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.

Hydrogen-bonding in cyclic imides and amide carboxylic acid derivatives from the facile reaction of cis-cyclohexane-1,2-carboxylic anhydride with o- and p-anisidine and m- and p-aminobenzoic acids

The structures of the open chain amide carboxylic acid rac-cis-[2-(2-methoxyphenyl)carbamoyl]cyclohexane-1-carboxylic acid, C15H19NO4, (I) and the cyclic imides rac-cis-2-(4-methoxyphenyl)-3a,4,5,6,7,7-hexahydroisoindole-1,3-dione,C15H17NO3, (II), chiral cis-2-(3-carboxyphenyl)-3a,4,5,6,7,7a-hexahydroisoindole-1,3-dione, C15H15NO4,(III) and rac-cis-2-(4-carboxyphenyl)- 3a,4,5,6,7,7a-hexahydroisoindole-1,3-dione monohydrate, C15H15NO4. H2O) (IV), are reported. In the amide acid (I), the phenylcarbamoyl group is essentially planar [maximum deviation from the least-squares plane = 0.060(1)Ang. for the amide O atom], the molecules form discrete centrosymmetric dimers through intermolecular cyclic carboxy-carboxy O-H...O hydrogen-bonding interactions [graph set notation R2/2(8)]. The cyclic imides (II)--(IV) are conformationally similar, with comparable phenyl ring rotations about the imide N-C(aromatic) bond [dihedral angles between the benzene and isoindole rings = 51.55(7)deg. in (II), 59.22(12)deg. in (III) and 51.99(14)deg. in (IV). Unlike (II) in which only weak intermolecular C-H...O(imide) hydrogen bonding is present, the crystal packing of imides (III) and (IV) shows strong intermolecular carboxylic acid O-H...O hydrogen-bonding associations. With (III), these involve imide O-atom acceptors, giving one-dimensional zigzag chains [graph set C(9)], while with the monohydrate (IV), the hydrogen bond involves the partially disordered water molecule which also bridges molecules through both imide and carboxyl O-atom acceptors in a cyclic R4/4(12) association, giving a two-dimensional sheet structure. The structures reported here expand the structural data base for compounds of this series formed from the facile reaction of cis-cyclohexane-1,2-dicarboxylic anhydride with substituted anilines, in which there is a much larger incidence of cyclic imides compared to amide carboxylic acids.

Two-dimensional coordination polymers in rubidium and caesium complexes with orthanilic acid

The crystal structures of the rubidium and caesium complexes with 2-aminobenzenesulfonic acid (orthanilic acid), [Rb4(C6H6NO3S)4(H2O)]n (1) and [Cs(C6H6NO3S)]n (2) and have been determined at 200 K. Complex 1 has a repeating unit comprising four independent and different Rb coordination centres, (RbO8), (RbO7), (RbN2O4) and (RbO10), each having irregular stereochemistry and involving a number of bidentate chelate sulfonate-O,O’-metal and bridging interactions, giving a two-dimensional polymeric layered structure. Anhydrous complex 2 is also polymeric with the irregular (CsO7) coordination polyhedron comprising six sulfonate oxygen donors from three separate bidentate chelate sulfonate ligands and one monodentate bridging sulfonate oxygen, giving a two-dimensional layered structure.

Combination of MEK-ERK inhibitor and hyaluronic acid has a synergistic effect on anti-hypertrophic and pro-chondrogenic activities in osteoarthritis treatment

