An algebraic approach for determination of DG parameters to support voltage profiles in radial distribution networks

Rapidly increasing electricity demands and capacity shortage of transmission and distribution facilities are the main driving forces for the growth of Distributed Generation (DG) integration in power grids. One of the reasons for choosing a DG is its ability to support voltage in a distribution system. Selection of effective DG characteristics and DG parameters is a significant concern of distribution system planners to obtain maximum potential benefits from the DG unit. This paper addresses the issue of improving the network voltage profile in distribution systems by installing a DG of the most suitable size, at a suitable location. An analytical approach is developed based on algebraic equations for uniformly distributed loads to determine the optimal operation, size and location of the DG in order to achieve required levels of network voltage. The developed method is simple to use for conceptual design and analysis of distribution system expansion with a DG and suitable for a quick estimation of DG parameters (such as optimal operating angle, size and location of a DG system) in a radial network. A practical network is used to verify the proposed technique and test results are presented.

Two-scale computational modelling of unsaturated flow in soils exhibiting small scale heterogeneities

Unsaturated water flow in soil is commonly modelled using Richards’ equation, which requires the hydraulic properties of the soil (e.g., porosity, hydraulic conductivity, etc.) to be characterised. Naturally occurring soils, however, are heterogeneous in nature, that is, they are composed of a number of interwoven homogeneous soils each with their own set of hydraulic properties. When the length scale of these soil heterogeneities is small, numerical solution of Richards’ equation is computationally impractical due to the immense effort and refinement required to mesh the actual heterogeneous geometry. A classic way forward is to use a macroscopic model, where the heterogeneous medium is replaced with a fictitious homogeneous medium, which attempts to give the average flow behaviour at the macroscopic scale (i.e., at a scale much larger than the scale of the heterogeneities). Using the homogenisation theory, a macroscopic equation can be derived that takes the form of Richards’ equation with effective parameters. A disadvantage of the macroscopic approach, however, is that it fails in cases when the assumption of local equilibrium does not hold. This limitation has seen the introduction of two-scale models that include at each point in the macroscopic domain an additional flow equation at the scale of the heterogeneities (microscopic scale). This report outlines a well-known two-scale model and contributes to the literature a number of important advances in its numerical implementation. These include the use of an unstructured control volume finite element method and image-based meshing techniques, that allow for irregular micro-scale geometries to be treated, and the use of an exponential time integration scheme that permits both scales to be resolved simultaneously in a completely coupled manner. Numerical comparisons against a classical macroscopic model confirm that only the two-scale model correctly captures the important features of the flow for a range of parameter values.

Time-domain hydroelastic analysis of a flexible marine structure using state-space models

This article deals with time-domain hydroelastic analysis of a marine structure. The convolution terms associated with fluid memory effects are replaced by an alternative state-space representation, the parameters of which are obtained by using realization theory. The mathematical model established is validated by comparison to experimental results of a very flexible barge. Two types of time-domain simulations are performed: dynamic response of the initially inert structure to incident regular waves and transient response of the structure after it is released from a displaced condition in still water. The accuracy and the efficiency of the simulations based on the state-space model representations are compared to those that integrate the convolutions.

Letters & Numbers : a vehicle to illustrate mathematical and computing fundamentals

The television quiz program Letters and Numbers, broadcast on the SBS network, has recently become quite popular in Australia. This paper explores the potential of this game to illustrate and engage student interest in a range of fundamental concepts of computer science and mathematics. The Numbers Game in particular has a rich mathematical structure whose analysis and solution involves concepts of counting and problem size, discrete (tree) structures, language theory, recurrences, computational complexity, and even advanced memory management. This paper presents an analysis of these games and their teaching applications, and presents some initial results of use in student assignments.

A nonlinear observer for estimating transverse stability parameters of marine surface vessels

This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel's centre of gravity due to, for example, water on deck and also in changes in the buoyancy triggered by variations in the water-plane area produced by longitudinal waves -- propagating along the fore-aft direction along the hull. These variations in the restoring can change dramatically the dynamics of the roll motion leading to dangerous resonance. Therefore, it is of interest to estimate and detect such changes.

