Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Regulating Prostitution: Different Problems, Different Solutions, Same Old Story

This article looks at three main models of intervention that have informed recent policy and practice with people involved in the sex trade. It reveals the inherent contradictions within attempts to both help and punish workers in the existing prostitution strategy.

Unexpected issues and solutions: Emerge from environmental manipulation strategy

Environmental manipulation removes students from their everyday worlds to unfamiliar worlds, to facil- itate learning. This article reports that this strategy was effective when applied in a university design unit, using the tactic of immersion in the Second Life online virtual environment. The objective was for teams of stu- dents each to design a series of modules for an orbiting space station using supplied data. The changed and futuristic environment led the students to an important but previously unconsidered design decision which they were able to address in novel ways because of, rather than in spite of, the Second Life immersion.

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.

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.

Synthesis and characterisation of layered double hydroxides and their application for water purification

Layered doubly hydroxides (LDHs) also known as hydrotalcites or anionic clays are a group of clay minerals that have shown promise for the removal of toxic anions from water through both anion exchange and a process known as the reformation effect. This project has involved the preparation and characterisation of LDH materials as well as the investigation of their ability to remove selected anions from aqueous solutions by the reformation effect. The LDH materials were successfully prepared from magnesium, aluminium, zinc and chromium chloride salts using the co-precipitation method. Samples were characterised using powder X-ray diffraction (XRD) and thermogravimetry (TG) to confirm the presence of LDHs. Powder XRD revealed a characteristic LDH structure for all LDH samples. Thermal Analysis showed decomposition usual occurred through a three or four step process as expected for LDHs. Preliminary investigations of the removal of sulfate, nitrate and fluoride by an Mg/Al LDH were carried out, and the products were characterised using XRD and TG which showed that an LDH material similar to the original hydrotalcite was formed after reformation. A Zn/Al LDH was investigated as a potential sorbent material for the removal of iodine and iodide from water. It was found that the LDH was a suitable adsorbent which is able to remove almost all of the iodine present in the test solutions. Again, the products were characterised by XRD, TG and evolved gas mass spectrometry (EGMS) in an attempt to better understand the iodine removal process. Powder XRD showed successful reformation of the LDH structure and TG/EGMS showed that only a small amount of iodine species were lost during thermal decomposition. Finally, the mineral stichtite a Mg/Cr LDH was successfully synthesised and investigated using XRD, TG and EGMS. Unfortunately, due to lack of time it was not possible to identify any new uses for the mineral stichtite in the current project.

Coal seam gas waters - their geochemical signature and potential environmental implications

Coal Seam Gas (CSG) is a form of natural gas (mainly methane) sorbed in underground coal beds. To mine this gas, wells are drilled directly into an underground coal seam and groundwater (CSG water) is pumped out to the surface. This lowers the downhole piezometric pressure and enables gas desporption from the coal matrix. In the United States, this gas has been extracted commercially since the 1980s. The economic success of US CSG projects has inspired exploration and development in Australia and New Zealand. In Australia, Queensland’s Bowen and Surat basins have been the subject of increased CSG development over the last decade. CSG growth in other Australian basins has not matured to the same level but exploration and development are taking place at an accelerated pace in the Sydney Basin (Illawarra and the Hunter Valley, NSW) and in the Gunnedah Basin. Similarly, CSG exploration in New Zealand has focused in the Waikato region (Maramarua and Huntly), in the West Coast region (Buller, Reefton, and Greymouth), and in Southland (Kaitangata, Mataura, and Ohai). Figure 1 shows a Shcoeller diagram with CSG samples from selected basins in Australia, New Zealand, and the USA. CSG water from all of these basins exhibit the same geochemical signature – low calcium, low magnesium, high bicarbonate, low sulphate and, sometimes, high chloride. This water quality is a direct result of specific biological and geological processes that have taken part in the formation of CSG. In general, these processes include the weathering of rocks (carbonates, dolomite, and halite), cation exchange with clays (responsible for enhanced sodium and depleted calcium and magnesium), and biogenic processes (accounting for the presence of high bicarbonate concentrations). The salinity of CSG waters tends to be brackish (TDS < 30000 mg/l) with a fairly neutral pH. These particular characteristics need to be taken into consideration when assessing water management and disposal alternatives. Environmental issues associated with CSG water disposal have been prominent in developed basins such as the Powder River Basin (PRB) in the United States. When disposed on the land or used for irrigation, water having a high dissolved salts content may reduce water availability to crops thus affecting crop yield. In addition, the high sodium, low calcium and low magnesium concentrations increase the potential to disperse soils and significantly reduce the water infiltration rate. Therefore, CSG waters need to be properly characterised, treated, and disposed to safeguard the environment without compromising other natural resources.

