A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Metallic and Carbon Nanotube-Catalyzed Coupling of Hydrogenation in Magnesium

Synergistic effect of metallic couple and carbon nanotubes on Mg results in an ultrafast kinetics of hydrogenation that overcome a critical barrier of practical use of Mg as hydrogen storage materials. The ultrafast kinetics is attributed to the metal−H atomic interaction at the Mg surface and in the bulk (energy for bonding and releasing) and atomic hydrogen diffusion along the grain boundaries (aggregation of carbon nanotubes) and inside the grains. Hence, a hydrogenation mechanism is presented.

Hydrogen spillover mechanism on a pd-doped mg surface as revealed by ab initio density functional calculation

The hydrogenation kinetics of Mg is slow, impeding its application for mobile hydrogen storage. We demonstrate by ab initio density functional theory (DFT) calculations that the reaction path can be greatly modified by adding transition metal catalysts. Contrasting with Ti doping, a Pd dopant will result in a very small activation barrier for both dissociation of molecular hydrogen and diffusion of atomic H on the Mg surface. This new computational finding supports for the first time by ab initio simulationthe proposed hydrogen spillover mechanism for rationalizing experimentally observed fast hydrogenation kinetics for Pd-capped Mg materials.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

Deformation with coupled chemical diffusion

The deformation of rocks is commonly intimately associated with metamorphic reactions. This paper is a step towards understanding the behaviour of fully coupled, deforming, chemically reacting systems by considering a simple example of the problem comprising a single layer system with elastic-power law viscous constitutive behaviour where the deformation is controlled by the diffusion of a single chemical component that is produced during a metamorphic reaction. Analysis of the problem using the principles of non-equilibrium thermodynamics allows the energy dissipated by the chemical reaction-diffusion processes to be coupled with the energy dissipated during deformation of the layers. This leads to strain-rate softening behaviour and the resultant development of localised deformation which in turn nucleates buckles in the layer. All such diffusion processes, in leading to Herring-Nabarro, Coble or “pressure solution” behaviour, are capable of producing mechanical weakening through the development of a “chemical viscosity”, with the potential for instability in the deformation. For geologically realistic strain rates these chemical feed-back instabilities occur at the centimetre to micron scales, and so produce structures at these scales, as opposed to thermal feed-back instabilities that become important at the 100–1000 m scales.

Mathematical modelling of controlled drug release from polymer micro-spheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems

Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion. In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research. The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting. The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.

Hydrogen bonding in two ammonium salts of 5-sulfosalicylic acid : ammonium 3-carboxy-4-hydroxybenzenesulfonate monohydrate and triammonium 3-carboxy-4-hydroxybenzenesulfonate 3-carboxylato-4-hydroxybenzenesulfonate

The structures of two ammonium salts of 3-carboxy-4-hydroxybenzenesulfonic acid (5-sulfosalicylic acid, 5-SSA) have been determined at 200 K. In the 1:1 hydrated salt, ammonium 3-carboxy-4-hydroxybenzenesulfonate monohydrate, NH4+·C7H5O6S-·H2O, (I), the 5-SSA- monoanions give two types of head-to-tail laterally linked cyclic hydrogen-bonding associations, both with graph-set R44(20). The first involves both carboxylic acid O-HOwater and water O-HOsulfonate hydrogen bonds at one end, and ammonium N-HOsulfonate and N-HOcarboxy hydrogen bonds at the other. The second association is centrosymmetric, with end linkages through water O-HOsulfonate hydrogen bonds. These conjoined units form stacks down c and are extended into a three-dimensional framework structure through N-HO and water O-HO hydrogen bonds to sulfonate O-atom acceptors. Anhydrous triammonium 3-carboxy-4-hydroxybenzenesulfonate 3-carboxylato-4-hydroxybenzenesulfonate, 3NH4+·C7H4O6S2-·C7H5O6S-, (II), is unusual, having both dianionic 5-SSA2- and monoanionic 5-SSA- species. These are linked by a carboxylic acid O-HO hydrogen bond and, together with the three ammonium cations (two on general sites and the third comprising two independent half-cations lying on crystallographic twofold rotation axes), give a pseudo-centrosymmetric asymmetric unit. Cation-anion hydrogen bonding within this layered unit involves a cyclic R33(8) association which, together with extensive peripheral N-HO hydrogen bonding involving both sulfonate and carboxy/carboxylate acceptors, gives a three-dimensional framework structure. This work further demonstrates the utility of the 5-SSA- monoanion for the generation of stable hydrogen-bonded crystalline materials, and provides the structure of a dianionic 5-SSA2- species of which there are only a few examples in the crystallographic literature.

