A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Reply to the comments on “A study of the phosphate mineral kapundaite NaCa(Fe3+)4(PO4)4(OH)3·5(H2O) using SEM/EDX and vibrational spectroscopic methods” by Frost et al. (2014)

"The authors agree with the statements made by Mills and Christy on the study of kapundaite [1]. These authors are correct and have removed any confusion about the origin of the sample kapundaite. The authors (Frost et al.) confirm the sample of kapundaite studied in this work is from the Tom‘s quarry, Australia and can be considered a type material. The authors do not accept the statements by Mills and Christy on “type minerals”. The sample of kapundaite from the Australian source is from the collection of the Geology Department of the Federal University of Ouro Preto, Minas Gerais, Brazil with sample code SAC-111. At least if our mineral sample is not a co-type mineral, our sample is from the same origin as the type mineral. Samples..."--publisher website.

Assessment of cone beam CT registration for prostate radiation therapy : fiducial marker and soft tissue methods

Introduction This investigation aimed to assess the consistency and accuracy of radiation therapists (RTs) performing cone beam computed tomography (CBCT) alignment to fiducial markers (FMs) (CBCTFM) and the soft tissue prostate (CBCTST). Methods Six patients receiving prostate radiation therapy underwent daily CBCTs. Manual alignment of CBCTFM and CBCTST was performed by three RTs. Inter-observer agreement was assessed using a modified Bland–Altman analysis for each alignment method. Clinically acceptable 95% limits of agreement with the mean (LoAmean) were defined as ±2.0 mm for CBCTFM and ±3.0 mm for CBCTST. Differences between CBCTST alignment and the observer-averaged CBCTFM (AvCBCTFM) alignment were analysed. Clinically acceptable 95% LoA were defined as ±3.0 mm for the comparison of CBCTST and AvCBCTFM. Results CBCTFM and CBCTST alignments were performed for 185 images. The CBCTFM 95% LoAmean were within ±2.0 mm in all planes. CBCTST 95% LoAmean were within ±3.0 mm in all planes. Comparison of CBCTST with AvCBCTFM resulted in 95% LoA of −4.9 to 2.6, −1.6 to 2.5 and −4.7 to 1.9 mm in the superior–inferior, left–right and anterior–posterior planes, respectively. Conclusions Significant differences were found between soft tissue alignment and the predicted FM position. FMs are useful in reducing inter-observer variability compared with soft tissue alignment. Consideration needs to be given to margin design when using soft tissue matching due to increased inter-observer variability. This study highlights some of the complexities of soft tissue guidance for prostate radiation therapy.

Comparative analysis of traffic state estimation ─ Cumulative counts-based and trajectory-based methods

The Macroscopic Fundamental Diagram (MFD) relates space-mean density and flow. Since the MFD represents the area-wide network traffic performance, studies on perimeter control strategies and network-wide traffic state estimation utilising the MFD concept have been reported. Most previous works have utilised data from fixed sensors, such as inductive loops, to estimate the MFD, which can cause biased estimation in urban networks due to queue spillovers at intersections. To overcome the limitation, recent literature reports the use of trajectory data obtained from probe vehicles. However, these studies have been conducted using simulated datasets; limited works have discussed the limitations of real datasets and their impact on the variable estimation. This study compares two methods for estimating traffic state variables of signalised arterial sections: a method based on cumulative vehicle counts (CUPRITE), and one based on vehicles’ trajectory from taxi Global Positioning System (GPS) log. The comparisons reveal some characteristics of taxi trajectory data available in Brisbane, Australia. The current trajectory data have limitations in quantity (i.e., the penetration rate), due to which the traffic state variables tend to be underestimated. Nevertheless, the trajectory-based method successfully captures the features of traffic states, which suggests that the trajectories from taxis can be a good estimator for the network-wide traffic states.

