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

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.

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.

Reconstruction of an unsteady flow from incomplete boundary data:Part I. Theory

Purpose – To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from knowledge of the velocity and fluid stress force given on a part of the boundary of a bounded domain. Design/methodology/approach – Earlier works have involved the similar problem but for stationary case (time-independent fluid flow). Extending these ideas a procedure is proposed and investigated also for the time-dependent case. Findings – The paper finds a novel variation method for the Cauchy problem. It proves convergence and also proposes a new boundary element method. Research limitations/implications – The fluid flow domain is limited to annular domains; this restriction can be removed undertaking analyses in appropriate weighted spaces to incorporate singularities that can occur on general bounded domains. Future work involves numerical investigations and also to consider Oseen type flow. A challenging problem is to consider non-linear Navier-Stokes equation. Practical implications – Fluid flow problems where data are known only on a part of the boundary occur in a range of engineering situations such as colloidal suspension and swimming of microorganisms. For example, the solution domain can be the region between to spheres where only the outer sphere is accessible for measurements. Originality/value – A novel variational method for the Cauchy problem is proposed which preserves the unsteady Stokes operator, convergence is proved and using recent for the fundamental solution for unsteady Stokes system, a new boundary element method for this system is also proposed.

The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

Using system dynamics in a discrete-event simulation study of a manufacturing plant

Purpose - To provide an example of the use of system dynamics within the context of a discrete-event simulation study. Design/methodology/approach - A discrete-event simulation study of a production-planning facility in a gas cylinder-manufacturing plant is presented. The case study evidence incorporates questionnaire responses from sales managers involved in the order-scheduling process. Findings - As the project progressed it became clear that, although the discrete-event simulation would meet the objectives of the study in a technical sense, the organizational problem of "delivery performance" would not be solved by the discrete-event simulation study alone. The case shows how the qualitative outcomes of the discrete-event simulation study led to an analysis using the system dynamics technique. The system dynamics technique was able to model the decision-makers in the sales and production process and provide a deeper understanding of the performance of the system. Research limitations/implications - The case study describes a traditional discrete-event simulation study which incorporated an unplanned investigation using system dynamics. Further, case studies using a planned approach to showing consideration of organizational issues in discrete-event simulation studies are required. Then the role of both qualitative data in a discrete-event simulation study and the use of supplementary tools which incorporate organizational aspects may help generate a methodology for discrete-event simulation that incorporates human aspects and so improve its relevance for decision making. Practical implications - It is argued that system dynamics can provide a useful addition to the toolkit of the discrete-event simulation practitioner in helping them incorporate a human aspect in their analysis. Originality/value - Helps decision makers gain a broader perspective on the tools available to them by showing the use of system dynamics to supplement the use of discrete-event simulation. © Emerald Group Publishing Limited.

Evaluating corporate performance:a critique of economic value added

There has been a revival of interest in economic techniques to measure the value of a firm through the use of economic value added as a technique for measuring such value to shareholders. This technique, based upon the concept of economic value equating to total value, is founded upon the assumptions of classical liberal economic theory. Such techniques have been subject to criticism both from the point of view of the level of adjustment to published accounts needed to make the technique work and from the point of view of the validity of such techniques in actually measuring value in a meaningful context. This paper critiques economic value added techniques as a means of calculating changes in shareholder value, contrasting such techniques with more traditional techniques of measuring value added. It uses the company Severn Trent plc as an actual example in order to evaluate and contrast the techniques in action. The paper demonstrates discrepancies between the calculated results from using economic value added analysis and those reported using conventional accounting measures. It considers the merits of the respective techniques in explaining shareholder and managerial behaviour and the problems with using such techniques in considering the wider stakeholder concept of value. It concludes that this economic value added technique has merits when compared with traditional accounting measures of performance but that it does not provide the universal panacea claimed by its proponents.

The spatial pattern of discrete beta-amyloid deposits in Alzheimer's disease reflects synaptic disconnection

The spatial pattern of discrete beta-amyloid (A beta) deposits was studied in the superficial laminae of cortical fields of different types and in the hippocampus in 6 cases of Alzheimer's disease (AD). In 41/42 tissues examined, discrete A beta deposits were aggregated into clusters and in 34/41 tissues (25/34 of the cortical tissues), there was evidence for a regular periodicity of the A beta deposit clusters parallel to the tissue boundary. The dimensions of the clusters varied from 400 to > 12,800 microns in different tissues. Although the A beta deposit clusters were larger than predicted, the regular periodicity suggests that they develop in relation to groups of cells associated with specific projections. This would be consistent with the hypothesis that the distribution of discrete A beta deposits in AD could reflect progressive synaptic disconnection along interconnected neuronal pathways. This implies that amyloid deposition could be a response to, rather than a cause of, synaptic disconnection in AD.

