A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

An iterative method for a Cauchy problem for the heat equation

An iterative method for reconstruction of the solution to a parabolic initial boundary value problem of second order from Cauchy data is presented. The data are given on a part of the boundary. At each iteration step, a series of well-posed mixed boundary value problems are solved for the parabolic operator and its adjoint. The convergence proof of this method in a weighted L2-space is included.

An iterative method for reconstruction of temperature

An iterative method for the reconstruction of a stationary three-dimensional temperature field, from Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L 2-space is include

Creating and managing value in collaborative networks

This is a theoretical paper that examines the interplay between individual and collective capabilities and competencies and value transactions in collaborative environments. The theory behind value creation is examined and two types of value are identified, internal value (Shareholder value) and external value (Value proposition). The literature on collaborative enterprises/network is also examined with particular emphasis on supply chains, extended/virtual enterprises and clusters as representatives of different forms and maturities of collaboration. The interplay of value transactions and competencies and capabilities are examined and discussed in detail. Finally, a model is presented which consists of value transactions and a table which compares the characteristics of different types of collaborative enterprises/networks. It is proposed that this model presents a platform for further research to develop an in-depth understanding into how value may be created and managed in collaborative enterprises/networks.

Time complexity and convergence analysis of domain theoretic Picard method

We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by Edalat and Pattinson [1]. Compared to Edalat and Pattinson's implementation, our algorithm uses a more efficient arithmetic based on an arbitrary precision floating-point library. Despite the additional overestimations due to floating-point rounding, we obtain a similar bound on the convergence rate of the produced approximations. Moreover, our convergence analysis is detailed enough to allow a static optimisation in the growth of the precision used in successive Picard iterations. Such optimisation greatly improves the efficiency of the solving process. Although a similar optimisation could be performed dynamically without our analysis, a static one gives us a significant advantage: we are able to predict the time it will take the solver to obtain an approximation of a certain (arbitrarily high) quality.

The effect of flow regimes in the distillation of systems containing two liquid phases

Single phase solutions containing three components have been observed to exhibit foaminess near a single to two liquid phase boundary. It was seen, in a sintered plate column under mass transfer conditions, that distillation systems where the liquid appeared as one phase in one part of a column and two phases in another part, exhibited foaminess when the liquid concentration was near the one phase to two phase boundary. Various ternary systems have been studied in a 50 plate. 30mm i.d. Oldershaw column and it was observed that severe foaming occurred in the middle section of the column near the one liquid phase to two liquid phase boundary and no foaming occurred at the end of the column where liquid was either one phase or two phase. This is known as Ross type foam. Mass transfer experiments with Ross type ternary systems have been carried out in a perspex simulator with small and large hole diameter trays. It was observed that by removal of the more volatile component, Ross type foam did not build up on the tray. Severe entrainment of liquid was observed in all cases leading to a 'dry' tray, even with a low free area small diameter hole tray which was expected to produce a bubbly mixture. Entrainment was more severe for high gas superficial velocities and large hole diameters. This behaviour is quite different from the build up of foam observed when one liquid phase/two liquid phase Ross systems were contacted with air above a small sintered disc or with vapour in an Oldershaw distillation column. This observation explains why distillation columns processing mixtures which change from one liquid phase to two liquid phases (or vice versa) must be severely derated to avoid flooding. Single liquid phase holdups at the spray to bubbly transition were measured using a perspex simulator similar to that of Porter & Wong (17). i.e. with no liquid cross flow. A light transmission technique was used to measure the transition from spray regime to bubbly regime. The effect of tray thickness and the ratio of hole diameter to tray thickness on the transition was evaluated using trays of the same hole diameter and free area but having thickness of 2.38 mm, 4 mm, and 6.35 mm. The liquid holdup at the transition was less with the thin metal trays. This result may be interpreted by the theory of Lockett (101), which predicts the transition liquid holdup in terms of the angle of the gas iet leaving the holes in the sieve plate. All the existing correlations have been compared and none were found to be satisfactory and these correlations have been modified in view of the experimental results obtained. A new correlation has been proposed which takes into account the effect of the hole diameter to tray thickness ratio on the transition and good agreement was obtained between the experimental results and the correlated values of the liquid holdup at the transition. Results have been obtained for two immiscible liquids [kerosene and water] on trays to determine whether foaming can be eliminated by operating in the spray regime. Kerosene was added to a fixed volume of water or water was added to a fixed volume of kerosene. In both cases, there was a transition from spray to bubbly. In the water fixed system. the liquid holdup at the transition was slightly less than the pure kerosene system. Whilst for the kerosene fixed system, the transition occurred at much lower liquid holdups. Trends In the results were similar to those for single liquid phase. New correlations have been proposed for the two cases. It has been found that Ross type foams, observed in a sintered plate column and in the Oldershaw column can be eliminated by either carrying out the separation in a packed column or by the addition of defoaming additives.

