Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

Fast evolution strategies

Evolution strategies are a class of general optimisation algorithms which are applicable to functions that are multimodal, nondifferentiable, or even discontinuous. Although recombination operators have been introduced into evolution strategies, the primary search operator is still mutation. Classical evolution strategies rely on Gaussian mutations. A new mutation operator based on the Cauchy distribution is proposed in this paper. It is shown empirically that the new evolution strategy based on Cauchy mutation outperforms the classical evolution strategy on most of the 23 benchmark problems tested in this paper. The paper also shows empirically that changing the order of mutating the objective variables and mutating the strategy parameters does not alter the previous conclusion significantly, and that Cauchy mutations with different scaling parameters still outperform the Gaussian mutation with self-adaptation. However, the advantage of Cauchy mutations disappears when recombination is used in evolution strategies. It is argued that the search step size plays an important role in determining evolution strategies' performance. The large step size of recombination plays a similar role as Cauchy mutation.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Women's satisfaction with general practice consultations

Objective: To determine women's satisfaction with general practice services. Design: Cross-sectional postal questionnaire conducted during April to September 1996 (part of the baseline survey of the Australian Longitudinal Study on Women's Health). Participants: Women aged 18-22 (n=14739), 45-49 (n=14013) and 70-74 (n=12941) years, randomly selected from the Medicare database, with oversampling of women from rural and remote areas. Main outcome measures: Frequency of use of general practice services; satisfaction with the most recent visit to a general practitioner (CP), prevalence of selected symptoms; preference for a female doctor. Results: The most recent visit to a GP was rated overall as good, very good or excellent by more than 80% of women, with increasing levels of satisfaction with increasing age of the women. However, satisfaction was lower for waiting room time and cost of the visit. A third of the young and middle-aged women living in rural and remote areas were dissatisfied with the cost of the visit. Young women were more likely to prefer a female doctor, and many were dissatisfied with their GP's skills at explaining their problem and giving them a chance to give an opinion and ask questions. The most prevalent symptoms for all women included headaches and tiredness, and many were not satisfied with the health services available to help them deal with these symptoms. Conclusions: Australian women have high levels of satisfaction with GP consultations. However, more effective strategies may be needed to improve communication with younger women, and there is an unmet need for services to help all women deal with some common symptoms. Dissatisfaction with cost of services and women's preference for female doctors have implications for future health policy.

What is a healthy weight for middle aged women?

OBJECTIVE: To explore associations between body mass index (BMI) and selected indicators of health and well-being and to suggest a healthy weight range (based on BMI) for middle aged Australian women. DESIGN: population based longitudinal study (cross-sectional baseline data). SUBJECTS: 13431 women aged 45-49 y who participated in the baseline survey for the Australian Longitudinal Study on Women's Health. RESULTS: Forty-eight percent of women had a BMI>25kg/m(2). Prevalence of medical problems (for example, hypertension, diabetes), surgical procedures (cholescystectomy, hysterectomy) and symptoms (for example, back pain) increased monotonically with BMI, while indicators of health care use (for example, visits to doctors) showed a 'J' shaped relationship with BMI. Scores for several sub-scales of the MOS short form health survey (SF36) (for example, general health, role limitations due to emotional difficulties, social function, mental health and vitality) were optimal when BMI was around 19-24 kg/m(2). After adjustment for area of residence, education, smoking, exercise and menopausal status, low BMI was associated with fewer physical health problems than mid-level or higher BMI, and the nationally recommended BMI range of 20-25 was associated with optimum mental health, lower prevalence of tiredness and lowest use of health services. CONCLUSIONS: Acknowledging the limitations of the cross-sectional nature of these data, the results firmly support the benefits of leanness in terms of reducing the risk of cardiovascular disease, diabetes and gall bladder disease. The findings are moderated, however, by the observation that both low and high BMI are associated with decreased vitality and poorer mental health. The optimal range for BMI appears to be about 19-24 kg/m(2). From a public health perspective this study provides strong support for the recommended BMI range of 20-25 as an appropriate target for the promotion of healthy weight in middle aged Australian women.

Solution of adsorption problems involving steep moving profiles

The moving finite element collocation method proposed by Kill et al. (1995) Chem. Engng Sci. 51 (4), 2793-2799 for solution of problems with steep gradients is further developed to solve transient problems arising in the field of adsorption. The technique is applied to a model of adsorption in solids with bidisperse pore structures. Numerical solutions were found to match the analytical solution when it exists (i.e. when the adsorption isotherm is linear). The method is simple yet sufficiently accurate for use in adsorption problems, where global collocation methods fail. (C) 1998 Elsevier Science Ltd. All rights reserved.

The eyes of deep-sea fish II. Functional morphology of the retina

Three different aspects of the morphological organisation of deep-sea fish retinae are reviewed: First, questions of general cell biological relevance are addressed with respect to the development and proliferation patterns of photoreceptors, and problems associated with the growth of multibank retinae, and with outer segment renewal are discussed in situations where there is no direct contact between the retinal pigment epithelium and the tips of rod outer segments. The second part deals with the neural portion of the deep-sea fish retina. Cell densities are greatly reduced, yet neurohistochemistry demonstrates that all major neurotransmitters and neuropeptides found in other vertebrate retinae are also present in deep-sea fish. Quantitatively, convergence rates in unspecialised parts of the retina are similar to those in nocturnal mammals. The differentiation of horizontal cells makes it unlikely that species with more than a single visual pigment are capable of colour vision. In the third part. the diversity of deep-sea fish retinae is highlighted. Based on the topography of ganglion cells, species are identified with areae or foveae located in various parts of the retina, giving them a greatly improved spatial resolving power in specific parts of their visual fields. The highest degree of specialisation is found in tubular eyes. This is demonstrated in a case study of the scopelarchid retina, where as many as seven regions with different degrees of differentiation can be distinguished, ranging from an area giganto cellularis, regions with grouped rods to retinal diverticulum. (C) 1998 Elsevier Science Ltd. All rights reserved.