Investigation and application of methods for enumerating heterotrophs and Escherichia coli in the air within piggery sheds

Aims: To investigate methods for the recovery of airborne bacteria within pig sheds and to then use the appropriate methods to determine the levels of heterotrophs and Escherichia coli in the air within sheds. Methods and Results: AGI-30 impingers and a six-stage Andersen multi-stage sampler (AMS) were used for the collection of aerosols. Betaine and catalase were added to impinger collection fluid and the agar plates used in the AMS. Suitable media for enumerating E. coli with the Andersen sampler were also evaluated. The addition of betaine and catalase gave no marked increase in the recovery of heterotrophs or E. coli. No marked differences were found in the media used for enumeration of E. coli. The levels of heterotrophs and E. coli in three piggeries, during normal pig activities, were 2Æ2 · 105 and 21 CFU m)3 respectively. Conclusions: The failure of the additives to improve the recovery of either heterotrophs or E. coli suggests that these organisms are not stressed in the piggery environment. The levels of heterotrophs in the air inside the three Queensland piggeries investigated are consistent with those previously reported in other studies. Flushing with ponded effluent had no marked or consistent effect on the heterotroph or E. coli levels. Significance and Impact of the Study: Our work suggests that levels of airborne heterotrophs and E. coli inside pig sheds have no strong link with effluent flushing. It would seem unlikely that any single management activity within a pig shed has a dominant influence on levels of airborne heterotrophs and E. coli

Indian developments in ultrasonics and acoustic emission methods

Fundamental investigations in ultrasonics in India date back to the early 20th century. But, fundamental and applied research in the field of nondestructive evaluation (NDE) came much later. In the last four decades it has grown steadily in academic institutions, national laboratories and industry. Currently, commensurate with rapid industrial growth and realisation of the benefits of NDE, the activity is becoming much stronger, deeper, broader and very wide spread. Acoustic Emission (AE) is a recent entry into the field of nondestructive evaluation. Pioneering efforts in India in AE were carried out at the Indian Institute of Science in the early 1970s. The nuclear industry was the first to utilise it. Current activity in AE in the country spans materials research, incipient failure detection, integrity evaluation of structures, fracture mechanics studies and rock mechanics. In this paper, we attempt to project the current scenario in ultrasonics and acoustic emission research in India.

Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Generalized Burgers equations and Euler-Painlev transcendents. I

Initial-value problems for the generalized Burgers equation (GBE) ut+u betaux+lambdaualpha =(delta/2)uxx are discussed for the single hump type of initial data both continuous and discontinuous. The numerical solution is carried to the self-similar ``intermediate asymptotic'' regime when the solution is given analytically by the self-similar form. The nonlinear (transformed) ordinary differential equations (ODE's) describing the self-similar form are generalizations of a class discussed by Euler and Painlevé and quoted by Kamke. These ODE's are new, and it is postulated that they characterize GBE's in the same manner as the Painlev equations categorize the Kortweg-de Vries (KdV) type. A connection problem for some related ODE's satisfying proper asymptotic conditions at x=±[infinity], is solved. The range of amplitude parameter is found for which the solution of the connection problem exists. The other solutions of the above GBE, which display several interesting features such as peaking, breaking, and a long shelf on the left for negative values of the damping coefficient lambda, are also discussed. The results are compared with those holding for the modified KdV equation with damping. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

From a tree to a stand in Finnish boreal forests: biomass estimation and comparison of methods

There is an increasing need to compare the results obtained with different methods of estimation of tree biomass in order to reduce the uncertainty in the assessment of forest biomass carbon. In this study, tree biomass was investigated in a 30-year-old Scots pine (Pinus sylvestris) (Young-Stand) and a 130-year-old mixed Norway spruce (Picea abies)-Scots pine stand (Mature-Stand) located in southern Finland (61º50' N, 24º22' E). In particular, a comparison of the results of different estimation methods was conducted to assess the reliability and suitability of their applications. For the trees in Mature-Stand, annual stem biomass increment fluctuated following a sigmoid equation, and the fitting curves reached a maximum level (from about 1 kg/yr for understorey spruce to 7 kg/yr for dominant pine) when the trees were 100 years old. Tree biomass was estimated to be about 70 Mg/ha in Young-Stand and about 220 Mg/ha in Mature-Stand. In the region (58.00-62.13 ºN, 14-34 ºE, ≤ 300 m a.s.l.) surrounding the study stands, the tree biomass accumulation in Norway spruce and Scots pine stands followed a sigmoid equation with stand age, with a maximum of 230 Mg/ha at the age of 140 years. In Mature-Stand, lichen biomass on the trees was 1.63 Mg/ha with more than half of the biomass occurring on dead branches, and the standing crop of litter lichen on the ground was about 0.09 Mg/ha. There were substantial differences among the results estimated by different methods in the stands. These results imply that a possible estimation error should be taken into account when calculating tree biomass in a stand with an indirect approach.

