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.

Retrospective evaluation of dosimetric quality for prostate carcinomas treated with 3D conformal, intensity-modulated and volumetric-modulated arc radiotherapy

Introduction This study examines and compares the dosimetric quality of radiotherapy treatment plans for prostate carcinoma across a cohort of 163 patients treated across 5 centres: 83 treated with three-dimensional conformal radiotherapy (3DCRT), 33 treated with intensity-modulated radiotherapy (IMRT) and 47 treated with volumetric-modulated arc therapy (VMAT). Methods Treatment plan quality was evaluated in terms of target dose homogeneity and organ-at-risk sparing, through the use of a set of dose metrics. These included the mean, maximum and minimum doses; the homogeneity and conformity indices for the target volumes; and a selection of dose coverage values that were relevant to each organ-at-risk. Statistical significance was evaluated using two-tailed Welch’s T-tests. The Monte Carlo DICOM ToolKit software was adapted to permit the evaluation of dose metrics from DICOM data exported from a commercial radiotherapy treatment planning system. Results The 3DCRT treatment plans offered greater planning target volume dose homogeneity than the other two treatment modalities. The IMRT and VMAT plans offered greater dose reduction in the organs-at-risk: with increased compliance with recommended organ-at-risk dose constraints, compared to conventional 3DCRT treatments. When compared to each other, IMRT and VMAT did not provide significantly different treatment plan quality for like-sized tumour volumes. Conclusions This study indicates that IMRT and VMAT have provided similar dosimetric quality, which is superior to the dosimetric quality achieved with 3DCRT.

Prospects for studying how high-intensity compression waves cause damage in human blast injuries

Since World War I, explosions have accounted for over 70% of all injuries in conflict. With the development of improved personnel protection of the torso, improved medical care and faster aeromedical evacuation, casualties are surviving with more severe injuries to the extremities. Understanding the processes involved in the transfer of blast-induced shock waves through biological tissues is essential for supporting efforts aimed at mitigating and treating blast injury. Given the inherent heterogeneities in the human body, we argue that studying these processes demands a highly integrated approach requiring expertise in shock physics, biomechanics and fundamental biological processes. This multidisciplinary systems approach enables one to develop the experimental framework for investigating the material properties of human tissues that are subjected to high compression waves in blast conditions and the fundamental cellular processes altered by this type of stimuli. Ultimately, we hope to use the information gained from these studies in translational research aimed at developing improved protection for those at risk and improved clinical outcomes for those who have been injured from a blast wave.

A variable diffusivity model for the drying of spherical food particulates

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2 value greater than 98.6% for all temperatures.

Comparison of intensity-based cut-points for the RT3 accelerometer in youth

OBJECTIVES: To compare the classification accuracy of previously published RT3 accelerometer cut-points for youth using energy expenditure, measured via portable indirect calorimetry, as a criterion measure. DESIGN: Cross-sectional cross-validation study. METHODS: 100 children (mean age 11.2±2.8 years, 61% male) completed 12 standardized activities trials (3 sedentary, 5 lifestyle and 4 ambulatory) while wearing an RT3 accelerometer. V˙O2 was measured concurrently using the Oxycon Mobile portable calorimeter. Cut-points by Vanhelst (VH), Rowlands (RW), Chu (CH), Kavouras (KV) and the RT3 manufacturer (RT3M) were used to classify PA intensity as sedentary (SED), light (LPA), moderate (MPA) or vigorous (VPA). Classification accuracy was evaluated using the area under the Receiver Operating Characteristic curve (ROC-AUC) and weighted Kappa (κ). RESULTS: For moderate-to-vigorous PA (MVPA), VH, KV and RW exhibited excellent accuracy classification (ROC-AUC≥0.90), while the CH and RT3M exhibited good classification accuracy (ROC-AUC>0.80). Classification accuracy for LPA was fair to poor (ROC-AUC<0.76). For SED, VH exhibited excellent classification accuracy (ROC-AUC>0.90), while RW, CH, and RT3M exhibited good classification accuracy (ROC-AUC>0.80). Kappa statistics ranged from 0.67 (VH) to 0.55 (CH). CONCLUSIONS: All cut-points provided acceptable classification accuracy for SED and MVPA, but limited accuracy for LPA. On the basis of classification accuracy over all four levels of intensity, the use of the VH cut-points is recommended.