Analysis of small signal stability margins using genetic optimization

Power system small signal stability analysis aims to explore different small signal stability conditions and controls, namely: (1) exploring the power system security domains and boundaries in the space of power system parameters of interest, including load flow feasibility, saddle node and Hopf bifurcation ones; (2) finding the maximum and minimum damping conditions; and (3) determining control actions to provide and increase small signal stability. These problems are presented in this paper as different modifications of a general optimization to a minimum/maximum, depending on the initial guesses of variables and numerical methods used. In the considered problems, all the extreme points are of interest. Additionally, there are difficulties with finding the derivatives of the objective functions with respect to parameters. Numerical computations of derivatives in traditional optimization procedures are time consuming. In this paper, we propose a new black-box genetic optimization technique for comprehensive small signal stability analysis, which can effectively cope with highly nonlinear objective functions with multiple minima and maxima, and derivatives that can not be expressed analytically. The optimization result can then be used to provide such important information such as system optimal control decision making, assessment of the maximum network's transmission capacity, etc. (C) 1998 Elsevier Science S.A. All rights reserved.

Effects of interventions in health care settings on physical activity or cardiorespiratory fitness

Introduction: This paper reviews studies of physical activity interventions in health care settings to determine effects on physical activity and/or fitness and characteristics of successful interventions. Methods: Studies testing interventions to promote physical activity in health care settings for primary prevention (patients without disease) and secondary prevention (patients with cardiovascular disease [CVD]) were identified by computerized search methods and reference lists of reviews and articles. Inclusion criteria included assignment to intervention and control groups, physical activity or cardiorespiratory fitness outcome measures, and, for the secondary prevention studies, measurement 12 or more months after randomization. The number of studies with statistically significant effects was determined overall as well as for studies testing interventions with various characteristics. Results: Twelve studies of primary prevention were identified, seven of which were randomized. Three of four randomized studies with short-term measurement (4 weeks to 3 months after randomization), and two of five randomized studies with long-term measurement (6 months after randomization) achieved significant effects on physical activity. Twenty-four randomized studies of CVD secondary prevention were identified; 13 achieved significant effects on activity and/or fitness at twelve or more months. Studies with measurement at two time points showed decaying effects over time, particularly if the intervention were discontinued. Successful interventions contained multiple contacts, behavioral approaches, supervised exercise, provision of equipment, and/or continuing intervention. Many studies had methodologic problems such as low follow-up rates. Conclusion: Interventions in health care settings can increase physical activity for both primary and secondary prevention. Long-term effects are more likely with continuing intervention and multiple intervention components such as supervised exercise, provision of equipment, and behavioral approaches. Recommendations for additional research are given.

Finite element modelling of temperature gradient driven rock alteration and mineralization in porous rock masses

We present finite element simulations of temperature gradient driven rock alteration and mineralization in fluid saturated porous rock masses. In particular, we explore the significance of production/annihilation terms in the mass balance equations and the dependence of the spatial patterns of rock alteration upon the ratio of the roll over time of large scale convection cells to the relaxation time of the chemical reactions. Special concepts such as the gradient reaction criterion or rock alteration index (RAI) are discussed in light of the present, more general theory. In order to validate the finite element simulation, we derive an analytical solution for the rock alteration index of a benchmark problem on a two-dimensional rectangular domain. Since the geometry and boundary conditions of the benchmark problem can be easily and exactly modelled, the analytical solution is also useful for validating other numerical methods, such as the finite difference method and the boundary element method, when they are used to dear with this kind of problem. Finally, the potential of the theory is illustrated by means of finite element studies related to coupled flow problems in materially homogeneous and inhomogeneous porous rock masses. (C) 1998 Elsevier Science S.A. All rights reserved.

Architecture and morphogenesis of grain sorghum, Sorghum bicolor (L.) Moench

Plant architecture has been neglected in most studies of biomass allocation in crops. To help redress this situation for grain sorghum (Sorghum bicolor (L.) Moench), we used a 3D digitiser to measure the dimensions and orientations of vegetative and reproductive structures and derived thermal time-based functions for architectural changes during morphogenesis. Our plants, which were grown in a greenhouse, controlled environment cabinets and the field, covered a large, three-fold, size range when mature. This allowed us to detect some general architectural relationships and to fit morphogenetic functions common across the size range we observed. For example, the relationship between the lengths of successive fully-expanded leaves within a plant was nearly constant for all plants. The lengths of existing leaf blades were accurate predictors of the lengths of up to six subsequently-formed blades in our plants. Similar constant relationships were detected for internode lengths in the panicle and for heights above ground of the collars of successive leaves, even though these traits varied a lot between growth conditions. We suggest that such architectural relationships may be used to link the effect of previous growth conditions to future growth potential, and in that way to predict future partitioning. Our results provide the basis for a preliminary model of sorghum morphogenesis which could eventually become useful in conjunction with crop models by allowing resource acquisition to be related to changes in plant architecture during development. (C) 1999 Elsevier Science B.V. All rights reserved.

Injuries and noncommunicable diseases: emerging health problems of children in developing countries

The present article identifies, for children living in developing countries, the major causes of ill-health that are inadequately covered by established health programmes. Injuries and noncommunicable diseases, notably asthma, epilepsy, dental caries, diabetes mellitus and rheumatic heart disease, are growing in significance. In countries where resources are scarce it is to be expected that increasing importance will be attached to the development and implementation of measures against these problems. Their control may benefit from the application of elements of programmes directed against infectious, nutritional and perinatal disorders, which continue to predominate.

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.