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.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Validation of a new hand-held electronic data capture method for continuous monitoring of subjective appetite sensations

Background When large scale trials are investigating the effects of interventions on appetite, it is paramount to efficiently monitor large amounts of human data. The original hand-held Electronic Appetite Ratings System (EARS) was designed to facilitate the administering and data management of visual analogue scales (VAS) of subjective appetite sensations. The purpose of this study was to validate a novel hand-held method (EARS II (HP® iPAQ)) against the standard Pen and Paper (P&P) method and the previously validated EARS. Methods Twelve participants (5 male, 7 female, aged 18-40) were involved in a fully repeated measures design. Participants were randomly assigned in a crossover design, to either high fat (>48% fat) or low fat (<28% fat) meal days, one week apart and completed ratings using the three data capture methods ordered according to Latin Square. The first set of appetite sensations was completed in a fasted state, immediately before a fixed breakfast. Thereafter, appetite sensations were completed every thirty minutes for 4h. An ad libitum lunch was provided immediately before completing a final set of appetite sensations. Results Repeated measures ANOVAs were conducted for ratings of hunger, fullness and desire to eat. There were no significant differences between P&P compared with either EARS or EARS II (p > 0.05). Correlation coefficients between P&P and EARS II, controlling for age and gender, were performed on Area Under the Curve ratings. R2 for Hunger (0.89), Fullness (0.96) and Desire to Eat (0.95) were statistically significant (p < 0.05). Conclusions EARS II was sensitive to the impact of a meal and recovery of appetite during the postprandial period and is therefore an effective device for monitoring appetite sensations. This study provides evidence and support for further validation of the novel EARS II method for monitoring appetite sensations during large scale studies. The added versatility means that future uses of the system provides the potential to monitor a range of other behavioural and physiological measures often important in clinical and free living trials.

Phenomenology as a method for exploring management practice

Phenomenology is a term that has been described as a philosophy, a research paradigm, a methodology, and equated with qualitative research. In this paper first we clarify phenomenology by tracing its movement both as a philosophy and as a research method. Next we make a case for the use of phenomenology in empirical investigations of management phenomena. The paper discusses a selection of central concepts pertaining to phenomenology as a scientific research method, which include description, phenomenological reduction and free imaginative variation. In particular, the paper elucidates the efficacy of Giorgi’s descriptive phenomenological research praxis as a qualitative research method and how its utility can be applied in creating a deeper and richer understanding of management practice.

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.

A hybrid smoothed finite element method (H-SFEM) to solid mechanics problems

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and Node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained by adjusting ; (2) there exists a preferable at which the H-SFEM can produce the ultrasonic accurate solution.

Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

An efficient numerical method to compute nonlinear solutions for two-dimensional steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996, J. Fluid Mech., 330, 339-347). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free-surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free-surface a priori while solving for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify eleven basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free-surface, given the free-surface shape itself.

Nanoporous Graphitic-C3N4@Carbon Metal-Free Electrocatalysts for Highly Efficient Oxygen Reduction

Based on theoretical prediction, a g-C3N4@carbon metal-free oxygen reduction reaction (ORR) electrocatalyst was designed and synthesized by uniform incorporation of g-C3N4 into a mesoporous carbon to enhance the electron transfer efficiency of g-C3N4. The resulting g-C3N4@carbon composite exhibited competitive catalytic activity (11.3 mA cm–2 kinetic-limiting current density at −0.6 V) and superior methanol tolerance compared to a commercial Pt/C catalyst. Furthermore, it demonstrated significantly higher catalytic efficiency (nearly 100% of four-electron ORR process selectivity) than a Pt/C catalyst. The proposed synthesis route is facile and low-cost, providing a feasible method for the development of highly efficient electrocatalysts.

Pharmacokinetics of isofraxidin in rat plasma after oral administration of the extract of acanthopanax senticosus using HPLC with solid phase extraction method

High-performance liquid chromatography coupled with solid phase extraction method was developed for determination of isofraxidin in rat plasma after oral administration of Acanthopanax senticosus extract (ASE), and pharmacokinetic parameters of isofraxidin either in ASE or pure compound were measured. The HPLC analysis was performed on a Dikma Diamonsil RP(18) column (4.6 mm x 150 mm, 5 microm) with the isocratic elution of solvent A (acetonitrile) and solvent B (0.1% aqueous phosphoric acid, v/v) (A : B = 22 : 78) and the detection wavelength was set at 343 nm. The calibration curve was linear over the range of 0.156-15.625 microg/ml. The limit of detection was 60 ng/ml. The intra-day precision was 5.8%, and the inter-day precision was 6.0%. The recovery was 87.30+/-1.73%. When the dosage of ASE is equal to pure compound caculated by the amount of isofraxidin, it has been found to have two maximum concentrations in plasma while the pure compound only showed one peak in the plasma concentration-time curve. The determined content of isofraxidin in plasma after oral administration of ASE is the total contents of free isofraxidin and its precursors in ASE in vitro. The pharmacokinetic characteristics of ASE showed the priority of the extract and the properities of traditional Chinese medicine.

