Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

Barriers to information transfer for multi-trauma patients upon discharge from the Emergency Department in a tertiary level hospital

Purpose: Communication is integral to effective trauma care provision. This presentation will report on barriers to meaningful information transfer for multi-trauma patients upon discharge from the Emergency Department (ED) to the care areas of Intensive Care Unit, High Dependency Unit, and Perioperative Services. This is an ongoing study at one tertiary level hospital in Queensland. Method: This is a multi-phase, mixed method study. In Phase 1 data were collected about information transfer. This Phase was initially informed by a comprehensive literature review, then via focus groups, chart audit, staff survey and review of national and international trauma forms. Results: The barriers identified related to nursing handover, documented information, time inefficiency, patient complexity and stability and time of transfer. Specifically this included differences in staff expectations and variation in the nursing handover processes, no agreed minimum dataset of information handed over, missing, illegible or difficult to find information in documentation (both medical and nursing), low compliance with some forms used for documentation. Handover of these patients is complex with information coming from many sources, dealing with issues is more difficult for these patients when transferred out of hours. Conclusions and further directions: This study investigated the current communication processes and standards of information transfer to identify barriers and issues. The barriers identified were the structure used for documentation, processes used (e.g. handover), patient acuity and time. This information is informing the development, implementation and evaluation of strategies to ameliorate the issues identified.

Technology transfer evaluation in the high technology industry : an interdisciplinary perspective

The underlying objective of this study was to develop a novel approach to evaluate the potential for commercialisation of a new technology. More specifically, this study examined the 'ex-ante'. evaluation of the technology transfer process. For this purpose, a technology originating from the high technology sector was used. The technology relates to the application of software for the detection of weak signals from space, which is an established method of signal processing in the field of radio astronomy. This technology has the potential to be used in commercial and industrial areas other than astronomy, such as detecting water leakages in pipes. Its applicability to detecting water leakage was chosen owing to several problems with detection in the industry as well as the impact it can have on saving water in the environment. This study, therefore, will demonstrate the importance of interdisciplinary technology transfer. The study employed both technical and business evaluation methods including laboratory experiments and the Delphi technique to address the research questions. There are several findings from this study. Firstly, scientific experiments were conducted and these resulted in a proof of concept stage of the chosen technology. Secondly, validation as well as refinement of criteria from literature that can be used for „ex-ante. evaluation of technology transfer has been undertaken. Additionally, after testing the chosen technology.s overall transfer potential using the modified set of criteria, it was found that the technology is still in its early stages and will require further development for it to be commercialised. Furthermore, a final evaluation framework was developed encompassing all the criteria found to be important. This framework can help in assessing the overall readiness of the technology for transfer as well as in recommending a viable mechanism for commercialisation. On the whole, the commercial potential of the chosen technology was tested through expert opinion, thereby focusing on the impact of a new technology and the feasibility of alternate applications and potential future applications.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Pedigree-free animal models : the relatedness matrix reloaded

Animal models typically require a known genetic pedigree to estimate quantitative genetic parameters. Here we test whether animal models can alternatively be based on estimates of relatedness derived entirely from molecular marker data. Our case study is the morphology of a wild bird population, for which we report estimates of the genetic variance-covariance matrices (G) of six morphological traits using three methods: the traditional animal model; a molecular marker-based approach to estimate heritability based on Ritland's pairwise regression method; and a new approach using a molecular genealogy arranged in a relatedness matrix (R) to replace the pedigree in an animal model. Using the traditional animal model, we found significant genetic variance for all six traits and positive genetic covariance among traits. The pairwise regression method did not return reliable estimates of quantitative genetic parameters in this population, with estimates of genetic variance and covariance typically being very small or negative. In contrast, we found mixed evidence for the use of the pedigree-free animal model. Similar to the pairwise regression method, the pedigree-free approach performed poorly when the full-rank R matrix based on the molecular genealogy was employed. However, performance improved substantially when we reduced the dimensionality of the R matrix in order to maximize the signal to noise ratio. Using reduced-rank R matrices generated estimates of genetic variance that were much closer to those from the traditional model. Nevertheless, this method was less reliable at estimating covariances, which were often estimated to be negative. Taken together, these results suggest that pedigree-free animal models can recover quantitative genetic information, although the signal remains relatively weak. It remains to be determined whether this problem can be overcome by the use of a more powerful battery of molecular markers and improved methods for reconstructing genealogies.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

Performance assessment of exponential Rosenbrock method for large systems of ODE

This paper studies time integration methods for large stiff systems of ordinary differential equations (ODEs) of the form u'(t) = g(u(t)). For such problems, implicit methods generally outperform explicit methods, since the time step is usually less restricted by stability constraints. Recently, however, explicit so-called exponential integrators have become popular for stiff problems due to their favourable stability properties. These methods use matrix-vector products involving exponential-like functions of the Jacobian matrix, which can be approximated using Krylov subspace methods that require only matrix-vector products with the Jacobian. In this paper, we implement exponential integrators of second, third and fourth order and demonstrate that they are competitive with well-established approaches based on the backward differentiation formulas and a preconditioned Newton-Krylov solution strategy.

Using patterns co-occurrence matrix for cleaning closed sequential patterns for text mining

With the overwhelming increase in the amount of texts on the web, it is almost impossible for people to keep abreast of up-to-date information. Text mining is a process by which interesting information is derived from text through the discovery of patterns and trends. Text mining algorithms are used to guarantee the quality of extracted knowledge. However, the extracted patterns using text or data mining algorithms or methods leads to noisy patterns and inconsistency. Thus, different challenges arise, such as the question of how to understand these patterns, whether the model that has been used is suitable, and if all the patterns that have been extracted are relevant. Furthermore, the research raises the question of how to give a correct weight to the extracted knowledge. To address these issues, this paper presents a text post-processing method, which uses a pattern co-occurrence matrix to find the relation between extracted patterns in order to reduce noisy patterns. The main objective of this paper is not only reducing the number of closed sequential patterns, but also improving the performance of pattern mining as well. The experimental results on Reuters Corpus Volume 1 data collection and TREC filtering topics show that the proposed method is promising.

