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.

Analytical solution for the Mollow and Autler-Townes probe absorption spectra of a three-level atom in a squeezed vacuum

The Mellow and Autler-Townes probe absorption spectra of a three-level atom in a cascade configuration with the lower transition coherently driven and also coupled to a narrow bandwidth squeezed-vacuum field are studied. Analytical studies of the modifications caused by the finite squeezed-vacuum bandwidth to the spectra are made for the case when the Rabi frequency of the driving field is much larger than the natural linewidth. The squeezed vacuum center frequency and the driving laser frequency are assumed equal. We show that the spectral features depend on the bandwidth of a squeezed vacuum field and whether the sources of the squeezing field are degenerate (DPA) or nondegenerate (NDPA) parametric amplifiers. In a broadband or narrow bandwidth squeezed vacuum generated by a NDPA, the central component of the Mellow spectrum can be significantly narrower than that in the normal vacuum. When the source of the squeezed vacuum is a DPA, the central feature is insensitive to squeezing. The Rabi sidebands, however, can be significantly narrowed only in the squeezed vacuum produced by the DPA. The two lines of the Autler-Townes absorption spectrum can be narrowed only in a narrow bandwidth squeezed vacuum, whereas they are independent of the phase and are always broadened in a broadband squeezed vacuum.

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.

A state-contingent production approach to principal-agent problems with an application to point-source pollution control

Two basic representations of principal-agent relationships, the 'state-space' and 'parameterized distribution' formulations, have emerged. Although the state-space formulation appears more natural, analytical studies using this formulation have had limited success. This paper develops a state-space formulation of the moral-hazard problem using a general representation of production under uncertainty. A closed-form solution for the agency-cost problem is derived. Comparative-static results are deduced. Next we solve the principal's problem of selecting the optimal output given the agency-cost function. The analysis is applied to the problem of point-source pollution control. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

Red Parkes quasars: Evidence for soft X-ray absorption

The Parkes Half-Jansky Flat-Spectrum Sample contains a large number of sources with unusually red optical-to-near-infrared (NIR) continua. If this is to be interpreted as extinction by dust in the line of sight, then associated material might also give rise to absorption in the soft X-ray regime. This hypothesis is tested using broadband (0.1-2.4 keV) data from the ROSAT All-Sky Survey. Significant (>3 sigma confidence level) correlations between the optical (and NIR)-to-soft X-ray continuum slope and optical extinction are found in the data, consistent with absorption by material with metallicity and a range in the gas-to-dust ratio as observed in the local ISM. Under this simple model, the soft X-rays are absorbed at a level consistent with the range of extinctions (0 < A(V) < 6 mag) implied by the observed optical reddening. Excess X-ray absorption by warm (ionized) gas, (i.e., a warm absorber) is not required by the data.

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 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.

Absorption spectrum of a strongly driven atom in a detuned squeezed vacuum

We present numerical and analytical results for the Mollow probe absorption spectrum of a coherently driven two-level system in a narrow bandwidth squeezed vacuum field. The spectra are calculated for the case where the Rabi frequency of the driving field is much larger than the natural linewidth and the squeezed vacuum carrier frequency is detuned from the driving laser frequency. The driving laser is on resonance. We show that in a detuned squeezed vacuum the standard Mellow features are each split into triplets. The central components of each triplet are weakly dependent on the squeezing phase but the sidebands strongly depend on the phase and can have dispersive or absorptive/emissive profiles. We also derive approximate analytical expressions for the spectral features and find that the multi-peak structure of the spectrum can be interpreted either via the eigenfrequencies of a generalized Floquet Hamiltonian or in terms of three-photon transitions between dressed stales involving a probe field photon and a correlated photon pair from the squeezed vacuum field.

Absorption of sunscreens across human skin: an evaluation of commercial products for children and adults

Aims Topical sunscreens are routinely applied to the skin by a large percentage of the population. This study assessed the extent of absorption of a number of common chemical sunscreen agents into and through human skin following application of commercially available products. Methods Sunscreen products were applied to excised human epidermis in Franz diffusion cells with the amount penetrating into and across the epidermis assessed by h.p.l.c. for 8 h following application. Results All sunscreen agents investigated penetrated into the skin (0.25 g m(-2) or 14% of applied dose), but only benzophenone-3 passed through the skin in significant amounts (0.08 g m(-2) or 10% of the applied dose). With one exception, suncreen agents in corresponding products marketed for adults and children had similar skin penetration profiles. Conclusions Whilst limited absorption across the skin was observed for the majority of the sunscreens tested, benzophenone-3 demonstrated sufficiently high penetration to warrant further investigation of its continued application.