Proton-transfer compounds with 4-amino-N-(4,6-dimethylpyrimidin-2-yl)benzenesulfonamide (sulfamethazine): the structures and hydrogen-bonding in the salts with 5-nitrosalicylic acid and picric acid

The structures of the anhydrous proton-transfer compounds of the sulfa drug sulfamethazine with 5-nitrosalicylic acid and picric acid, namely 2-(4-aminobenzenesulfonamido)-4,6-dimethylpyrimidinium 2-hydroxy-5-nitrobenzoate, C12H15N4O2S(+)·C7H4NO4(-), (I), and 2-(4-aminobenzenesulfonamido)-4,6-dimethylpyrimidinium 2,4,6-trinitrophenolate, C12H15N4O2S(+)·C6H2N3O7(-), (II), respectively, have been determined. In the asymmetric unit of (I), there are two independent but conformationally similar cation-anion heterodimer pairs which are formed through duplex intermolecular N(+)-H...Ocarboxylate and N-H...Ocarboxylate hydrogen-bond pairs, giving a cyclic motif [graph set R2(2)(8)]. These heterodimers form separate and different non-associated substructures through aniline N-H...O hydrogen bonds, one one-dimensional, involving carboxylate O-atom acceptors, the other two-dimensional, involving both carboxylate and hydroxy O-atom acceptors. The overall two-dimensional structure is stabilized by π-π interactions between the pyrimidinium ring and the 5-nitrosalicylate ring in both heterodimers [minimum ring-centroid separation = 3.4580 (8) Å]. For picrate (II), the cation-anion interaction involves a slightly asymmetric chelating N-H...O R2(1)(6) hydrogen-bonding association with the phenolate O atom, together with peripheral conjoint R1(2)(6) interactions between the same N-H groups and O atoms of the ortho-related nitro groups. An inter-unit amine N-H...Osulfone hydrogen bond gives one-dimensional chains which extend along a and inter-associate through π-π interactions between the pyrimidinium rings [centroid-centroid separation = 3.4752 (9) Å]. The two structures reported here now bring to a total of four the crystallographically characterized examples of proton-transfer salts of sulfamethazine with strong organic acids.

Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions...

Influence of drying conditions on the moisture diffusion during single stage and two stage fluidized bed drying of bovine intestine for pet food

Bovine intestine samples were heat pump fluidized bed dried at atmospheric pressure and at temperatures below and above the material freezing points equipped with a continuous monitoring system. The investigation of the drying characteristics has been conducted in the temperature range -10~25oC and the airflow in the range 1.5~2.5 m/s. Some experiments were conducted as a single temperature drying experiments and others as two stage drying experiments employing two temperatures. An Arrhenius-type equation was used to interpret the influence of the drying air parameters on the effective diffusivity, calculated with the method of slopes in terms of energy activation, and this was found to be sensitivity of the temperature. The effective diffusion coefficient of moisture transfer was determined by Fickian method using uni-dimensional moisture movement in both moisture, removal by evaporation and combined sublimation and evaporation. Correlations expressing the effective moisture diffusivity and drying temperature are reported.

Adsorption of heavy metals by road deposited solids

The research study discussed in the paper investigated the adsorption/desorption behaviour of heavy metals commonly deposited on urban road surfaces, namely, Zn, Cu, Cr and Pb for different particle size ranges of solids. The study outcomes, based on field studies and batch experiments confirmed that road deposited solids particles contain a significantly high amount of vacant charge sites with the potential to adsorb additional heavy metals. Kinetic studies and adsorption experiments indicated that Cr is the most preferred metal element to associate with solids due to the relatively high electro negativity and high charge density of trivalent cation (Cr3+). However, the relatively low availability of Cr in the urban road environment could influence this behaviour. Comparing total adsorbed metals present in solids particles, it was found that Zn has the highest capacity for adsorption to solids. Desorption experiments confirmed that a low concentration of Cu, Cr and Pb in solids was present in water-soluble and exchangeable form, whilst a significant fraction of adsorbed Zn has a high likelihood of being released back into solution. Among heavy metals, Zn is considered to be the most commonly available metal among road surface pollutants.

