Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

Case-based reasoning enabling database mining for cryo-preserving algae applications

Case-based Reasoning's (CBR) origins were stimulated by a desire to understand how people remember information and are in turn reminded of information, and that subsequently it was recognized that people commonly solve problems by remembering how they solved similar problems in the past. Thus CBR became an appropriate way to find out the most suitable solution method for a new problem based on the old methods for the same or even similar problems. The research highlights how to use CBR to aid biologists in finding the best method to cryo preserve algae. The study found CBR could be used successfully to find the similarity percentage between the new algae and old cases in the case base. The prediction result showed approximately 93.75% accuracy, which proves the CBR system can offer appropriate recommendations for most situations. © 2011 IEEE.

Knowledge management in a New Zealand tree farming company:Ambiguity and resistance to the "technology solution"

Purpose - Managers at the company attempt to implement a knowledge management information system in an attempt to avoid loss of expertise while improving control and efficiency. The paper seeks to explore the implications of the technological solution to employees within the company. Design/methodology/approach - The paper reports qualitative research conducted in a single organization. Evidence is presented in the form of interview extracts. Findings - The case section of the paper presents the accounts of organizational participants. The accounts reveal the workers' reactions to the technology-based system and something of their strategies of resistance to the system. These accounts also provide glimpses of the identity construction engaged in by these knowledge workers. The setting for the research is in a knowledge-intensive primary industry. Research was conducted through observation and interviews. Research limitations/implications - The issues identified are explored in a single case-study setting. Future research could look at the relevance of the findings to other settings. Practical implications - The case evidence presented indicates some of the complexity of implementation of information systems in organizations. This could certainly be seen as more evidence of the uncertainty associated with organizational change and of the need for managers not to expect an easy adoption of intrusive IT solutions. Originality/value - This paper adds empirical insight to a largely conceptual literature. © Emerald Group Publishing Limited.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

A finite-element method for the solution of turbine-generation end-zone fields

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Stability analysis of tree structured decision functions

In multicriteria decision problems many values must be assigned, such as the importance of the different criteria and the values of the alternatives with respect to subjective criteria. Since these assignments are approximate, it is very important to analyze the sensitivity of results when small modifications of the assignments are made. When solving a multicriteria decision problem, it is desirable to choose a decision function that leads to a solution as stable as possible. We propose here a method based on genetic programming that produces better decision functions than the commonly used ones. The theoretical expectations are validated by case studies. © 2003 Elsevier B.V. All rights reserved.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Canonical solution groups of a homomorphism : manipulator kinematics, nonparametric regression and distributed object systems

The kinematic mapping of a rigid open-link manipulator is a homomorphism between Lie groups. The homomorphisrn has solution groups that act on an inverse kinematic solution element. A canonical representation of solution group operators that act on a solution element of three and seven degree-of-freedom (do!) dextrous manipulators is determined by geometric analysis. Seven canonical solution groups are determined for the seven do! Robotics Research K-1207 and Hollerbach arms. The solution element of a dextrous manipulator is a collection of trivial fibre bundles with solution fibres homotopic to the Torus. If fibre solutions are parameterised by a scalar, a direct inverse funct.ion that maps the scalar and Cartesian base space coordinates to solution element fibre coordinates may be defined. A direct inverse pararneterisation of a solution element may be approximated by a local linear map generated by an inverse augmented Jacobian correction of a linear interpolation. The action of canonical solution group operators on a local linear approximation of the solution element of inverse kinematics of dextrous manipulators generates cyclical solutions. The solution representation is proposed as a model of inverse kinematic transformations in primate nervous systems. Simultaneous calibration of a composition of stereo-camera and manipulator kinematic models is under-determined by equi-output parameter groups in the composition of stereo-camera and Denavit Hartenberg (DH) rnodels. An error measure for simultaneous calibration of a composition of models is derived and parameter subsets with no equi-output groups are determined by numerical experiments to simultaneously calibrate the composition of homogeneous or pan-tilt stereo-camera with DH models. For acceleration of exact Newton second-order re-calibration of DH parameters after a sequential calibration of stereo-camera and DH parameters, an optimal numerical evaluation of DH matrix first order and second order error derivatives with respect to a re-calibration error function is derived, implemented and tested. A distributed object environment for point and click image-based tele-command of manipulators and stereo-cameras is specified and implemented that supports rapid prototyping of numerical experiments in distributed system control. The environment is validated by a hierarchical k-fold cross validated calibration to Cartesian space of a radial basis function regression correction of an affine stereo model. Basic design and performance requirements are defined for scalable virtual micro-kernels that broker inter-Java-virtual-machine remote method invocations between components of secure manageable fault-tolerant open distributed agile Total Quality Managed ISO 9000+ conformant Just in Time manufacturing systems.

