Thrust allocation with linear constrained quadratic cost function

In this paper, a method of thrust allocation based on a linearly constrained quadratic cost function capable of handling rotating azimuths is presented. The problem formulation accounts for magnitude and rate constraints on both thruster forces and azimuth angles. The advantage of this formulation is that the solution can be found with a finite number of iterations for each time step. Experiments with a model ship are used to validate the thrust allocation system.

Development of a log-quadratic model to describe microbial inactivation, illustrated by thermal inactivation of Clostridium botulinum

In the commercial food industry, demonstration of microbiological safety and thermal process equivalence often involves a mathematical framework that assumes log-linear inactivation kinetics and invokes concepts of decimal reduction time (DT), z values, and accumulated lethality. However, many microbes, particularly spores, exhibit inactivation kinetics that are not log linear. This has led to alternative modeling approaches, such as the biphasic and Weibull models, that relax strong log-linear assumptions. Using a statistical framework, we developed a novel log-quadratic model, which approximates the biphasic and Weibull models and provides additional physiological interpretability. As a statistical linear model, the log-quadratic model is relatively simple to fit and straightforwardly provides confidence intervals for its fitted values. It allows a DT-like value to be derived, even from data that exhibit obvious "tailing." We also showed how existing models of non-log-linear microbial inactivation, such as the Weibull model, can fit into a statistical linear model framework that dramatically simplifies their solution. We applied the log-quadratic model to thermal inactivation data for the spore-forming bacterium Clostridium botulinum and evaluated its merits compared with those of popular previously described approaches. The log-quadratic model was used as the basis of a secondary model that can capture the dependence of microbial inactivation kinetics on temperature. This model, in turn, was linked to models of spore inactivation of Sapru et al. and Rodriguez et al. that posit different physiological states for spores within a population. We believe that the log-quadratic model provides a useful framework in which to test vitalistic and mechanistic hypotheses of inactivation by thermal and other processes. Copyright © 2009, American Society for Microbiology. All Rights Reserved.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

Assessment of body composition of Sri Lankan Australian children using ethnic specific equations

Since ethnic differences exist in body composition, assessment methods need to be validated prior to use in different populations. This study attempts to validate the use of Sri Lankan based body composition assessment tools on a group of 5 - 15 year old Australian children of Sri Lankan origin. The study was conducted at the Body Composition Laboratory of the Children’s Nutrition Research Centre at the Royal Children’s Hospital, Brisbane, Australia. Height (Ht), weight (Wt), segmental length (Lsegment name) and skinfold thickness (SFT) were measured. The whole body and segmental bio impedance analysis (BIA) were also measured. The body composition determined by the deuterium dilution technique (criterion method) was compared with the assessments done using prediction equations developed on Sri Lankan children. 27 boys and 15 girls were studied. All predictions of body composition parameters, except percentage fat mass (FM) assessed by the SFT-FM equation in girls gave statistically significant correlations with the criterion method. They had a low mean bias and most were not influenced by the measured parameter. Although living in a different socioeconomic state, the equations developed on children of the same ethnic background gives a better predictive value of body composition. This highlights the ethnic influence on body composition.

Use of Skin-Fold Thickness in Sri Lankan Children: Comparison of Several Prediction Equations

Objective There are many prediction equations available in the literature for the assessment of body composition from skinfold thickness (SFT). This study aims to cross validate some of those prediction equations to determine the suitability of their use on Sri Lankan children. Methods Height, weight and SFT of 5 different sites were measured. Total body water was assessed using the isotope dilution method (D2O). Percentage Fat mass (%FM) was estimated from SFT using prediction equations described by five authors in the literature. Results Five to 15 year old healthy, 282 Sri Lankan children were studied. The equation of Brook gave Ihe lowest bias but limits of agreement were high. Equations described by Deurenberg et al gave slightly higher bias but limits of agreement were narrowest and bias was not influence by extremes of body fat. Although prediction equations did not estimate %FM adequately, the association between %FM and SFT measures, were quite satisfactory. Conclusion We conclude that SFT can be used effectively in the assessment of body composition in children. However, for the assessment of body composition using SFT, either prediction equations should be derived to suit the local populations or existing equations should be cross-validated to determine the suitability before its application.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.