Numerical simulation of anomalous infiltration in porous media

Nonlinear time-fractional diffusion equations have been used to describe the liquid infiltration for both subdiffusion and superdiffusion in porous media. In this paper, some problems of anomalous infiltration with a variable-order timefractional derivative in porous media are considered. The time-fractional Boussinesq equation is also considered. Two computationally efficient implicit numerical schemes for the diffusion and wave-diffusion equations are proposed. Numerical examples are provided to show that the numerical methods are computationally efficient.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

Book Review: "Metal Rules the Globe: Heavy Metal Music around the World". Durham, NC: Duke University Press.

It is rare to find an anthology that realizes the possibilities of the form. We tend to regard our edited collections as lesser siblings, and forget their special value. But at times, a subject seems to require an edited collection much more than it does a classic monograph. So it is with the subject showcased here, which concerns the global circulation, performance and consumption of heavy metal. This is a relatively new and emerging body of work, hitherto scattered disparately in the broader popular music studies, but quickly gaining status as a “studies” with the establishment of a global conference, a journal, and publication of this anthology, all in recent years. Metal Rules the Globe took the editors’ a decade to compile. That they have thought deeply about how they want the collection to speak shows through in the book’s thoughtful arrangement and design, and in the way in which they draw on the contributions herein to develop for the field a research agenda that will take it forward...

Autonomous hot metal carrier

This paper reports work involved with the automation of a Hot Metal Carrier — a 20 tonne forklift-type vehicle used to move molten metal in aluminium smelters. To achieve efficient vehicle operation, issues of autonomous navigation and materials handling must be addressed. We present our complete system and experiments demontrating reliable operation. One of the most significant experiments was five-hours of continuous operation where the vehicle travelled over 8 km and conducted 60 load handling operations. We also describe an experiment where the vehicle and autonomous operation were supervised from the other side of the world via a satellite phone network.

Liquid Business Process Model Collections

Many organizations realize that increasing amounts of data (“Big Data”) need to be dealt with intelligently in order to compete with other organizations in terms of efficiency, speed and services. The goal is not to collect as much data as possible, but to turn event data into valuable insights that can be used to improve business processes. However, data-oriented analysis approaches fail to relate event data to process models. At the same time, large organizations are generating piles of process models that are disconnected from the real processes and information systems. In this chapter we propose to manage large collections of process models and event data in an integrated manner. Observed and modeled behavior need to be continuously compared and aligned. This results in a “liquid” business process model collection, i.e. a collection of process models that is in sync with the actual organizational behavior. The collection should self-adapt to evolving organizational behavior and incorporate relevant execution data (e.g. process performance and resource utilization) extracted from the logs, thereby allowing insightful reports to be produced from factual organizational data.

Transition metal layered double hydroxides for energy storage

Various types of layered double hydroxides, a type of clay, were synthesised. They were then electrochemically tested to determine whether the samples would be suitable to store energy as supercapacitors. A manganese aluminium layered double hydroxide was electrochemically tested for the first time and found to have a large capacitance.

Oral liquid nutritional supplements for people with dementia in residential aged care facilities

AIM: This systematic review investigated the prescription, administration and effectiveness of oral liquid nutritional supplements (OLNS) for people with dementia in residential aged care facilities (RACF). METHODS: A comprehensive search of relevant databases, hand searching and cross-referencing found 15 relevant articles from a total of 2910 possible results. Articles which met the inclusion criteria were critically appraised by two independent reviewers using the relevant Joanna Briggs Institute (JBI) appraisal checklist. Data were extracted using the relevant JBI extraction instruments. No data synthesis was possible due to clinical and methodological heterogeneity. RESULTS: Included studies examined a range of strategies, issues and results related to OLNS for persons with dementia in RACFs; however there appear to be significant gaps in the current body of research, particularly in relation to examinations of effectiveness. CONCLUSIONS: This review was unable to produce a definitive finding regarding effectiveness. OLNS may improve the nutritional state of residents with dementia and help prevent weight loss, and there is some suggestion that it may slow the rate of cognitive decline. However, in order for OLNS to be effective, nursing and care staff need to ensure that sufficient attention is paid to the issues of prescription and administration.

The structures of the isomorphous potassium and rubidium salts of 4-nitrobenzoic acid and an overview of the metal complex stereochemistries of the alkali metal salt series with this ligand