Comparison of accelerometer cut points for predicting activity intensity in youth

The absence of comparative validity studies has prevented researchers from reaching consensus regarding the application of intensity-related accelerometer cut points for children and adolescents. PURPOSE This study aimed to evaluate the classification accuracy of five sets of independently developed ActiGraph cut points using energy expenditure, measured by indirect calorimetry, as a criterion reference standard. METHODS A total of 206 participants between the ages of 5 and 15 yr completed 12 standardized activity trials. Trials consisted of sedentary activities (lying down, writing, computer game), lifestyle activities (sweeping, laundry, throw and catch, aerobics, basketball), and ambulatory activities (comfortable walk, brisk walk, brisk treadmill walk, running). During each trial, participants wore an ActiGraph GT1M, and VO 2 was measured breath-by-breath using the Oxycon Mobile portable metabolic system. Physical activity intensity was estimated using five independently developed cut points: Freedson/Trost (FT), Puyau (PU), Treuth (TR), Mattocks (MT), and Evenson (EV). Classification accuracy was evaluated via weighted κ statistics and area under the receiver operating characteristic curve (ROC-AUC). RESULTS Across all four intensity levels, the EV (κ = 0.68) and FT (κ = 0.66) cut points exhibited significantly better agreement than TR (κ = 0.62), MT (κ = 0.54), and PU (κ = 0.36). The EV and FT cut points exhibited significantly better classification accuracy for moderate-to vigorous-intensity physical activity (ROC-AUC = 0.90) than TR, PU, or MT cut points (ROC-AUC = 0.77-0.85). Only the EV cut points provided acceptable classification accuracy for all four levels of physical activity intensity and performed well among children of all ages. The widely applied sedentary cut point of 100 counts per minute exhibited excellent classification accuracy (ROC-AUC = 0.90). CONCLUSIONS On the basis of these findings, we recommend that researchers use the EV ActiGraph cut points to estimate time spent in sedentary, light-, moderate-, and vigorous-intensity activity in children and adolescents. Copyright © 2011 by the American College of Sports Medicine.

The feasibility of a home-based moderate-intensity physical activity intervention in obese children and adolescents

Objective To explore the feasibility of conducting a 10-week home-based physical activity (PA) programme and evaluate the changes in insulin sensitivity (S I) commensurate with the programme in obese young people. Design Open-labelled intervention. Setting Home-based intervention with clinical assessments at a tertiary paediatric hospital. Subjects 18 obese (body mass index (BMI)>International Obesity Task Force age and sex-specifi c cut-offs) children and adolescents (8-18 years, 11 girls/7 boys) were recruited. 15 participants (nine girls/six boys, mean±SE age 11.8±0.6 years, BMI-SD scores (BMI-SDS) 3.5±0.1, six prepubertal/nine pubertal) completed the intervention. Intervention The programme comprised biweekly home visits over 10 weeks with personalised plans implemented aiming to increase moderate-intensity PA. Pedometers and PA diaries were used as self-monitoring tools. The goals were to (1) teach participants behavioural skills related to adopting and maintaining an active lifestyle and (2) increase daily participation in PA. Outcome measures Mean steps/day were assessed. SI assessed by the frequently sampled intravenous glucose tolerance test and other components of the insulin resistance syndrome were measured. Results Mean steps/day increased significantly from 10 363±927 (baseline) to 13 013±1131 (week 10) (p<0.05). S I was also significantly increased, despite no change in BMI-SDS, and remained so after an additional 10-week follow-up. Conclusions The results suggest that such a homebased PA programme is feasible. S I improved without changes in BMI-SDS. More rigorous evaluations of such programmes are warranted.

Modeling and analysis of a novel variable-speed cage induction generator

This paper introduces a novel cage induction generator and presents a mathematical model, through which its behavior can be accurately predicted. The proposed generator system employs a three-phase cage induction machine and generates single-phase and constant-frequency electricity at varying rotor speeds without an intermediate inverter stage. The technique uses any one of the three stator phases of the machine as the excitation winding and the remaining two phases, which are connected in series, as the power winding. The two-series-connected-and-one-isolated (TSCAOI) phase winding configuration magnetically decouples the two sets of windings, enabling independent control. Electricity is generated through the power winding at both sub- and super-synchronous speeds with appropriate excitation to the isolated single winding at any frequency of generation. A dynamic mathematical model, which accurately predicts the behavior of the proposed generator, is also presented and implemented in MATLAB/Simulink. Experimental results of a 2-kW prototype generator under various operating conditions are presented, together with theoretical results, to demonstrate the viability of the TSCAOI power generation. The proposed generator is simple and capable of both storage and retrieval of energy through its excitation winding and is expected to be suitable for applications, such as small wind turbines and microhydro systems.

