. Further resources are also available at www.cambridge.edu.au/academic/literacy. Written by an expert author team and featuring real-world examples from literacy teachers and learners. Literacy in Early Childhood and Primary Education will help pre-service teachers feel confident teaching literacy to diverse age groups and abilities.

An assessment tool for selection of appropriate daylighting solutions for buildings in tropical and subtropical regions : Validation using radiance simulation

A new decision-making tool that will assist designers in the selection of appropriate daylighting solutions for buildings in tropical locations has been previously proposed by the authors. Through an evaluation matrix that prioritizes the parameters that best respond to the needs of tropical climates (e.g. reducing solar gain and protection from glare) the tool determines the most appropriate devices for specific climate and building inputs. The tool is effective in demonstrating the broad benefits and limitations of the different daylight strategies for buildings in the tropics. However for thorough analysis and calibration of the tool, validation is necessary. This paper presents a first step in the validation process. RADIANCE simulations were conducted to compare simulation performance with the performance predicted by the tool. To this end, an office building case study in subtropical Brisbane, Australia, and five different daylighting devices including openings, light guiding systems and light transport systems were simulated. Illuminance, light uniformity, daylight penetration and glare analysis were assessed for each device. The results indicate the tool can appropriately rank and recommend daylighting strategies based on specific building inputs for tropical and subtropical regions, making it a useful resource for designers.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Workable solutions : the intersubjective careers of women with families

This chapter considers to what degree the careers of women with young families, both in and out of paid employment, are lived as contingent, intersubjective projects pursued across time and space, in the social condition of growing biographical possibilities and uneven social/ideological change. Their resolutions of competing priorities by engaging in various permutations of home-work and paid work are termed ‘workable solutions’, with an intentional play on the double sense of ‘work’ – firstly as labour, thus being able to perform work, whether paid or not; secondly as in being able to make things work or function in the family unit’s best interests, however defined.

Numerical solutions of stochastic differential equations – implementation and stability issues

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively.

A generic framework and runtime environment for development and evaluation of behavioral biometrics solutions

Increasing use of computerized systems in our daily lives creates new adversarial opportunities for which complex mechanisms are exploited to mend the rapid development of new attacks. Behavioral Biometrics appear as one of the promising response to these attacks. But it is a relatively new research area, specific frameworks for evaluation and development of behavioral biometrics solutions could not be found yet. In this paper we present a conception of a generic framework and runtime environment which will enable researchers to develop, evaluate and compare their behavioral biometrics solutions with repeatable experiments under the same conditions with the same data.

Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

An efficient numerical method to compute nonlinear solutions for two-dimensional steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996, J. Fluid Mech., 330, 339-347). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free-surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free-surface a priori while solving for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify eleven basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free-surface, given the free-surface shape itself.

Neutralization of acid sulfate solutions using bauxite refinery residues and its derivatives

This investigation has shown that by transforming free caustic in red mud (RM) to Bayer hydrotalcite (during the seawater neutralization (SWN) process) enables a more controlled release mechanism for the neutralization of acid sulfate soils. The formation of hydrotalcite has been confirmed by X-ray diffraction (XRD) and differential thermalgravimetric analysis (DTG), while the dissolution of hydrotalcite and sodalite has been observed through XRD, DTG, pH plots, and ICP-OES. Coupling of all techniques enabled three neutralization mechanisms to be determined: (1) free alkali, (2) hydrotalcite dissolution, and (3) sodalite dissolution. The mechanisms are determined on the basis of ICP-OES and kinetic information. When the mass of RM or SWN-RM is greater than 0.08 g/50 mL, the pH of solution increases to a suitable value for plant life with aluminum leaching kept at a minimum. To obtain a neutralization pH greater than 6 in 10 min, the following ratio of bauxite residue (g) in 50 mL with a known iron sulfate (Fe2(SO4)3) concentration can be determined as follows: 0.04 g:50 mL:0.1 g/L of Fe2(SO4)3.

Laboratory and pilot scale pretreatment of sugarcane bagasse by acidified aqueous glycerol solutions

Pretreatment of sugarcane bagasse with acidified aqueous glycerol solution was evaluated at both laboratory and pilot scales. Laboratory scale pretreatment (4.00 g dry mass in 40.00 g liquid) with glycerol solutions containing ≤ 20 wt% water and 1.2 wt% HCl at 130 °C for 60 min resulted in biomass having glucan digestibilities of ≥ 88%. Comparable glucan enzymatic digestibility of 90% was achieved with bagasse pretreated at pilot scale (10 kg dry mass in 60 kg liquid) using a glycerol solution containing 0.4 wt% HCl and 17 wt% water at 130 °C for 15 min. We attribute more efficient pretreatment at pilot scale (despite shorter reaction time and reduced acid content) to improved mixing and heat transfer in a horizontal reactor. Pretreatment of sugarcane bagasse with acid-catalysed glycerol solutions likely produces glycerol-glycosides, which together with hydrolysed lignin are potential substrates for the production of biopolymers.

Aspects of the kinetics and solubility of silica and calcium oxalate composites in sugar solutions

Fouling of industrial surfaces by silica and calcium oxalate can be detrimental to a number of process streams. Solution chemistry plays a large roll in the rate and type of scale formed on industrial surfaces. This study is on the kinetics and thermodynamics of SiO2 and calcium oxalate composite formation in solutions containing Mg2+ ions, trans-aconitic acid and sucrose, to mimic factory sugar cane juices. The induction time (ti) of silicic acid polymerization is found to be dependent on the sucrose concentration and SiO2 supersaturation ratio (SS). Generalized kinetic and solubility models are developed for SiO2 and calcium oxalate in binary systems using response surface methodology. The role of sucrose, Mg, trans-aconitic acid, a mixture of Mg and trans-aconitic acid, SiO2 SS ratio and Ca in the formation of com- posites is explained using the solution properties of these species including their ability to form complexes.

Analysis of regionally enhanced GPS orbit and clock solutions and contribution to improvement of real-time precise point positioning

This work experimentally examines the performance benefits of a regional CORS network to the GPS orbit and clock solutions for supporting real-time Precise Point Positioning (PPP). The regionally enhanced GPS precise orbit solutions are derived from a global evenly distributed CORS network added with a densely distributed network in Australia and New Zealand. A series of computational schemes for different network configurations are adopted in the GAMIT-GLOBK and PANDA data processing. The precise GPS orbit results show that the regionally enhanced solutions achieve the overall orbit improvements with respect to the solutions derived from the global network only. Additionally, the orbital differences over GPS satellite arcs that are visible by any of the five Australia-wide CORS stations show a higher percentage of overall improvements compared to the satellite arcs that are not visible from these stations. The regional GPS clock and Uncalibrated Phase Delay (UPD) products are derived using the PANDA real time processing module from Australian CORS networks of 35 and 79 stations respectively. Analysis of PANDA kinematic PPP and kinematic PPP-AR solutions show certain overall improvements in the positioning performance from a denser network configuration after solution convergence. However, the clock and UPD enhancement on kinematic PPP solutions is marginal. It is suggested that other factors, such as effects of ionosphere, incorrectly fixed ambiguities, may be the more dominating, deserving further research attentions.