Hybrid graphene and graphitic carbon nitride nanocomposite : gap opening, electron–hole puddle, interfacial charge transfer, and enhanced visible light response

Opening up a band gap and finding a suitable substrate material are two big challenges for building graphene-based nanodevices. Using state-of-the-art hybrid density functional theory incorporating long range dispersion corrections, we investigate the interface between optically active graphitic carbon nitride (g-C3N4) and electronically active graphene. We find an inhomogeneous planar substrate (g-C3N4) promotes electronrich and hole-rich regions, i.e., forming a well-defined electron−hole puddle, on the supported graphene layer. The composite displays significant charge transfer from graphene to the g-C3N4 substrate, which alters the electronic properties of both components. In particular, the strong electronic coupling at the graphene/g-C3N4 interface opens a 70 meV gap in g-C3N4-supported graphene, a feature that can potentially allow overcoming the graphene’s band gap hurdle in constructing field effect transistors. Additionally, the 2-D planar structure of g-C3N4 is free of dangling bonds, providing an ideal substrate for graphene to sit on. Furthermore, when compared to a pure g-C3N4 monolayer, the hybrid graphene/g-C3N4 complex displays an enhanced optical absorption in the visible region, a promising feature for novel photovoltaic and photocatalytic applications.

Combined electrophoretic deposition–anodization method to fabricate reduced graphene oxide–TiO2 nanotube films

We directly constructed reduced graphene oxide–titanium oxide nanotube (RGO–TNT) film using a single-step, combined electrophoretic deposition–anodization (CEPDA) method. This method, based on the simultaneous anodic growth of tubular TiO2 and the electrophoretic-driven motion of RGO, allowed the formation of an effective interface between the two components, thus improving the electron transfer kinetics. Composites of these graphitic carbons with different levels of oxygen-containing groups, electron conductivity and interface reaction time were investigated; a fine balance of these parameters was achieved.

Heat and mass transfer modeling of the osmo-convective drying of yacon roots (Smallanthus sonchifolius)

Osmotic treatments are often applied prior to convective drying of foods to impart sensory appeal aspects. During this process a multicomponent mass flow, composed mainly of water and osmotic agent, takes place. In this work, a heat and mass transfer model for the osmo-convective drying of yacon was developed and solved by the Finite Element Method using COMSOL Multiphysics®, considering a 2-D axisymmetric geometry and moisture dependent thermophysical properties. Yacon slices were osmotically dehydrated for 2 hours in a solution of sucralose and then dried in a tray dryer for 3 hours. The model was validated by experimental data of temperature, moisture content and sucralose uptake (R²> 0.90).

Preparation of metal-TCNQ charge-transfer complexes on conducting and insulating surfaces by photocrystallization

A generic method for the synthesis of metal-7,7,8,8-tetracyanoquinodimethane (TCNQ) charge-transfer complexes on both conducting and nonconducting substrates is achieved by photoexcitation of TCNQ in acetonitrile in the presence of a sacrificial electron donor and the relevant metal cation. The photochemical reaction leads to reduction of TCNQ to the TCNQ- monoanion. In the presence of Mx+(MeCN), reaction with TCNQ-(MeCN) leads to deposition of Mx+[TCNQ]x crystals onto a solid substrate with morphologies that are dependent on the metal cation. Thus, CuTCNQ phase I photocrystallizes as uniform microrods, KTCNQ as microrods with a random size distribution, AgTCNQ as very long nanowires up to 30 μm in length and with diameters of less than 180 nm, and Co[TCNQ]2(H2O)2 as nanorods and wires. The described charge-transfer complexes have been characterized by optical and scanning electron microscopy and IR and Raman spectroscopy. The CuTCNQ and AgTCNQ complexes are of particular interest for use in memory storage and switching devices. In principle, this simple technique can be employed to generate all classes of metal−TCNQ complexes and opens up the possibility to pattern them in a controlled manner on any type of substrate.

Method of making metal oxides

A method for producing particles having at least regions of at least one metal oxide having nano-sized grains comprises providing particles of material having an initial, non-equiaxed particle shape, making a mixture of the particles of material and one or more precursors of the metal oxide, and treating the mixture such that the one or more precursors of the metal oxide react with the particles of material to thereby form at least regions of metal oxide on or within the particles, wherein atoms from the particles of material form part of a matrix of the at least one metal oxide and the at least one metal oxide has nano-sized grains and wherein at least some of the regions of metal oxide on or within the particles have a non-equiaxed grain shape.

Method for making a material, particularly for emission control catalyst

A method for forming a material comprising a metal oxide supported on a support particle comprising the steps of: (a) providing a precursor mixt. comprising a soln. contg. one or more metal cations and (i) a surfactant; or (ii) a hydrophilic polymer; said precursor mixt. further including support particles; and (b) treating the precursor mixt. from (a) above by heating to remove the surfactant or hydrophilic polymer and form metal oxide having nanosized grains, wherein at least some of the metal oxide formed in step (b) is deposited on or supported by the support particles and the metal oxide has an oxide matrix that includes metal atoms derived solely from sources other than the support particles. The disclosure and examples pertain to emission control catalysts. [on SciFinder(R)]