We hypothesised that a potentially disease-modifying osteoarthritis (OA) drug such as hyaluronic acid (HA) given in combination with anti-inflammatory signalling agents such as mitogen-activated protein kinase kinase–extracellular signal-regulated kinase (MEK-ERK) signalling inhibitor (U0126) could result in additive or synergistic effects on preventing the degeneration of articular cartilage. Chondrocyte differentiation and hypertrophy were evaluated using human OA primary cells treated with either HA or U0126, or the combination of HA + U0126. Cartilage degeneration in menisectomy (MSX) induced rat OA model was investigated by intra-articular delivery of either HA or U0126, or the combination of HA + U0126. Histology, immunostaining, RT-qPCR, Western blotting and zymography were performed to assess the expression of cartilage matrix proteins and hypertrophic markers. Phosphorylated ERK (pERK)1/2-positive chondrocytes were significantly higher in OA samples compared with those in healthy control suggesting the pathological role of that pathway in OA. It was noted that HA + U0126 significantly reduced the levels of pERK, chondrocyte hypertrophic markers (COL10 and RUNX2) and degenerative markers (ADAMTs5 and MMP-13), however, increased the levels of chondrogenic markers (COL2) compared to untreated or the application of HA or U0126 alone. In agreement with the results in vitro, intra-articular delivery of HA + U0126 showed significant therapeutic improvement of cartilage in rat MSX OA model compared with untreated or the application of HA or U0126 alone. Our study suggests that the combination of HA and MEK-ERK inhibition has a synergistic effect on preventing cartilage degeneration.

Cyclic Imide and Open-Chain Amide Carboxylic Acid Derivatives from the Facile Reaction of cis-Cyclohexane-1,2-dicarboxylic Anhydride with Three Substituted Anilines

The structures of the compounds from the reaction of cis-cyclohexane-1,2-dicarboxylic anhydride with 4-chloroaniline [rac-N-(4-chlorophenyl)-2-carboxycycloclohexane-1-carboxamide] (1), 4-bromoaniline [2-(4-bromophenyl)-perhydroisoindolyl-1,3-dione] (2) and 3-hydroxy-4-carboxyaniline (5-aminosalicylic acid) [2-(3-hydroxy-4-carboxyphenyl)-perhydroisoindolyl-1,3-dione] (3) have been determined at 200 K. Crystals of the open-chain amide carboxylic acid 1 are orthorhombic, space group Pbcn, with unit cell dimensions a = 20.1753(10), b = 8.6267(4), c = 15.9940(9) Å, and Z = 8. Compounds 2 and 3 are cyclic imides, with 1 monoclinic having space group P21 and cell dimensions a = 11.5321(3), b = 6.7095(2), c = 17.2040(5) Å, β = 102.527(3)o. Compound 3 is orthorhombic with cell dimensions a = 6.4642(3), b = 12.8196(5), c = 16.4197(7) Å. Molecules of 1 form hydrogen-bonded cyclic dimers which are extended into a two-dimensional layered structure through amide-group associations: 3 forms into one-dimensional zigzag chains through carboxylic acid…imide O-atom hydrogen bonds, while compound 2 is essentially unassociated. With both cyclic imides 2 and 3, disorder is found which involves the presence of partial enantiomeric replacement of the cis-cyclohexane-1,2-substituted ring systems.

A novel cyclization product from the polyphosphoric acid catalyzed addition of propanal to limonene

The polyphosphoric acid catalyzed addition of propanal to limonene yielded a novel bicyclic ether 2,2,6-trimethyl-4-ethyl-3-oxabicyclo[3.3.1]non-6-ene (I). The yield of (I) was significantly increased by carrying out the reaction under nitrogen rather than in air.

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.

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.