First-principle studies of the formation and diffusion of hydrogen vacancies in magnesium hydride

Ab initio density functional theory (DFT) calculations are performed to study the formation and diffusion of hydrogen vacancies on MgH2(110) surface and in bulk. We find that the formation energies for a single H-vacancy increase slightly from the surface to deep layers. The energies for creating adjacent surface divancacies at two inplane sites and at an inplane and a bridge site are even smaller than that for the formation of a single H-vacancy, a fact that is attributed to the strong vacancy−vacancy interactions. The diffusion of an H-vacancy from an in-plane site to a bridge site on the surface has the smallest activation barrier calculated at 0.15 eV and should be fast at room temperature. The activation barriers computed for H-vacancy diffusion from the surface into sublayers are all less than 0.70 eV, which is much smaller than the activation energy for desorption of hydrogen on the MgH2(110) surface (1.78−2.80 eV/H2). This suggests that surface desorption is more likely than vacancy diffusion to be rate determining, such that finding effective catalyst on the MgH2 surface to facilitate desorption will be very important for improving overall dehydrogenation performance.

Atomic hydrogen diffusion in novel magnesium nanostructures : the impact of incorporated subsurface carbon atoms

Ab initio Density Functional Theory (DFT) calculations are performed to study the diffusion of atomic hydrogen on a Mg(0001) surface and their migration into the subsurface layers. A carbon atom located initially on a Mg(0001) surface can migrate into the sub-surface layer and occupy a fcc site, with charge transfer to the C atom from neighboring Mg atoms. The cluster of postively charged Mg atoms surrounding a sub-surface C is then shown to facilitate the dissociative chemisorption of molecular hydrogen on the Mg(0001) surface, and the surface migration and subsequent diffusion into the subsurface of atomic hydrogen. This helps rationalize the experimentally-observed improvement in absorption kinetics of H2 when graphite or single walled carbon nanotubes (SWCNT) are introduced into the Mg powder during ball milling.

Computer modeling of diffusion in biological tissues

Molecular-level computer simulations of restricted water diffusion can be used to develop models for relating diffusion tensor imaging measurements of anisotropic tissue to microstructural tissue characteristics. The diffusion tensors resulting from these simulations can then be analyzed in terms of their relationship to the structural anisotropy of the model used. As the translational motion of water molecules is essentially random, their dynamics can be effectively simulated using computers. In addition to modeling water dynamics and water-tissue interactions, the simulation software of the present study was developed to automatically generate collagen fiber networks from user-defined parameters. This flexibility provides the opportunity for further investigations of the relationship between the diffusion tensor of water and morphologically different models representing different anisotropic tissues.

A study of the diffusion characteristics of normal, delipidized and relipidized articular cartilage using magnetic resonance imaging

This paper assesses the capacity to provide semipermeability of the synthetic layer of surface-active phospholipids created to replace the depleted surface amorphous layer of articular cartilage. The surfaces of articular cartilage specimens in normal, delipidized, and relipidized conditions following incubation in dipalmitoyl-phosphatidylcholine and palmitoyl-oleoyl-phosphatidylcholine components of the joint lipid mixture were characterized nanoscopically with the atomic force microscope and also imaged as deuterium oxide (D2O) diffused transiently through these surfaces in a magnetic resonance imaging enclosure. The MR images were then used to determine the apparent diffusion coefficients in a purpose-built MATLAB®-based algorithm. Our results revealed that all surfaces were permeable to D2O, but that there was a significant difference in the semipermeability of the surfaces under the different conditions, relative to the apparent diffusion coefficients. Based on the results and observations, it can be concluded that the synthetic lipid that is deposited to replace the depleted SAL of articular cartilage is capable of inducing some level of semipermeability.