A comparison of mathematical models for phase separation in high-rate LiFePO4 cathodes

We construct a two-scale mathematical model for modern, high-rate LiFePO4cathodes. We attempt to validate against experimental data using two forms of the phase-field model developed recently to represent the concentration of Li+ in nano-sized LiFePO4crystals. We also compare this with the shrinking-core based model we developed previously. Validating against high-rate experimental data, in which electronic and electrolytic resistances have been reduced is an excellent test of the validity of the crystal-scale model used to represent the phase-change that may occur in LiFePO4material. We obtain poor fits with the shrinking-core based model, even with fitting based on “effective” parameter values. Surprisingly, using the more sophisticated phase-field models on the crystal-scale results in poorer fits, though a significant parameter regime could not be investigated due to numerical difficulties. Separate to the fits obtained, using phase-field based models embedded in a two-scale cathodic model results in “many-particle” effects consistent with those reported recently.

Simulation-based fully Bayesian experimental design for mixed effects models

In this paper, we present fully Bayesian experimental designs for nonlinear mixed effects models, in which we develop simulation-based optimal design methods to search over both continuous and discrete design spaces. Although Bayesian inference has commonly been performed on nonlinear mixed effects models, there is a lack of research into performing Bayesian optimal design for nonlinear mixed effects models that require searches to be performed over several design variables. This is likely due to the fact that it is much more computationally intensive to perform optimal experimental design for nonlinear mixed effects models than it is to perform inference in the Bayesian framework. In this paper, the design problem is to determine the optimal number of subjects and samples per subject, as well as the (near) optimal urine sampling times for a population pharmacokinetic study in horses, so that the population pharmacokinetic parameters can be precisely estimated, subject to cost constraints. The optimal sampling strategies, in terms of the number of subjects and the number of samples per subject, were found to be substantially different between the examples considered in this work, which highlights the fact that the designs are rather problem-dependent and require optimisation using the methods presented in this paper.

Heat transfer analysis of viscous incompressible fluid by combined natural convection and radiation in an open cavity

The effect of radiation on natural convection of Newtonian fluid contained in an open cavity is investigated in this study. The governing partial differential equations are solved numerically using the Alternate Direct Implicit method together with the Successive Over Relaxation method. The study is focused on studying the flow pattern and the convective and radiative heat transfer rates are studied for different values of radiation parameters namely, the optical thickness of the fluid, scattering albedo, and the Planck number. It was found that in the optically thin limit, an increase in the optical thickness of the fluid raises the temperature and radiation heat transfer of the fluid. However, a further increase in the optical thickness decreases the radiative heat transfer rate due to increase in the energy level of the fluid, which ultimately reduces the total heat transfer rate within the fluid.

Segmental torso masses in adolescent idiopathic scoliosis

Background Adolescent Idiopathic Scoliosis is the most common type of spinal deformity whose aetiology remains unclear. Studies suggest that gravitational forces in the standing position play an important role in scoliosis progression, therefore anthropometric data are required to develop biomechanical models of the deformity. Few studies have analysed the trunk by vertebral level and none have performed investigations of the scoliotic trunk. The aim of this study was to determine the centroid, thickness, volume and estimated mass, for sections of the trunk in Adolescent Idiopathic Scoliosis patients. Methods Existing low-dose Computed Tomography scans were used to estimate vertebral level-by-level torso masses for 20 female Adolescent Idiopathic Scoliosis patients. ImageJ processing software was used to analyse the Computed Tomography images and enable estimation of the segmental torso mass corresponding to each vertebral level. Findings The patients’ mean age was 15.0 (SD 2.7) years with mean major Cobb Angle of 52° (SD 5.9) and mean patient weight of 58.2 (SD 11.6) kg. The magnitude of torso segment mass corresponding to each vertebral level increased by 150% from 0.6kg at T1 to 1.5kg at L5. Similarly, the segmental thickness corresponding to each vertebral level from T1-L5 increased inferiorly from a mean 18.5 (SD 2.2) mm at T1 to 32.8 (SD 3.4) mm at L5. The mean total trunk mass, as a percentage of total body mass, was 27.8 (SD 0.5) % which was close to values reported in previous literature. Interpretation This study provides new anthropometric reference data on segmental (vertebral level-by-level) torso mass in Adolescent Idiopathic Scoliosis patients, useful for biomechanical models of scoliosis progression and treatment.

