A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

Optimization of physical distribution problem in logistics management

Physical distribution plays an imporant role in contemporary logistics management. Both satisfaction level of of customer and competitiveness of company can be enhanced if the distribution problem is solved optimally. The multi-depot vehicle routing problem (MDVRP) belongs to a practical logistics distribution problem, which consists of three critical issues: customer assignment, customer routing, and vehicle sequencing. According to the literatures, the solution approaches for the MDVRP are not satisfactory because some unrealistic assumptions were made on the first sub-problem of the MDVRP, ot the customer assignment problem. To refine the approaches, the focus of this paper is confined to this problem only. This paper formulates the customer assignment problem as a minimax-type integer linear programming model with the objective of minimizing the cycle time of the depots where setup times are explicitly considered. Since the model is proven to be MP-complete, a genetic algorithm is developed for solving the problem. The efficiency and effectiveness of the genetic algorithm are illustrated by a numerical example.

The limits of open innovation:openness and (quasi-)markets in the organization of innovation

Recent studies have stressed the importance of ‘open innovation’ as a means of enhancing innovation performance. The essence of the open innovation model is to take advantage of external as well as internal knowledge sources in developing and commercialising innovation, so avoiding an excessively narrow internal focus in a key area of corporate activity. Although the external aspect of open innovation is often stressed, another key aspect involves maximising the flow of ideas and knowledge from different sources within the firm, for example through knowledge sharing via the use of cross-functional teams. A fully open innovation approach would therefore combine both aspects i.e. cross-functional teams with boundary-spanning knowledge linkages. This suggests that there should be complementarities between the use cross-functional teams with boundary-spanning knowledge linkages i.e. the returns to implementing open innovation in one innovation activity is should be greater if open innovation is already in place in another innovation activity. However, our findings – based on a large sample of UK and German manufacturing plants – do not support this view. Our results suggest that in practice the benefits envisaged in the open innovation model are not generally achievable by the majority of plants, and that instead the adoption of open innovation across the whole innovation process is likely to reduce innovation outputs. Our results provide some guidance on the type of activities where the adoption of a market-based governance structure such as open innovation may be most valuable. This is likely to be in innovation activities where search is deterministic, activities are separable, and where the required level of knowledge sharing is correspondingly moderate – in other words those activities which are more routinized. For this type of activity market-based governance mechanisms (i.e. open innovation) may well be more efficient than hierarchical governance structures. For other innovation activities where outcomes are more uncertain and unpredictable and the risks of knowledge exchange hazards are greater, quasi-market based governance structures such as open innovation are likely to be subject to rapidly diminishing returns in terms of innovation outputs.

Evaluation of the quality and promotion of open learning materials

In the UK, Open Learning has been used in industrial training for at least the last decade. Trainers and Open Learning practitioners have been concerned about the quality of the products and services being delivered. The argument put forward in this thesis is that there is ambiguity amongst industrialists over the meanings of `Open Learning' and `Quality in Open Learning'. For clarity, a new definition of Open Learning is proposed which challenges the traditional learner-centred approach favoured by educationalists. It introduces the concept that there are benefits afforded to the trainer/employer/teacher as well as to the learner. This enables a focussed view of what quality in Open Learning really means. Having discussed these issues, a new quantitative method of evaluating Open Learning is proposed. This is based upon an assessment of the degree of compliance with which products meet Parts 1 & 2 of the Open Learning Code of Practice. The vehicle for these research studies has been a commercial contract commissioned by the Training Agency for the Engineering Industry Training Board (EITB) to examine the quality of Open Learning products supplied to the engineering industry. A major part of this research has been the application of the evaluation technique to a range of 67 Open Learning products (in eight subject areas). The findings were that good quality products can be found right across the price range - so can average and poor quality ones. The study also shows quite convincingly that there are good quality products to be found at less than 50. Finally the majority (24 out of 34) of the good quality products were text based.

Dynamic learning as entrepreneurial action in the context of open innovation:an instrumental case from a communities-of-practice perspective

Recent scholarly discussion on open innovation put forward the notion that an organisation's ability to internalise external knowledge and learn from various sources in undertaking new product development is crucial to its competitive performance. Nevertheless, little attention has been paid to how growth-oriented small firms identify and exploit entrepreneurial opportunities (i.e. take entrepreneurial action) related to such development, in an open innovation context, from a social learning perspective. This chapter, based on an instrumental case-firm, demonstrates analytically how learning as entrepreneurial action takes place, drawing on situated learning theory. It is argued that such learning is dynamic in nature and is founded on specific organising principles that foster both inter- and intracommunal learning. © 2012, IGI Global.

On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.

On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion

We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical investigations are presented both for the direct and inverse problems, and these results show in particular that the displacement vector on the boundary of the inclusion can be found in an accurate and stable way with small computational cost.

Governance of open content creation:a conceptualization and analysis of control and guiding mechanisms in the open content domain

The open content creation process has proven itself to be a powerful and influential way of developing text-based content, as demonstrated by the success of Wikipedia and related sites. Distributed individuals independently edit, revise, or refine content, thereby creating knowledge artifacts of considerable breadth and quality. Our study explores the mechanisms that control and guide the content creation process and develops an understanding of open content governance. The repertory grid method is employed to systematically capture the experiences of individuals involved in the open content creation process and to determine the relative importance of the diverse control and guiding mechanisms. Our findings illustrate the important control and guiding mechanisms and highlight the multifaceted nature of open content governance. A range of governance mechanisms is discussed with regard to the varied levels of formality, the different loci of authority, and the diverse interaction environments involved. Limitations and opportunities for future research are provided.