Current and emerging screening methods to identify post-head-emergence frost adaptation in wheat and barley

Cereal crops can suffer substantial damage if frosts occur at heading. Identification of post-head-emergence frost (PHEF) resistance in cereals poses a number of unique and difficult challenges. Many decades of research have failed to identify genotypes with PHEF resistance that could offer economically significant benefit to growers. Research and breeding gains have been limited by the available screening systems. Using traditional frost screening systems, genotypes that escape frost injury in trials due to spatial temperature differences and/or small differences in phenology can be misidentified as resistant. We believe that by improving techniques to minimize frost escapes, such ofalse-positive' results can be confidently identified and eliminated. Artificial freezing chambers or manipulated natural frost treatments offer many potential advantages but are not yet at the stage where they can be reliably used for frost screening in breeding programmes. Here we describe the development of a novel photoperiod gradient method (PGM) that facilitates screening of genotypes of different phenology under natural field frosts at matched developmental stages. By identifying frost escapes and increasing the efficiency of field screening, the PGM ensures that research effort can be focused on finding genotypes with improved PHEF resistance. To maximize the likelihood of identifying PHEF resistance, we propose that the PGM form part of an integrated strategy to (i) source germplasm;(ii) facilitate high throughput screening; and (iii) permit detailed validation. PGM may also be useful in other studies where either a range of developmental stages and/or synchronized development are desired.

Lantibiotic Nisin and Its Detection Methods

The type A lantibiotic nisin produced by several Lactococcus lactis strains, and one Streptococcus uberis strainis a small antimicrobial peptide that inhibits the growth of a wide range of gram-positive bacteria, such as Bacillus, Clostridium, Listeria and Staphylococcus species. It is nontoxic to humans and used as a food preservative (E234) in more than 50 countries including the EU, the USA, and China. National legislations concerning maximum addition levels of nisin in different foods vary greatly. Therefore, there is a demand for non-laborious and sensitive methods to identify and quantify nisin reliably from different food matrices. The horizontal inhibition assay, based on the inhibitory effect of nisin to Micrococcus luteus is the base for most quantification methods developed so far. However, the sensitivity and accuracy of the agar diffusion method is affected by several parameters. Immunological tests have also been described. Taken into account the sensitivity of immunological methods to interfering substances within sample matrices, and possible cross-reactivities with lantibiotics structurally close to nisin, their usefulness for nisin detection from food samples remains limited. The proteins responsible for nisin biosynthesis, and producer self-immunity are encoded by genes arranged into two inducible operons, nisA/Z/QBTCIPRK and nisFEG, which also contain internal, constitutive promoters PnisI and PnisR. The transmembrane histidine kinase NisK and the response regulator NisR form a two-component signal transduction system, in which NisK autophosphorylates after exposure to extra cellular nisin, and subsequently transfers the phosphate to NisR. The phosphorylated NisR then relays the signal downstream by binding to two regulated promoters in the nisin gene cluster, i.e the nisA/Z/Qand the nisF promoters, thus activating transcription of the structural gene nisA/Z/Q and the downstream genes nisBTCIPRK from the nisA/Z/Q promoter, and the genes nisFEG from the nisF promoter. In this work two novel and highly sensitive nisin bioassays were developed. Both of these quantification methods were based on NisRK mediated, nisin induced Green Fluorescent Protein (GFP) fluorescence. The suitabilities of these assays for quantifica¬tion of nisin from food samples were evaluated in several food matrices. These bioassays had nisin sensitivities in the nanogram or picogram levels. In addition, shelf life of nisin in cooked sausages and retainment of the induction activity of nisin in intestinal chyme (intestinal content) was assessed.

Statistical and Information-Theoretic Methods for Data-Analysis

In this Thesis, we develop theory and methods for computational data analysis. The problems in data analysis are approached from three perspectives: statistical learning theory, the Bayesian framework, and the information-theoretic minimum description length (MDL) principle. Contributions in statistical learning theory address the possibility of generalization to unseen cases, and regression analysis with partially observed data with an application to mobile device positioning. In the second part of the Thesis, we discuss so called Bayesian network classifiers, and show that they are closely related to logistic regression models. In the final part, we apply the MDL principle to tracing the history of old manuscripts, and to noise reduction in digital signals.