Antimicrobial efficacy of chlorhexidine digluconate alone and in combination with eucalyptus oil, tea tree oil and thymol against planktonic and biofilm cultures of Staphylococcus epidermidis

Objectives Effective skin antisepsis and disinfection of medical devices are key factors in preventing many healthcare-acquired infections associated with skin microorganisms, particularly Staphylococcus epidermidis. The aim of this study was to investigate the antimicrobial efficacy of chlorhexidine digluconate (CHG), a widely used antiseptic in clinical practice, alone and in combination with tea tree oil (TTO), eucalyptus oil (EO) and thymol against planktonic and biofilm cultures of S. epidermidis. Methods Antimicrobial susceptibility assays against S. epidermidis in a suspension and in a biofilm mode of growth were performed with broth microdilution and ATP bioluminescence methods, respectively. Synergy of antimicrobial agents was evaluated with the chequerboard method. Results CHG exhibited antimicrobial activity against S. epidermidis in both suspension and biofilm (MIC 2–8 mg/L). Of the essential oils thymol exhibited the greatest antimicrobial efficacy (0.5–4 g/L) against S. epidermidis in suspension and biofilm followed by TTO (2–16 g/L) and EO (4–64 g/L). MICs of CHG and EO were reduced against S. epidermidis biofilm when in combination (MIC of 8 reduced to 0.25–1 mg/L and MIC of 32–64 reduced to 4 g/L for CHG and EO, respectively). Furthermore, the combination of EO with CHG demonstrated synergistic activity against S. epidermidis biofilm with a fractional inhibitory concentration index of <0.5. Conclusions The results from this study suggest that there may be a role for essential oils, in particular EO, for improved skin antisepsis when combined with CHG.

Hairpin vortex solution in planar Couette flow: a tapestry of knotted vortices

A numerical continuation method has been carried out seeking solutions for two distinct flow configurations, planar Couette flow (PCF) and laterally heated flow in a vertical slot (LHF). We found that the spanwise vortex solution in LHF identifies a new solution in PCF. The vortical structure of our new solution has the shape of a hairpin observed ubiquitously in high-Reynolds-number turbulent flow, and we believe this discovery may provide the paradigm for a hierarchical organization of coherent structures in turbulent shear layers.

Expert systems for fault tree synthesis

Hazard and operability (HAZOP) studies on chemical process plants are very time consuming, and often tedious, tasks. The requirement for HAZOP studies is that a team of experts systematically analyse every conceivable process deviation, identifying possible causes and any hazards that may result. The systematic nature of the task, and the fact that some team members may be unoccupied for much of the time, can lead to tedium, which in turn may lead to serious errors or omissions. An aid to HAZOP are fault trees, which present the system failure logic graphically such that the study team can readily assimilate their findings. Fault trees are also useful to the identification of design weaknesses, and may additionally be used to estimate the likelihood of hazardous events occurring. The one drawback of fault trees is that they are difficult to generate by hand. This is because of the sheer size and complexity of modern process plants. The work in this thesis proposed a computer-based method to aid the development of fault trees for chemical process plants. The aim is to produce concise, structured fault trees that are easy for analysts to understand. Standard plant input-output equation models for major process units are modified such that they include ancillary units and pipework. This results in a reduction in the nodes required to represent a plant. Control loops and protective systems are modelled as operators which act on process variables. This modelling maintains the functionality of loops, making fault tree generation easier and improving the structure of the fault trees produced. A method, called event ordering, is proposed which allows the magnitude of deviations of controlled or measured variables to be defined in terms of the control loops and protective systems with which they are associated.

Using interior point algorithms for the solution of linear programs with special structural features

Linear Programming (LP) is a powerful decision making tool extensively used in various economic and engineering activities. In the early stages the success of LP was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is reported here. The preconditional conjugate gradient method is one of the most powerful tools for the solution of the least square problem, present in every iteration of all interior point methods. The effect of using different preconditioners on a range of problems with various condition numbers is presented. Decomposition algorithms has been one of the main fields of research in linear programming over the last few years. After reviewing the latest decomposition techniques, three promising methods were chosen the implemented. Sparsity is again a consideration and suggestions have been included to allow improvements when solving problems with these methods. Finally, experimental results on randomly generated data are reported and compared with an interior point method. The efficient implementation of the decomposition methods considered in this study requires the solution of quadratic subproblems. A review of recent work on algorithms for convex quadratic was performed. The most promising algorithms are discussed and implemented taking sparsity into account. The related performance of these algorithms on randomly generated separable and non-separable problems is also reported.

