Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

Optimal input states and feedback for interferometric phase estimation

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2 for states considered bq previous authors. We prove, that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However. we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above N-2. With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of N-1. For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

The management of rice grown on raised beds with continuous furrow irrigation

A field experiment compared two rice (Oryza sativa L.) cropping systems: paddy or raised beds with continuous furrow irrigation; and trialled four cultivars: Starbonnet, Lemont, Amaroo and Ceysvoni, and one test line YRL39; that may vary in adaptation to growth on raised beds. The grain yield of rice ranged from 740 to 1250 g/m(2) and was slightly greater in paddy than on raised beds. Although there were early growth responses to fertilizer nitrogen on raised beds, the crop nitrogen content at maturity mostly exceeded 20 g/m(2) in both systems, so nitrogen was unlikely to have limited yield. Ceysvoni yielded best in both systems, a result of good post-anthesis growth and larger grain size, although its whole-grain mill-out percentage was poor relative to the other cultivars. Starbonnet and Lemont yielded poorly on raised beds, associated with too few tillers and too much leaf area. When grown on raised beds all cultivars experienced a delay in anthesis resulting in more tillers, leaf area and dry weight at anthesis, and probably a greater yield potential. The growth of rice after anthesis, however, was similar on raised beds and in paddy, so reductions in harvest index and grain size on raised beds were recorded. The data indicated that water supply was not a major limitation to rice growth on raised beds, but slower crop development was an issue that would affect the use of raised beds in a cropping system, especially in rice-growing areas where temperatures are too cool for optimal crop development. (C) 2001 Elsevier Science B.V. All rights reserved.

Pediculus humanus capitis infestations in the community: A pilot study into transmission, treatment and factors affecting control

Head lice (Pediculus humanus capitis) infestations affect schoolchildren worldwide, creating social, economic and health consequences for families. Problems with self-detection, chronic infestations and classroom transmission are compounded by increasing resistance of the lice to pediculicides. Public health strategies are based on limited research and little is known about transmission dynamics. Mismanagement and transmission in the general community are blamed for control failure. The purpose of this study was to explore community head-lice experience in Brisbane, Australia, and to identify critical factors underlying control failure. A home-based pilot survey used physical examination to verify transmission and treatment patterns which were self-reported by a group of trace-contact families in addition to other unconnected participants. The survey was enlarged to further compare therapy outcomes and suspected risk factors. The findings reinforce those of previous studies - that children attending school and early childhood centres, and subsequently their families, are most at risk of contracting pediculosis capitis, and some may carry lice for years. First-line (pediculicidal) treatment and even additional physical methods of hand-picking and fine-toothed combing usually fail to eradicate lice quickly and completely (overall cure-rate 39 per cent, n = 84 cases). Failures were linked to hair characteristics. Public education alone may not control pediculosis. Accurate diagnosis requires considerable experience; a strong case exists for returning to institutional surveillance.

A phylogeny for the genus Isoodon and a range extension for I-obesulus peninsulae based on mtDNA control region and morphology

Short-nosed bandicoots, Isoodon, have undergone marked range contractions since European colonisation of Australia and are currently divided into many subspecies, the validity of which is debated. Discriminant function analysis of morphology and a phylogeny of Isoodon based on mtDNA control region sequences indicate a clear split between two of the three recognised species, I. macrourus and I. obesulus/auratus. However, while all previously recognised taxa within the I. obesulus/auratus group are morphologically distinct, I. auratus and I. obesulus are not phylogenetically distinct for mtDNA. The genetic divergence between I. obesulus and I. auratus (2.6%) is similar to that found among geographic isolates of the former (I. o. obesulus and I. o. peninsulae: 2.7%). Further, the divergence between geographically close populations of two different species (I. o. obesulus from Western Australia and I. a. barrowensis: 1.2%) is smaller than that among subspecies within I. auratus (I. a. barrowensis and I. auratus from northern Western Australia: 1.7%). A newly discovered population of Isoodon in the Lamb Range, far north Queensland, sympatric with a population of I. m. torosus, is shown to represent a range extension of I. o. peninsulae (350 km). It seems plausible that what is currently considered as two species, I. obesulus and I. auratus, was once one continuous species now represented by isolated populations that have diverged morphologically as a consequence of adaptation to the diverse environments that occur throughout their range. The taxonomy of these populations is discussed in relation to their morphological distinctiveness and genetic similarity.

The application of statistical process control charts to the detection and monitoring of hospital-acquired infections

The monitoring of infection control indicators including hospital-acquired infections is an established part of quality maintenance programmes in many health-care facilities. However, surveillance data use can be frustrated by the infrequent nature of many infections. Traditional methods of analysis often provide delayed identification of increasing infection occurrence, placing patients at preventable risk. The application of Shewhart, Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) statistical process control charts to the monitoring of indicator infections allows continuous real-time assessment. The Shewhart chart will detect large changes, while CUSUM and EWMA methods are more suited to recognition of small to moderate sustained change. When used together, Shewhart and EWMA methods are ideal for monitoring bacteraemia and multiresistant organism rates. Shewhart and CUSUM charts are suitable for surgical infection surveillance.