Fresh water and acid sensitivity of authigenic clays in sandstone reservoirs

Authigenic illite-smectite and chlorite in reservoir sandstones from several Pacific rim sedimentary basins in Australia and New Zealand have been examined using an Electroscan Environmental Scanning Electron Microscope (ESEM) before, during, and after treatment with fresh water and HCl, respectively. These dynamic experiments are possible in the ESEM because, unlike conventional SEMs that require a high vacuum in the sample chamber (10-6 torr), the ESEM will operate at high pressures up to 20 torr. This means that materials and processes can be examined at high magnifications in their natural states, wet or dry, and over a range of temperatures (-20 to 1000 degrees C) and pressures. Sandstones containing the illite-smectite (60-70% illite interlayers) were flushed with fresh water for periods of up to 12 hours. Close examination of the same illite-smectite lines or filled pores, both before and after freshwater treatments, showed that the morphology of the illite-smectite was not changed by prolonged freshwater treatment. Chlorite-bearing sandstones (Fe-rich chlorite) were reacted with 1M to 10M HCl at temperatures of up to 80 degrees C and for periods of up to 48 hours. Before treatment the chlorites showed typically platy morphologies. After HCl treatment the chlorite grains were coated with an amorphous gel composed of Ca, Cl, and possibly amorphous Si, as determined by EDS analyses on the freshly treated rock surface. Brief washing in water removed this surface coating and revealed apparently unchanged chlorite showing no signs of dissolution or acid attack. However, although the chlorite showed no morphological changes, elemental analysis only detected silicon and oxygen.

Natural improvements of geochemical conditions of acid sulfate soils caused by free tidal inundation and its effects on the mangrove seedlings

Acid sulfate soils (ASS) are one of the stressor factors that cause many mangrove restoration projects to fail. Achieving successful rehabilitation in an ASS affected area requires an understanding of the geochemical conditions that influence the establishment and growth of mangrove seedlings. This study evaluated the effect of tidal inundation on geochemical conditions on sub layer to better understand their impacts on the density, establishment, and growth of mangrove seedlings. This study also examined the geochemical conditions under which mangrove seedlings can establish naturally, and/or be replanted in abandoned aquaculture ponds. The study area was in an area of abandoned aquaculture ponds situated in the Mare District, adjacent to Bone Bay, South Sulawesi, Indonesia.The pH, pHfox, redox potential, organic content, water soluble sulfate, SKCl, SPOS, and grain size of the soil from the sediment core at + 10 - 15 cm depth near roots were measured using. Pyrite analysis were conducted for the top and sub sediments. The density, establishment, and the relative root growth of Rhizophoraceae were also determined. Free tidal inundation at abandoned pond sites improved the sediment quality. The high density, establishment, and growth of mangrove seedlings were characterized by freely drained areas with a higher pH (field and oxidisable), lower organic content, and high proportion of silt/clay. Higher density and growth also correlated to reduced environments. Sulfur species did not influence the density, establishment, and growth of the seedlings directly. The supply of propagules from the mangrove stands, or access from good waterways were also important for seedlings to establish naturally.

Elevated uric acid correlates with wound severity

Chronic venous leg ulcers are a major health issue and represent an often overlooked area of biomedical research. Nevertheless, it is becoming increasingly evident that new approaches to enhance healing outcomes may arise through better understanding the processes involved in the formation of chronic wounds. We have for the first time shown that the terminal purine catabolite uric acid (UA) is elevated in wound fluid (WF) from chronic venous leg ulcers with relative concentrations correlating with wound chronicity. We have also shown a corresponding depletion in UA precursors, including adenosine, with increased wound severity. Further, we have shown that xanthine oxidase, the only enzyme in humans that catalyses the production of UA in conjunction with a burst of free radicals, is active in chronic WF. Taken together, this provides compelling evidence that xanthine oxidase may play a critical role in the formation of chronic wounds by prolonging the inflammatory process.

4-Amino-N-(4,6-dimethylpyrimidin-2-yl)benzenesulfonamide--2-nitrobenzoic acid (1/1)

In the asymmetric unit of the title co-crystal, C12H14N4O2S·C7H5NO4, the sulfamethazine and 2-nitrobenzoic acid molecules form a heterodimer through intermolecular amide-carboxylic acid N-HO and carboxylic acid-pyrimidine O-HN hydrogen-bond pairs, giving a cyclic motif [graph set R22(8)]. The dihedral angle between the two aromatic ring systems in the sulfamethazine molecule is 88.96 (18)° and the nitro group of the acid is 50% rotationally disordered. Secondary aniline N-HOsulfone hydrogen-bonding associations give a two-dimensional structure lying parallel to the ab plane.