The use of open learning in the training of neurotechnologists:a regional case study

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Rutting-induced permeability loss of open graded friction course mixtures

Functionality of an open graded friction course (OGFC) depends on the high interconnected air voids or pores of the OGFC mixture. The authors' previous study indicated that the pores in the OGFC mixture were easily clogged by rutting deformation. Such a deformation-related clogging can cause a significant rutting-induced permeability loss in the OGFC mixture. The objective of this study was to control and reduce the rutting-induced permeability loss of the OGFC based on mixture design and layer thickness. Eight types of the OGFC mixtures with different air void contents, gradations, and nominal maximum aggregate sizes were fabricated in the laboratory. Wheel-tracking rutting tests were conducted on the OGFC slabs to simulate the deformation-related clogging. Permeability tests after different wheel load applications were performed on the rutted OGFC slabs using a falling head permeameter developed in the authors' previous study. The relationships between permeability loss and rutting depth as well as dynamic stability were developed based on the eight OGFC mixtures' test results. The thickness effects of the single-layer and the two-layer OGFC slabs were also discussed in terms of deformation-related clogging and the rutting-induced permeability loss. Results showed that the permeability coefficient decreases linearly with an increasing rutting depth of the OGFC mixtures. Rutting depth was recommended as a design index to control permeability loss of the OGFC mixture rather than the dynamic stability. Permeability loss due to deformation-related clogging can be effectively reduced by using a thicker single-layer OGFC or two-layer OGFC.

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.

Planar solid oxide fuel cell modeling and optimization targeting the stack's temperature gradient minimization

Minimization of undesirable temperature gradients in all dimensions of a planar solid oxide fuel cell (SOFC) is central to the thermal management and commercialization of this electrochemical reactor. This article explores the effective operating variables on the temperature gradient in a multilayer SOFC stack and presents a trade-off optimization. Three promising approaches are numerically tested via a model-based sensitivity analysis. The numerically efficient thermo-chemical model that had already been developed by the authors for the cell scale investigations (Tang et al. Chem. Eng. J. 2016, 290, 252-262) is integrated and extended in this work to allow further thermal studies at commercial scales. Initially, the most common approach for the minimization of stack's thermal inhomogeneity, i.e., usage of the excess air, is critically assessed. Subsequently, the adjustment of inlet gas temperatures is introduced as a complementary methodology to reduce the efficiency loss due to application of excess air. As another practical approach, regulation of the oxygen fraction in the cathode coolant stream is examined from both technical and economic viewpoints. Finally, a multiobjective optimization calculation is conducted to find an operating condition in which stack's efficiency and temperature gradient are maximum and minimum, respectively.

Modelling of transient heat transfer in annealing furnaces

This is a study of heat transfer in a lift-off furnace which is employed in the batch annealing of a stack of coils of steel strip. The objective of the project is to investigate the various factors which govern the furnace design and the heat transfer resistances, so as to reduce the time of the annealing cycle, and hence minimize the operating costs. The work involved mathematical modelling of patterns of gas flow and modes of heat transfer. These models are: Heat conduction and its conjectures in the steel coils;Convective heat transfer in the plates separating the coils in the stack and in other parts of the furnace; and Radiative and convective heat transfer in the furnace by using the long furnace model. An important part of the project is the development of numerical methods and computations to solve the transient models. A limited number of temperature measurements was available from experiments on a test coil in an industrial furnace. The mathematical model agreed well with these data. The model has been used to show the following characteristics of annealing furnaces, and to suggest further developments which would lead to significant savings: - The location of the limiting temperature in a coil is nearer to the hollow core than to the outer periphery. - Thermal expansion of the steel tends to open the coils, reduces their thermal conductivity in the radial direction, and hence prolongs the annealing cycle. Increasing the tension in the coils and/or heating from the core would overcome this heat transfer resistance. - The shape and dimensions of the convective channels in the plates have significant effect on heat convection in the stack. An optimal design of a channel is shown to be of a width-to-height ratio equal to 9. - Increasing the cooling rate, by using a fluidized bed instead of the normal shell and tube exchanger, would shorten the cooling time by about 15%, but increase the temperature differential in the stack. - For a specific charge weight, a stack of different-sized coils will have a shorter annealing cycle than one of equally-sized coils, provided that production constraints allow the stacking order to be optimal. - Recycle of hot flue gases to the firing zone of the furnace would produce a. decrease in the thermal efficiency up to 30% but decreases the heating time by about 26%.

Automated mapping of environmental variables from a SEIS or SISE perspective

The INTAMAP FP6 project has developed an interoperable framework for real-time automatic mapping of critical environmental variables by extending spatial statistical methods and employing open, web-based, data exchange protocols and visualisation tools. This paper will give an overview of the underlying problem, of the project, and discuss which problems it has solved and which open problems seem to be most relevant to deal with next. The interpolation problem that INTAMAP solves is the generic problem of spatial interpolation of environmental variables without user interaction, based on measurements of e.g. PM10, rainfall or gamma dose rate, at arbitrary locations or over a regular grid covering the area of interest. It deals with problems of varying spatial resolution of measurements, the interpolation of averages over larger areas, and with providing information on the interpolation error to the end-user. In addition, monitoring network optimisation is addressed in a non-automatic context.