The structures of the isomorphous potassium and rubidium polymeric coordination complexes with 4-nitrobenzoic acid, poly[mu2-aqua-aqua-mu3-(4-nitrobenzoato)-potassium], [K(C7H4N2O2)(H2O)2]n, (I) and poly[mu3-aqua-aqua-mu5-(4-nitrobenzoato)-rubidium], [Rb(C7H4N2O2)(H2O)2]n, (II) have been determined. In (I) the very distorted KO6 coordination sphere about the K+ centres in the repeat unit comprise two bridging nitro O-atom donors, a single bridging carboxyl O-atom donor and two water molecules, one of which is bridging. In the the Rb complex (II), the same basic MO6 coordination is found in the repeat unit but is expanded to RbO9 through a slight increase in the accepted Rb-O bond length range and includes an additional Rb-O(carboxyl) bond, completing a bidentate O,O'-chelate interaction, and additional bridging Rb-Onitro) and Rb-O(water) bonds. The comparative K-O and Rb-O bond length ranges are 2.738(3)-3.002(3)Ang. (I) and 2.884(2)-3.182(2)Ang. (II). The structure of (II) is also isomorphous as well as isostructural with the known structure of the nine-coordinate caesium 4-nitrobenzoate analogue, [Cs(C7H4N2O~2~)(H~2~O)2]n, (III) in which the Cs---O range is 3.047(4)-3.338(4)Ang. In all three complexes, common basic polymeric extensions are found, including two different centrosymmetric bridging interactions through both water and nitro groups as well as extensions along c through the p-related carboxyl group, giving a two-dimensional structure in (I). In (II) and (III), three-dimensional structures are generated through additional bridges through the nitro and water O-atoms. In all structures, both water molecules are involved in similar intra-polymer O-H...O hydrogen-bonding interactions to both carboxyl as well as water O-atom acceptors. A comparison of the varied coordination behaviour of the full set of Li-Cs salts with 4-nitrobenzoic acid is also made.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

Modelling intermittent microwave convective drying (IMCD) of food materials

This thesis develops comprehensive mathematical models for an advanced drying technology Intermittent Microwave Convective Drying (IMCD). The models provide an improved physical understanding of the heat and mass transport during the drying process, which will help to improve the quality of dried food and energy efficiency of the process, as well as will increase the ability of automation and optimization. The final model in this thesis represents the most comprehensive fundamental multiphase model for IMCD that considers 3D electromagnetics coupled with multiphase porous media transport processes. The 3D electromagnetics considers Maxwell's equation and multiphase transport model considers three different phases: solid matrix, liquid water and gas consisting water vapour and air. The multiphase transport includes pressure-driven flow, capillary diffusion, binary diffusion, and evaporation. The models developed in this thesis were validated with extensive experimental investigations.

Extending genetic linkage analysis to diffusion tensor images to map single gene effects on brain fiber architecture

We extended genetic linkage analysis - an analysis widely used in quantitative genetics - to 3D images to analyze single gene effects on brain fiber architecture. We collected 4 Tesla diffusion tensor images (DTI) and genotype data from 258 healthy adult twins and their non-twin siblings. After high-dimensional fluid registration, at each voxel we estimated the genetic linkage between the single nucleotide polymorphism (SNP), Val66Met (dbSNP number rs6265), of the BDNF gene (brain-derived neurotrophic factor) with fractional anisotropy (FA) derived from each subject's DTI scan, by fitting structural equation models (SEM) from quantitative genetics. We also examined how image filtering affects the effect sizes for genetic linkage by examining how the overall significance of voxelwise effects varied with respect to full width at half maximum (FWHM) of the Gaussian smoothing applied to the FA images. Raw FA maps with no smoothing yielded the greatest sensitivity to detect gene effects, when corrected for multiple comparisons using the false discovery rate (FDR) procedure. The BDNF polymorphism significantly contributed to the variation in FA in the posterior cingulate gyrus, where it accounted for around 90-95% of the total variance in FA. Our study generated the first maps to visualize the effect of the BDNF gene on brain fiber integrity, suggesting that common genetic variants may strongly determine white matter integrity.

Brain fiber architecture, genetics, and intelligence: a high angular resolution diffusion imaging (HARDI) study

We developed an analysis pipeline enabling population studies of HARDI data, and applied it to map genetic influences on fiber architecture in 90 twin subjects. We applied tensor-driven 3D fluid registration to HARDI, resampling the spherical fiber orientation distribution functions (ODFs) in appropriate Riemannian manifolds, after ODF regularization and sharpening. Fitting structural equation models (SEM) from quantitative genetics, we evaluated genetic influences on the Jensen-Shannon divergence (JSD), a novel measure of fiber spatial coherence, and on the generalized fiber anisotropy (GFA) a measure of fiber integrity. With random-effects regression, we mapped regions where diffusion profiles were highly correlated with subjects' intelligence quotient (IQ). Fiber complexity was predominantly under genetic control, and higher in more highly anisotropic regions; the proportion of genetic versus environmental control varied spatially. Our methods show promise for discovering genes affecting fiber connectivity in the brain.

Mapping genetic influences on brain fiber architecture with high angular resolution diffusion imaging (HARDI)

We report the first 3D maps of genetic effects on brain fiber complexity. We analyzed HARDI brain imaging data from 90 young adult twins using an information-theoretic measure, the Jensen-Shannon divergence (JSD), to gauge the regional complexity of the white matter fiber orientation distribution functions (ODF). HARDI data were fluidly registered using Karcher means and ODF square-roots for interpol ation; each subject's JSD map was computed from the spatial coherence of the ODFs in each voxel's neighborhood. We evaluated the genetic influences on generalized fiber anisotropy (GFA) and complexity (JSD) using structural equation models (SEM). At each voxel, genetic and environmental components of data variation were estimated, and their goodness of fit tested by permutation. Color-coded maps revealed that the optimal models varied for different brain regions. Fiber complexity was predominantly under genetic control, and was higher in more highly anisotropic regions. These methods show promise for discovering factors affecting fiber connectivity in the brain.

Fluid registration of diffusion tensor images using information theory

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or $J$-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the $J$-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.