Quality Assurance Through a Continuous Curriculum Review (CCR) Strategy: Reflections on a Pilot Project

Institutional research can be defined as "the activity in which the research effort of an academic institution is directed at the solution of its own problems and to the enhancement of its own performance" (Woodward, 1993, p. 113). This paper describes and reflects on an attempt at the University of Queensland to address the need for course quality appraisal for improvement. The strategy, Continuous Curriculum Review (CCR) is simply an attempt to trial and promote regular comprehensive data collection for developing 'snapshot' views of whole curricula so that decisions about what to change and what to change first can be made in an empirically defensible and timely manner. The strategy and reporting protocols that were developed are described, and the costs and benefits of engaging in this kind of data gathering exercise for quality assurance and quality enhancement purposes are discussed.

Transient mesenteric ischaemic episodes tracked by continuous jejunal PCO2 monitoring during liquid feeding

Objective: To test the effect of liquid feeds on the responses to splanchnic ischaemia of a continuous rapid response PCO2 sensor inserted in the jejunum. Design: Prospective experimental animal study in a university research laboratory. Subjects: Adult male Wistar rats. Interventions: Adult male Wistar rats (285-425 g) were anaethetised with sodium pentobarbitone 60 mg/ kg i.p. and ventilated with 100 % oxygen and isoflurane via tracheostomy to a PaCO2 of 30-40 mmHg. A sensor was inserted into the mid-jejunum to record PCO2 every second. Distal aortic pressure was transduced. Four control rats received no feeds whilst in another four rats liquid feed was infused into the proximal jejunum at 3 ml/h. In each rat five episodes of splanchnic ischaemia were induced by 2-min elevations of an aortic sling to a mean distal aortic pressure of 30 mmHg. Measurements and main results: PCO2 elevations were always detectable, usually less than a minute from the onset of splanchnic ischaemia in both fed and unfed rats, with no difference in mean times to detectable response. In the fed rats there was a small but significant increase in the time to peak sensor response (196 +/- 16 vs. 180 +/- 12 s) and a trend towards an elevated mean baseline luminal PCO2 (67 +/- 9 vs. 55 +/- 4 mmHg). Conclusions: Brief episodes of splanchnic ischaemia were tracked successfully by a rapid response jejunal continuous PCO2 sensor during the infusion of a proprietary liquid feed preparation despite minor changes in PCO2 response characteristics and a possible elevation in baseline luminal PCO2.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Economic and environmental impacts of pollution control in a system of environment and economic interdependence

The importance of the rate of change of the pollution stock in determining the damage to the environment has been an issue of increasing concern in the literature. This paper uses a three-sector (economy, population and environment), non-linear, discrete time, calibrated model to examine pollution control. The model explicitly links economic growth to the health of the environment. The stock of natural resources is affected by the rate of pollution flows, through their impact on the regenerative capacity of the natural resource stock. This can shed useful insights into pollution control strategies, particularly in developing countries where environmental resources are crucial for production in many sectors of the economy. Simulation exercises suggested that, under plausible assumptions, it is possible to reverse undesirable transient dynamics through pollution control expenditure, but this is dependent upon the strategies used for control. The best strategy is to spend money fostering the development of production technologies that reduce pollution rather than spending money dealing with the effects of the pollution flow into the environment. (C) 2001 Elsevier Science Ltd. All rights reserved.

A hedging point strategy - balancing effluent quality, economy and robustness in the control of wastewater treatment plants

An operational space map is an efficient tool to compare a large number of operational strategies to find an optimal choice of setpoints based on a multicriterion. Typically, such a multicriterion includes a weighted sum of cost of operation and effluent quality. Due to the relative high cost of aeration such a definition of optimality result in a relatively high fraction of the effluent total nitrogen in the form of ammonium. Such a strategy may however introduce a risk into operation because a low degree of ammonium removal leads to a low amount of nitrifiers. This in turn leads to a reduced ability to reject event disturbances, such as large variations in the ammonium load, drop in temperature, the presence of toxic/inhibitory compounds in the influent etc. Hedging is a risk minimisation tool, with the aim to "reduce one's risk of loss on a bet or speculation by compensating transactions on the other side" (The Concise Oxford Dictionary (1995)). In wastewater treatment plant operation hedging can be applied by choosing a higher level of ammonium removal to increase the amount of nitrifiers. This is a sensible way to introduce disturbance rejection ability into the multi criterion. In practice, this is done by deciding upon an internal effluent ammonium criterion. In some countries such as Germany, a separate criterion already applies to the level of ammonium in the effluent. However, in most countries the effluent criterion applies to total nitrogen only. In these cases, an internal effluent ammonium criterion should be selected in order to secure proper disturbance rejection ability.

Control of chaotic motion in a dual-spin spacecraft with nutational damping

Control of chaotic vibrations in a dual-spin spacecraft with an axial nutational damper is achieved using two techniques. The control methods are implemented on two realistic spacecraft parameter configurations that have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude motion and, consequently, could have disastrous effects on its operation. The two control methods, recursive proportional feedback and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamic systems. Each technique is outlined and the effectiveness on this model compared and contrasted. Numerical simulations are performed, and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents, and bifurcation diagrams.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.