Precedent-free fault isolation in a diesel engine exhaust gas recirculation system

In this paper, a recently introduced model-based method for precedent-free fault detection and isolation (FDI) is modified to deal with multiple input, multiple output (MIMO) systems and is applied to an automotive engine with exhaust gas recirculation (EGR) system. Using normal behavior data generated by a high fidelity engine simulation, the growing structure multiple model system (GSMMS) approach is used to construct dynamic models of normal behavior for the EGR system and its constituent subsystems. Using the GSMMS models as a foundation, anomalous behavior is detected whenever statistically significant departures of the most recent modeling residuals away from the modeling residuals displayed during normal behavior are observed. By reconnecting the anomaly detectors (ADs) to the constituent subsystems, EGR valve, cooler, and valve controller faults are isolated without the need for prior training using data corresponding to particular faulty system behaviors.

Rapid synthesis of porous honeycomb Cu/Pd through a hydrogen-bubble templating method

A rapid electrochemical method based on using a clean hydrogen-bubble template to form a bimetallic porous honeycomb Cu/Pd structure has been investigated. The addition of palladium salt to a copper-plating bath under conditions of vigorous hydrogen evolution was found to influence the pore size and bulk concentration of copper and palladium in the honeycomb bimetallic structure. The surface was characterised by X-ray photoelectron spectroscopy, which revealed that the surface of honeycomb Cu/Pd was found to be rich with a Cu/Pd alloy. The inclusion of palladium in the bimetallic structure not only influenced the pore size, but also modified the dendritic nature of the internal wall structure of the parent copper material into small nanometre-sized crystallites. The chemical composition of the bimetallic structure and substantial morphology changes were found to significantly influence the surface-enhanced Raman spectroscopic response for immobilised rhodamine B and the hydrogen-evolution reaction. The ability to create free-standing films of this honeycomb material may also have many advantages in the areas of gas- and liquid-phase heterogeneous catalysis.

Training-free probability models for whole-image based place recognition

Whole-image descriptors such as GIST have been used successfully for persistent place recognition when combined with temporal filtering or sequential filtering techniques. However, whole-image descriptor localization systems often apply a heuristic rather than a probabilistic approach to place recognition, requiring substantial environmental-specific tuning prior to deployment. In this paper we present a novel online solution that uses statistical approaches to calculate place recognition likelihoods for whole-image descriptors, without requiring either environmental tuning or pre-training. Using a real world benchmark dataset, we show that this method creates distributions appropriate to a specific environment in an online manner. Our method performs comparably to FAB-MAP in raw place recognition performance, and integrates into a state of the art probabilistic mapping system to provide superior performance to whole-image methods that are not based on true probability distributions. The method provides a principled means for combining the powerful change-invariant properties of whole-image descriptors with probabilistic back-end mapping systems without the need for prior training or system tuning.

Towards training-free appearance-based localization : probabilistic models for whole-image descriptors

Whole image descriptors have recently been shown to be remarkably robust to perceptual change especially compared to local features. However, whole-image-based localization systems typically rely on heuristic methods for determining appropriate matching thresholds in a particular environment. These environment-specific tuning requirements and the lack of a meaningful interpretation of these arbitrary thresholds limits the general applicability of these systems. In this paper we present a Bayesian model of probability for whole-image descriptors that can be seamlessly integrated into localization systems designed for probabilistic visual input. We demonstrate this method using CAT-Graph, an appearance-based visual localization system originally designed for a FAB-MAP-style probabilistic input. We show that using whole-image descriptors as visual input extends CAT-Graph’s functionality to environments that experience a greater amount of perceptual change. We also present a method of estimating whole-image probability models in an online manner, removing the need for a prior training phase. We show that this online, automated training method can perform comparably to pre-trained, manually tuned local descriptor methods.

Rapid quantification of free cholesterol in tears using direct insertion/electron ionization-Mass spectrometry

Purpose. To establish a simple and rapid analytical method, based on direct insertion/electron ionization-mass spectrometry (DI/EI-MS), for measuring free cholesterol in tears from humans and rabbits. Methods. A stable-isotope dilution protocol employing DI/EI-MS in selected ion monitoring mode was developed and validated. It was used to quantify the free cholesterol content in human and rabbit tear extracts. Tears were collected from adult humans (n = 15) and rabbits (n = 10) and lipids extracted. Results. Screening, full-scan (m/z 40-600) DI/EI-MS analysis of crude tear extracts showed that diagnostic ions located in the mass range m/z 350 to 400 were those derived from free cholesterol, with no contribution from cholesterol esters. DI/EI-MS data acquired using selected ion monitoring (SIM) were analyzed for the abundance ratios of diagnostic ions with their stable isotope-labeled analogues arising from the D6-cholesterol internal standard. Standard curves of good linearity were produced and an on-probe limit of detection of 3 ng (at 3:1 signal to noise) and limit of quantification of 8 ng (at 10:1 signal to noise). The concentration of free cholesterol in human tears was 15 ± 6 μg/g, which was higher than in rabbit tears (10 ± 5 μg/g). Conclusions. A stable-isotope dilution DI/EI-SIM method for free cholesterol quantification without prior chromatographic separation was established. Using this method demonstrated that humans have higher free cholesterol levels in their tears than rabbits. This is in agreement with previous reports. This paper provides a rapid and reliable method to measure free cholesterol in small-volume clinical samples. © 2013 The Association for Research in Vision and Ophthalmology, Inc.