Political representation in France: a crisis of democracy?

The past two decades have witnessed growing political disaffection and a widening mass/elite disjuncture in France, reflected in opinion polls, rising abstentionism, electoral volatility and fragmentation, with sustained voting against incumbent governments. Though the electoral system has preserved the duopoly of the mainstream coalitions, they have suffered loss of public confidence and swings in electoral support. Stable parliamentary majorities conceal a political landscape of assorted anti-system parties and growing support for far right and far left. The picture is paradoxical: the French express alienation from political parties yet relate positively to their political institutions; they berate national politicians but retain strong bonds with those elected locally; they appear increasingly disengaged from politics yet forms of ‘direct democracy’ are finding new vigour. While the electoral, attitudinal and systemic factors reviewed here may not signal a crisis of democracy, they point to serious problems of political representation in contemporary France.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Integrated component scheduling models for chip shooter machines

This paper focuses on minimizing printed circuit board (PCB) assembly time for a chipshootermachine, which has a movable feeder carrier holding components, a movable X–Y table carrying a PCB, and a rotary turret with multiple assembly heads. The assembly time of the machine depends on two inter-related optimization problems: the component sequencing problem and the feeder arrangement problem. Nevertheless, they were often regarded as two individual problems and solved separately. This paper proposes two complete mathematical models for the integrated problem of the machine. The models are verified by two commercial packages. Finally, a hybrid genetic algorithm previously developed by the authors is presented to solve the model. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total assembly time.

Appearance of bound states in random potentials with applications to soliton theory

We analyze the stochastic creation of a single bound state (BS) in a random potential with a compact support. We study both the Hermitian Schrödinger equation and non-Hermitian Zakharov-Shabat systems. These problems are of special interest in the inverse scattering method for Korteveg–de-Vries and the nonlinear Schrödinger equations since soliton solutions of these two equations correspond to the BSs of the two aforementioned linear eigenvalue problems. Analytical expressions for the average width of the potential required for the creation of the first BS are given in the approximation of delta-correlated Gaussian potential and additionally different scenarios of eigenvalue creation are discussed for the non-Hermitian case.

Properties and performance of polymer modified cements and mortars

Polymer modified cements and mortars have become popular for use as patch repair materials. General evidence suggests that these materials offer considerable improvements compared to traditional mortars although the mechanisms for this are not fully understood. This work elucidates the factors which govern some properties and performance of different polymer systems. In view of the wide range of commercial systems available, investigations concentrated on the use of three of the most commonly available groups of polymers. These were: (1) Styrene Butadiene Rubber (SBR), (2) Acrylics and, (3) Ethylene Vinyl Acetates (EVA). The later two were in the form of both emulsions and redispersible powders. Experiments concentrated on: (1) Rheological behaviour of polymer modified cement pastes; (2) Workability of polymer modified mortars; (3) Influence of curing conditions on the pore size distribution and diffusion of chloride ions; (4) Bond strength of polymer modified cement and mortar patches; and (5) Microscopic examination and semi-quantitative analyses of the bulk and interfacial microstructures. The following main conclusions were reached: (1) The addition of polymer emulsions have a considerable influence on the workability of fresh cement pastes, the extent of this depending on the type of system used. (2) The rheological parameters of fresh polymer modified mortars can be established using a two-point workability test which may be used when comparing the properties of different systems at constant workability. (3) Curing conditions affect the properties of polymer modified systems and a wet/dry curing regime was essential for good adhesion of these materials to mortar substrates. (4) In contrast, the wet/dry curing regime resulted in a curing affected zone at the surface of patch materials. This can result in a much coarser pore structure and enhanced diffusion of e.g. chloride ions. (5) The microstructure of polymer modified systems was very different compared with the unmodified cement/mortar and varied depending on curing conditions.