Exact solution of the Bragg-diffraction problem in sillenites

A method for the exact solution of the Bragg-difrraction problem for a photorefractive grating in sillenite crystals based on Pauli matrices is proposed. For the two main optical configurations explicit analytical expressions are found for the diffraction efficiency and the polarization of the scattered wave. The exact solution is applied to a detailed analysis of a number of particular cases. For the known limiting cases there is agreement with the published results.

The appraisal and management of multi-storey dwelling blocks using large concrete panel systems

This exploratory study is concerned with the integrated appraisal of multi-storey dwelling blocks which incorporate large concrete panel systems (LPS). The first step was to look at U.K. multi-storey dwelling stock in general, and under the management of Birmingham City Council in particular. The information has been taken from the databases of three departments in the City of Birmingham, and rearranged in a new database using a suite of PC software called `PROXIMA' for clarity and analysis. One hundred of their stock were built large concrete panel system. Thirteen LPS blocks were chosen for the purpose of this study as case-studies depending mainly on the height and age factors of the block. A new integrated appraisal technique has been created for the LPS dwelling blocks, which takes into account the most physical and social factors affecting the condition and acceptability of these blocks. This appraisal technique is built up in a hierarchical form moving from the general approach to particular elements (a tree model). It comprises two main approaches; physical and social. In the physical approach, the building is viewed as a series of manageable elements and sub-elements to cover every single physical or environmental factor of the block, in which the condition of the block is analysed. A quality score system has been developed which depends mainly on the qualitative and quantitative conditions of each category in the appraisal tree model, and leads to physical ranking order of the study blocks. In the social appraisal approach, the residents' satisfaction and attitude toward their multi-storey dwelling block was analysed in relation to: a. biographical and housing related characteristics; and b. social, physical and environmental factors associated with this sort of dwelling, block and estate in general.The random sample consisted of 268 residents living in the 13 case study blocks. Data collected was analysed using frequency counts, percentages, means, standard deviations, Kendall's tue, r-correlation coefficients, t-test, analysis of variance (ANOVA) and multiple regression analysis. The analysis showed a marginally positive satisfaction and attitude towards living in the block. The five most significant factors associated with the residents' satisfaction and attitude in descending order were: the estate, in general; the service categories in the block, including heating system and lift services; vandalism; the neighbours; and the security system of the block. An important attribute of this method, is that it is relatively inexpensive to implement, especially when compared to alternatives adopted by some local authorities and the BRE. It is designed to save time, money and effort, to aid decision making, and to provide ranked priority to the multi-storey dwelling stock, in addition to many other advantages. A series of solution options to the problems of the block was sought for selection and testing before implementation. The traditional solutions have usually resulted in either demolition or costly physical maintenance and social improvement of the blocks. However, a new solution has now emerged, which is particularly suited to structurally sound units. The solution of `re-cycling' might incorporate the reuse of an entire block or part of it, by removing panels, slabs and so forth from the upper floors in order to reconstruct them as low-rise accommodations.

A method for automatically eliciting node weights in a hierarchical knowledge-based structure for reasoning with uncertainty

Hierarchical knowledge structures are frequently used within clinical decision support systems as part of the model for generating intelligent advice. The nodes in the hierarchy inevitably have varying influence on the decisionmaking processes, which needs to be reflected by parameters. If the model has been elicited from human experts, it is not feasible to ask them to estimate the parameters because there will be so many in even moderately-sized structures. This paper describes how the parameters could be obtained from data instead, using only a small number of cases. The original method [1] is applied to a particular web-based clinical decision support system called GRiST, which uses its hierarchical knowledge to quantify the risks associated with mental-health problems. The knowledge was elicited from multidisciplinary mental-health practitioners but the tree has several thousand nodes, all requiring an estimation of their relative influence on the assessment process. The method described in the paper shows how they can be obtained from about 200 cases instead. It greatly reduces the experts’ elicitation tasks and has the potential for being generalised to similar knowledge-engineering domains where relative weightings of node siblings are part of the parameter space.