The impacts of variable speed limit on speed variation and headway distribution

This thesis investigates the impacts of variable speed limit on motorway speed variation and headway distribution. Initiative techniques of traffic flow categorisation study contribute in analysing the effects of variable speed limit on various traffic states. The project focuses on the speed harmonisation impacts within and across lanes as well as the uniformity of headway spread in the application of variable speed limit.

Imputing a continuous income variable from a bracketed income variable with special attention to missing observations

This paper proposes a method, based on polychotomous discrete choice methods, to impute a continuous measure of income when only a bracketed measure of income is available and for only a subset of the obsevations. The method is shown to perform well with CP5 data. © 1991.

The eight variable homogeneous degree three bent functions

We determine the affine equivalence classes of the eight variable degree three homogeneous bent functions using a new algorithm. Our algorithm applies to general bent functions and can systematically determine the automorphism groups. We provide a partial verification of the enumeration of eight variable degree three homogeneous bent functions obtained by Meng et al. We determine the affine equivalence classes of these functions.

Vibrational spectroscopic characterization of the sulphate–halide mineral sulphohalite – implications for evaporites

The mineral sulphohalite – Na6(SO4)2FCl is a rare sodium halogen sulphate and occurs associated with evaporitic deposits. Sulphohalite formation is important in saline evaporites and in pipe scales. Sulphohalite is an anhydrous sulphate–halide with an apparent variable anion ratio of formula Na6(SO4)2FCl. Such a formula with oxyanions lends itself to vibrational spectroscopy. The Raman band at 1003 cm−1 is assigned to the (SO4)2− ν1 symmetric stretching mode. Shoulders to this band are found at 997 and 1010 cm−1. The low intensity Raman bands at 1128, 1120 and even 1132 cm−1 are attributed to the (SO4)2− ν3 antisymmetric stretching vibrations. Two symmetric sulphate stretching modes are observed indicating at least at the molecular level the non-equivalence of the sulphate ions in the sulphohalite structure. The Raman bands at 635 and 624 cm−1 are assigned to the ν4 SO42− bending modes. The ν2 (SO4)2− bending modes are observed at 460 and 494 cm−1. The observation of multiple bands supports the concept of a reduction in symmetry of the sulphate anion from Td to C3v or even C2v. No evidence of bands attributable to the halide ions was found.

Correlates of foot pain severity in adults with hallux valgus : a cross-sectional study

Background Hallux valgus (HV) is highly prevalent and associated with progressive first metatarsophalangeal joint subluxation and osteoarthritis. The link between structural HV deformity and foot pain is unclear. This study investigated possible explanatory factors surrounding foot pain in HV, including radiographic HV angle and signs of joint degeneration. Methods Participants were 60 adults (53 female) with HV aged 20 to 75 years. Participant demographics and a range of radiographic, clinical and functional measures were considered potential correlates of foot pain. Self-reported foot pain (visual analogue scales and a dichotomous definition) was considered the dependent variable. Multivariate modelling was used to determine which characteristics and measures explained pain, with univariate analyses first used to screen potential variables. Results Approximately 20 to 30% of the variance in foot pain associated with HV could be explained by patient characteristics such as poorer general health status, lower educational attainment and increased occupational physical activity levels, in combination with some dynamic physical characteristics such as hallux plantarflexion weakness and reduced force-time integral under the second metatarsal during gait. Neither increasing lateral deviation of the hallux (HV angle) nor presence of first metatarsophalangeal joint osteoarthritis was associated with foot pain. Conclusions This study shows that passive structural factors, including HV angle, do not appear to be significant correlates of foot pain intensity in HV. Our data demonstrate the importance of considering patient characteristics such as general health and physical activity levels when assessing foot pain associated with HV.

Evolution of Langmuir waves in a plasma contaminated by variable-charge impurities

The propagation of Langmuir waves in nonisothermal plasmas contaminated by fine dust particles with variable charge is investigated for a self-consistent closed system. Dust charge relaxation, ionization, recombination, and collisional dissipation are taken into account. It is shown that the otherwise unstable coupling of the Langmuir and dust-charge relaxation modes becomes stable and the Langmuir waves are frequency down-shifted.