Ethanol intake of paediatric intensive care patients

Background - Limiting the amount of alcohol in children's medicines is advisable but as alcohol is the second most common solvent used in liquid preparations, paediatric patients with increased medication intake may be exposed to a considerable alcohol intake. Few medicines are specifically designed for children in Paediatric Intensive Care (PICU), and therefore adult formulations are frequently administered, with high medication use further exposing a PICU patient to undesired alcohol intake. Aims - This small pilot study aimed to examiine the intake of a sample of PICU patients, highlight common medicines used on PICU containing alcohol, provide alternatives where possible and where alternatives are not possible, provide the prescriber with a list of the higher alcohol containing medicines. Method - A retrospective medication chart review was undertaken as a two point snap shot. Data collected included age, weight, medications prescribed and the formulations used at time of the study. The patients' sedation score was recorded. The electronic medicine compendium (EMC) was consulted for any ethanol content for the commercially available products. The manufacturer was contacted for ethanol content of all ‘specials’ and any commercial products found to contain ethanol from the EMC. The PICU patient's daily intake of ethanol was calculated. The calculation was converted to an adult equivalent alcohol unit intake and although this method of conversion is crude and does not take physiological differences of adult and children into account, it was done in order to provide the clinician with commonly used terminology in deciding the risk to the patient. Results - Twenty-eight patients were prescribed a range of 69 different medications. Of the 69 medicines, 12 products were found to contain ethanol. Patient ages ranged from a 26 week premature infant to 15 years old, weights ranges from 0.7 kg to 45 kg. Only 2 out of the 28 patients did not receive ethanol containing medications, and most patients were prescribed at least two medicines containing ethanol. Daily ethanol intake uncorrected for weight ranged from 0.006 ml to 2.18 ml (median 0.26 ml). Converting this to adult units per week, alcohol intake ranged from 0.07 to 15.2 units (median 1.4 units). The two patients receiving above 15 units/week adult equivalent were prescribed an oral morphine weaning regimen, therefore the high alcohol exposure was short term. The most common drugs prescribed containing alcohol were found to be nystatin, ranitidine, furosemide and morphine. No commercially available alcohol-free oral liquid preparations were found for ranitidine, furosemide or morphine at the time of the study. Correlation of the sedation score against ethanol intake was difficult to analyse as most patients were actively sedated. Conclusions - Polypharmacy in PICU patients increases the exposure to alcohol. Some commercially available medicines provide excessive ethanol intake, providing the clinician with ethical, potentially economical dilemmas of prescribing an unlicensed medicine to minimise ethanol exposure. Further research is required to evaluate the scope of the problem, effects of exposure and provision of alcohol free formulations.

Disaster risk reduction infrastructure requirements for South-Western Bangladesh:perspectives of local communities

Purpose: Development of effective disaster risk reduction (DRR) strategies for communities at risk of being affected by natural disasters is considered essential, especially in the wake of devastating disaster events reported worldwide. As part of a wider research study investigating community perspectives on existing and potential strategies for enhancing resilience to natural disasters, community perspectives on infrastructure and structural protection requirements were investigated. The paper aims to discuss these issues. Design/methodology/approach: Patuakhali region in South-Western Bangladesh is a region significantly at risk of multiple natural hazards. In order to engage local communities and obtain their perspectives, focus group discussions were held with local community leaders and policy makers of at-risk communities in Patuakhali region, South-Western Bangladesh. Findings: Infrastructure and structural protection requirements highlighted included multi-purpose cyclone shelters, permanent embankments and improved transport infrastructure. Much of the discussions of focus group interviews were focused on cyclone shelters and embankments, suggesting their critical importance in reducing disaster risk and also dependence of coastal communities on those two measures. Originality/value: The research design adopted sought to answer the research questions raised and also to inform local policy makers on community perspectives. Local policy makers involved in DRR initiatives in the region were informed of community perspectives and requirements, thus contributing to community engagement in implementing DRR activities.

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.