On the solution of a class of capital investment problems

In this work the solution of a class of capital investment problems is considered within the framework of mathematical programming. Upon the basis of the net present value criterion, the problems in question are mainly characterized by the fact that the cost of capital is defined as a non-decreasing function of the investment requirements. Capital rationing and some cases of technological dependence are also included, this approach leading to zero-one non-linear programming problems, for which specifically designed solution procedures supported by a general branch and bound development are presented. In the context of both this development and the relevant mathematical properties of the previously mentioned zero-one programs, a generalized zero-one model is also discussed. Finally,a variant of the scheme, connected with the search sequencing of optimal solutions, is presented as an alternative in which reduced storage limitations are encountered.

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.

An appraisal of employment problems and policies at the micro-economic level

This study has concentrated on the development of an impact simulation model for use at the sub-national level. The necessity for the development of this model was demonstrated by the growth of local economic initiatives during the 1970's, and the lack of monitoring and evaluation exercise to assess their success and cost-effectiveness. The first stage of research involved the confirmation that the potential for micro-economic and spatial initiatives existed. This was done by identifying the existence of involuntary structural unemployment. The second stage examined the range of employment policy options from the macroeconomic, micro-economic and spatial perspectives, and focused on the need for evaluation of those policies. The need for spatial impact evaluation exercise in respect of other exogenous shocks, and structural changes was also recognised. The final stage involved the investigation of current techniques of evaluation and their adaptation for the purpose in hand. This led to a recognition of a gap in the armoury of techniques. The employment-dependency model has been developed to fill that gap, providing a low-budget model, capable of implementation at the small area level and generating a vast array of industrially disaggregate data, in terms of employment, employment-income, profits, value-added and gross income, related to levels of United Kingdom final demand. Thus providing scope for a variety of impact simulation exercises.

The application of contact mechanics to the numerical simulation of particulate material

Particulate solids are complex redundant systems which consist of discrete particles. The interactions between the particles are complex and have been the subject of many theoretical and experimental investigations. Invetigations of particulate material have been restricted by the lack of quantitative information on the mechanisms occurring within an assembly. Laboratory experimentation is limited as information on the internal behaviour can only be inferred from measurements on the assembly boundary, or the use of intrusive measuring devices. In addition comparisons between test data are uncertain due to the difficulty in reproducing exact replicas of physical systems. Nevertheless, theoretical and technological advances require more detailed material information. However, numerical simulation affords access to information on every particle and hence the micro-mechanical behaviour within an assembly, and can replicate desired systems. To use a computer program to numerically simulate material behaviour accurately it is necessary to incorporte realistic interaction laws. This research programme used the finite difference simulation program `BALL', developed by Cundall (1971), which employed linear spring force-displacement laws. It was thus necessary to incorporate more realistic interaction laws. Therefore, this research programme was primarily concerned with the implementation of the normal force-displacement law of Hertz (1882) and the tangential force-displacement laws of Mindlin and Deresiewicz (1953). Within this thesis the contact mechanics theories employed in the program are developed and the adaptations which were necessary to incorporate these laws are detailed. Verification of the new contact force-displacement laws was achieved by simulating a quasi-static oblique contact and single particle oblique impact. Applications of the program to the simulation of large assemblies of particles is given, and the problems in undertaking quasi-static shear tests along with the results from two successful shear tests are described.

On the 'classification' of neurodegenerative disorders:discrete entities, overlap or continuum?

The traditional method of classifying neurodegenerative diseases is based on the original clinico-pathological concept supported by 'consensus' criteria and data from molecular pathological studies. This review discusses first, current problems in classification resulting from the coexistence of different classificatory schemes, the presence of disease heterogeneity and multiple pathologies, the use of 'signature' brain lesions in diagnosis, and the existence of pathological processes common to different diseases. Second, three models of neurodegenerative disease are proposed: (1) that distinct diseases exist ('discrete' model), (2) that relatively distinct diseases exist but exhibit overlapping features ('overlap' model), and (3) that distinct diseases do not exist and neurodegenerative disease is a 'continuum' in which there is continuous variation in clinical/pathological features from one case to another ('continuum' model). Third, to distinguish between models, the distribution of the most important molecular 'signature' lesions across the different diseases is reviewed. Such lesions often have poor 'fidelity', i.e., they are not unique to individual disorders but are distributed across many diseases consistent with the overlap or continuum models. Fourth, the question of whether the current classificatory system should be rejected is considered and three alternatives are proposed, viz., objective classification, classification for convenience (a 'dissection'), or analysis as a continuum.