Ionic liquid pre-treatment and fractionation of sugarcane bagasse for the production of bioethanol

Pretretament is an essential and expensive processing step for the manufacturing of ethanol from lignocellulosic raw materials. Ionic liquids are a new class of solvents that have the potential to be used as pretreatment agents. The attractive characteristics of ionic liquid pretreatment of lignocellulosics such as thermal stability, dissolution properties, fractionation potential, cellulose decrystallisation capacity and saccharification impact are investigated in this thesis. Dissolution of bagasse with 1-butyl-3-methylimidazolium chloride ([C4mim]Cl) at high temperatures (110 �‹C to 160 �‹C) is investigated as a pretreatment process. Material balances are reported and used along with enzymatic saccharification data to identify optimum pretreatment conditions (150 �‹C for 90 min). At these conditions, the dissolved and reprecipitated material is enriched in cellulose, has a low crystallinity and the cellulose component is efficiently hydrolysed (93 %, 3 h, 15 FPU). At pretreatment temperatures < 150 �‹C, the undissolved material has only slightly lower crystallinity than the starting. At pretreatment temperatures . 150 �‹C, the undissolved material has low crystallinity and when combined with the dissolved material has a saccharification rate and extent similar to completely dissolved material (100 %, 3h, 15 FPU). Complete dissolution is not necessary to maximize saccharification efficiency at temperatures . 150 �‹C. Fermentation of [C4mim]Cl-pretreated, enzyme-saccharified bagasse to ethanol is successfully conducted (85 % molar glucose-to-ethanol conversion efficiency). As compared to standard dilute acid pretreatment, the optimised [C4mim]Cl pretreatment achieves substantially higher ethanol yields (79 % cf. 52 %) in less than half the processing time (pretreatment, saccharification, fermentation). Fractionation of bagasse partially dissolved in [C4mim]Cl to a polysaccharide rich and a lignin rich fraction is attempted using aqueous biphasic systems (ABSs) and single phase systems with preferential precipitation. ABSs of ILs and concentrated aqueous inorganic salt solutions are achievable (e.g. [C4mim]Cl with 200 g L-1 NaOH), albeit they exhibit a number of technical problems including phase convergence (which increases with increasing biomass loading) and deprotonation of imidazolium ILs (5 % - 8 % mol). Single phase fractionation systems comprising lignin solvents / cellulose antisolvents, viz. NaOH (2M) and acetone in water (1:1, volume basis), afford solids with, respectively, 40 % mass and 29 % mass less lignin than water precipitated solids. However, this delignification imparts little increase in saccharification rates and extents of these solids. An alternative single phase fractionation system is achieved simply by using water as an antisolvent. Regulating the water : IL ratio results in a solution that precipitates cellulose and maintains lignin in solution (0.5 water : IL mass ratio) in both [C4mim]Cl and 1-ethyl-3-methylimidazolium acetate ([C2mim]OAc)). This water based fractionation is applied in three IL pretreatments on bagasse ([C4mim]Cl, 1-ethyl-3-methyl imidazolium chloride ([C2mim]Cl) and [C2mim]OAc). Lignin removal of 10 %, 50 % and 60 % mass respectively is achieved although only 0.3 %, 1.5 % and 11.7 % is recoverable even after ample water addition (3.5 water : IL mass ratio) and acidification (pH . 1). In addition the recovered lignin fraction contains 70 % mass hemicelluloses. The delignified, cellulose-rich bagasse recovered from these three ILs is exposed to enzyme saccharification. The saccharification (24 h, 15 FPU) of the cellulose mass in starting bagasse, achieved by these pretreatments rank as: [C2mim]OAc (83 %)>>[C2mim]Cl (53 %)=[C4mim]Cl(53%). Mass balance determinations accounted for 97 % of starting bagasse mass for the [C4mim]Cl pretreatment , 81 % for [C2mim]Cl and 79 %for [C2mim]OAc. For all three IL treatments, the remaining bagasse mass (not accounted for by mass balance determinations) is mainly (more than half) lignin that is not recoverable from the liquid fraction. After pretreatment, 100 % mass of both ions of all three ILs were recovered in the liquid fraction. Compositional characteristics of [C2mim]OAc treated solids such as low lignin, low acetyl group content and preservation of arabinosyl groups are opposite to those of chloride IL treated solids. The former biomass characteristics resemble those imparted by aqueous alkali pretreatment while the latter resemble those of aqueous acid pretreatments. The 100 % mass recovery of cellulose in [C2mim]OAc as opposed to 53 % mass recovery in [C2mim]Cl further demonstrates this since the cellulose glycosidic bonds are protected under alkali conditions. The alkyl chain length decrease in the imidazolium cation of these ILs imparts higher rates of dissolution and losses, and increases the severity of the treatment without changing the chemistry involved.

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.