Calcium absorption in postmenopausal osteoporosis: Benefit of HRT plus calcitriol, but not HRT alone, in both malabsorbers and normal absorbers

In a randomized trial involving 71 postmenopausal osteoporotic women with vertebral compression fractures, radiocalcium absorption studies using the Ca-45 single isotope method (alpha) were performed at baseline and after 8 months of treatment with either continuous combined hormone replacement therapy (HRT, as piperazine estrone sulfate 0.625-0.937mg daily +/- medroxyprogesterone acetate 2.5 mg daily depending on uterine status) or HRT plus calcitriol 0.25 mu g twice daily. A calcium supplement of 600 mg nocte was given to only those women who had a daily calcium intake of less than 1 g per day at baseline, as assessed by recalled dietary intake. There was a significant decrease 0.74 (+/- 0.35 SD) to 0.58 (+/- 0.22), Delta alpha = -0.17 (+/- 0.26), p<0.0005] in alpha at 8 months compared with baseline in the HRT-treated group, but a significant increase [0.68 (+/- 0.31) to 0.84 (+/- 0.27), Delta alpha = +0.16 (+/- 0.30), p<0.003] in the HRT-plus-calcitriol treated patients, resulting in alpha being significantly higher after 8 months in the latter group than in the HRT-only group. Although 72% of the patients had been supplemented with calcium between the first and second studies, separate analyses revealed that the change in calcium intake had not affected the result. Further breakdown of the groups into baseline 'normal' absorbers (alpha greater than or equal to 0.55) and 'malabsorbers' (alpha <0.55) revealed that alpha decreased with HRT treatment only in the normal absorbers, and remained stable in the malabsorbers. Conversely, following HRT plus calcitriol treatment, alpha increased only in the malabsorbers, the normal absorbers in this group remaining unchanged. In conclusion, our data show that HRT, of the type and dose used in this study, did not produce an increase in absorption efficiency; it was in fact associated with a fall. increased absorption efficiency cannot be achieved unless calcitriol is used concurrently, and then only in patients with malabsorption. Calcitriol also had a significant effect in normal absorbers in that it prevented the decline in alpha seen with HRT alone, and thus should be considered in all patients with postmenopausal osteoporosis treated with HRT.

Mothers' mental illness and child behavior problems: Cause-effect association or observation bias

Objective: A number, of studies have consistently found that a mother's mental health (particularly her level of depression) is a strong predictor of mental health problems experienced by her child(ren). However, the validity of this finding is in doubt because the majority of these studies have relied on maternal reports as indicators of children's behavior. Method: This prospective, longitudinal study examines data an the mental health of the mother from prior to the birth of her child to when the child reaches 14 years of age. Child behavior is measured at 14 years of age using reports from mother and child. Mother and child responses are compared to provide an indication of the possible magnitude of maternal observation bias in the reporting of child behavior problems. Results: Anxious and/or depressed mothers tend to report more cases of child behavior problems than do their mentally healthy counterparts or children themselves. Differences between mothers and youths In reporting behavior problems appear to be related to the mothers' mental health. Conclusions: Current maternal mental health impairment appears to have a substantial effect on the reporting of child behavior problems by the mother, thereby raising questions about the validity of reports of child behavior by persons who are currently emotionally distressed.

X-ray absorption and phase contrast imaging to study the interplay between plant roots and soil structure

Plant performance is, at least partly, linked to the location of roots with respect to soil structure features and the micro-environment surrounding roots. Measurements of root distributions from intact samples, using optical microscopy and field tracings have been partially successful but are imprecise and labour-intensive. Theoretically, X-ray computed micro-tomography represents an ideal solution for non-invasive imaging of plant roots and soil structure. However, before it becomes fast enough and affordable or easily accessible, there is still a need for a diagnostic tool to investigate root/soil interplay. Here, a method for detection of undisturbed plant roots and their immediate physical environment is presented. X-ray absorption and phase contrast imaging are combined to produce projection images of soil sections from which root distributions and soil structure can be analyzed. The clarity of roots on the X-ray film is sufficient to allow manual tracing on an acetate sheet fixed over the film. In its current version, the method suffers limitations mainly related to (i) the degree of subjectivity associated with manual tracing and (ii) the difficulty of separating live and dead roots. The method represents a simple and relatively inexpensive way to detect and quantify roots from intact samples and has scope for further improvements. In this paper, the main steps of the method, sampling, image acquisition and image processing are documented. The potential use of the method in an agronomic perspective is illustrated using surface and sub-surface soil samples from a controlled wheat trial. Quantitative characterization of root attributes, e.g. radius, length density, branching intensity and the complex interplay between roots and soil structure, is presented and discussed.

Hybrid modelling of coupled pore fluid-solid deformation problems

A hybrid formulation for coupled pore fluid-solid deformation problems is proposed. The scheme is a hybrid in the sense that we use a vertex centered finite volume formulation for the analysis of the pore fluid and a particle method for the solid in our model. The pore fluid formally occupies the same space as the solid particles. The size of the particles is not necessarily equal to the physical size of materials. A finite volume mesh for the pore fluid flow is generated by Delaunay triangulation. Each triangle possesses an initial porosity. Changes of the porosity are specified by the translations of the mass centers of particles. Net pore pressure gradients are applied to the particle centers and are considered in the particle momentum balance. The potential of our model is illustrated by means of a simulation of coupled fracture and fluid flow developed in porous rock under biaxial compression condition.