The educational pipeline for health care professionals : understanding the source of racial differences

The underrepresentation of blacks in the healthcare professions may have direct implications for the health outcomes of minority patients, underscoring the importance of understanding movement through the educational pipeline into professional healthcare careers by race. We jointly model individuals' postsecondary decisions including enrollment, college type, degree completion, and choosing a healthcare occupation requiring an advanced degree. We estimate the parameters of the model with maximum likelihood using data from the NLS-72. Our results emphasize the importance of pre-collegiate factors and of jointly examining the full chain of educational decisions in understanding the sources of racial disparities in professional healthcare occupations.

Strategic play among family members when making long-term care decisions

This paper describes a strategic model of bargaining within a family to determine how to care for an elderly parent. We estimate the parameters of the model using data from the National Long-term Care Survey. We find that the parameter estimates generally make sense and that the model is consistent with the data. The results have strong implications for using less structural empirical models for policy analysis.

Long-term care and family bargaining

We present a structural model of how families decide who should care for elderly parents. We use data from the National Long-Term Care Survey to estimate and test the parameters of the model. Then we use the parameter estimates to simulate the effects of the existing long-term trends in terms of the common but untested explanations for them. Finally, we simulate the effects of alternative family bargaining rules on individual utility to measure the sensitivity of our results to the family decision-making assumptions we make.

Cohabitation, marriage, and divorce in a model of match quality

The objective of this research is to further our understanding of how and why individuals enter and leave coresidential relationships. We develop and estimate an economic model of nonmarital cohabitation, marriage, and divorce that is consistent with current data on the formation and dissolution of relationships. Jovanovic's (Journal of Political Economy 87 (1979), 972-90) theoretical matching model is extended to help explain household formation and dissolution behavior. Implications of the model reveal what factors influence the decision to start a relationship, what form this relationship will take, and the relative stability of the various types of unions. The structural parameters of the model are estimated using longitudinal data from a sample of female high school seniors from the United States. New numerical methods are developed to reduce computational costs associated with estimation. The empirical results have interesting interpretations given the structural model. They show that a significant cause of cohabitation is the need to learn about potential partners and to hedge against future bad shocks. The estimated parameters are used to conduct several comparative dynamic experiments. For example, we show that policy experiments changing the cost of divorce have little effect on relationship choices.

Gene electrotransfer into murine skeletal muscle: A systematic analysis of parameters for long-term gene expression

Skeletal muscle is an attractive target tissue for delivery of therapeutic genes, since it is well vascularized, easily accessible, and has a high capacity for protein synthesis. For efficient transfection in skeletal muscle, several protocols have been described, including delivery of low voltage electric pulses and a combination of high and low voltage electric pulses. The aim of this study was to determine the influence of different parameters of electrotransfection on short-term and long-term transfection efficiency in murine skeletal muscle, and to evaluate histological changes in the treated tissue. Different parameters of electric pulses, different time lags between plasmid DNA injection and application of electric pulses, and different doses of plasmid DNA were tested for electrotransfection of tibialis cranialis muscle of C57BI/6 mice using DNA plasmid encoding green fluorescent protein (GFP). Transfection efficiency was assessed on frozen tissue sections one week after electrotransfection using a fluorescence microscope and also noninvasively, followed by an in vivo imaging system using a fluorescence stereo microscope over a period of several months. Histological changes in muscle were evaluated immediately or several months after electrotransfection by determining infiltration of inflammatory mononuclear cells and presence of necrotic muscle fibers. The most efficient electrotransfection into skeletal muscle of C57BI/6 mice in our experiments was achieved when one high voltage (HV) and four low voltage (LV) electric pulses were applied 5 seconds after the injection of 30 μg of plasmid DNA. This protocol resulted in the highest short-term as well as long-term transfection. The fluorescence intensity of the transfected area declined after 2-3 weeks, but GFP fluorescence was still detectable 18 months after electrotransfection. Extensive inflammatory mononuclear cell infiltration was observed immediately after the electrotransfection procedure using the described parameters, but no necrosis or late tissue damage was observed. This study showed that electric pulse parameters, time lag between the injection of DNA and application of electric pulses, and dose of plasmid DNA affected the duration of transgene expression in murine skeletal muscle. Therefore, transgene expression in muscle can be controlled by appropriate selection of electrotransfection protocol.

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.