Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

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.

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.

Structure and physical properties of [µ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘')iron(II)] Bis(hexafluorophosphate), a new Fe(II) spin-crossover compound with a three-dimensional threefold interlocked crystal lattice

[μ-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4‘)iron(II)] bis(hexafluorophosphate), [Fe(btzb)3](PF6)2, crystallizes in a three-dimensional 3-fold interlocked structure featuring a sharp two-step spin-crossover behavior. The spin conversion takes place between 164 and 182 K showing a discontinuity at about T1/2 = 174 K and a hysteresis of about 4 K between T1/2 and the low-spin state. The spin transition has been independently followed by magnetic susceptibility measurements, 57Fe-Mössbauer spectroscopy, and variable temperature far and midrange FTIR spectroscopy. The title compound crystallizes in the trigonal space group P30¯(No. 147) with a unit cell content of one formula unit plus a small amount of disordered solvent. The lattice parameters were determined by X-ray diffraction at several temperatures between 100 and 300 K. Complete crystal structures were resolved for 9 of these temperatures between 100 (only low spin, LS) and 300 K (only high spin, HS), Z = 1 [Fe(btzb)3](PF  6)2:  300 K (HS), a = 11.258(6) Å, c = 8.948(6) Å, V = 982.2(10) Å3; 100 K (LS), a = 10.989(3) Å, c = 8.702(2) Å, V = 910.1(4) Å3. The molecular structure consists of octahedral coordinated iron(II) centers bridged by six N4,N4‘ coordinating bis(tetrazole) ligands to form three 3-dimensional networks. Each of these three networks is symmetry related and interpenetrates each other within a unit cell to form the interlocked structure. The Fe−N bond lengths change between 1.993(1) Å at 100 K in the LS state and 2.193(2) Å at 300 K in the HS state. The nearest Fe separation is along the c-axis and identical with the lattice parameter c.

Structured engagement in the extended enterprise

Discusses the necessity for the conscious recognition of the phenomenon known as the extended enterprise; this demands that product, process and supply chain design are all considered simultaneously. Structure must be given to the extended enterprise in order to understand and manage it efficaciously. The authors discuss multiple perspectives for doing this, and employ the notions of “3-dimensional concurrent engineering” and “holonic thinking” for conceiving what the structure may look like. Describes a current “action research” project that is investigating potential lead-time reductions within an extended enterprise’s product introduction process. This aims to produce process visualisations, a framework for structuring and sychronising phases and stage-gates within the extended enterprise, and a new simulation tool which will provide a synthetic distributed hypermedia network. These deliverables will be used to play strategic “games” to explore problem issues within the product introduction process that belongs to the extended enterprise, develop teamwork across autonomous companies, and ultimately, contribute to the design of future extended enterprise supply chains.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Simulation based knowledge elicitation:effect of visual representation and model parameters

Since much knowledge is tacit, eliciting knowledge is a common bottleneck during the development of knowledge-based systems. Visual interactive simulation (VIS) has been proposed as a means for eliciting experts’ decision-making by getting them to interact with a visual simulation of the real system in which they work. In order to explore the effectiveness and efficiency of VIS based knowledge elicitation, an experiment has been carried out with decision-makers in a Ford Motor Company engine assembly plant. The model properties under investigation were the level of visual representation (2-dimensional, 2½-dimensional and 3-dimensional) and the model parameter settings (unadjusted and adjusted to represent more uncommon and extreme situations). The conclusion from the experiment is that using a 2-dimensional representation with adjusted parameter settings provides the better simulation-based means for eliciting knowledge, at least for the case modelled.

A CFD approach on the effect of particle size on char entrainment in bubbling fluidised bed reactors

The fluid – particle interaction inside a 41.7 mg s-1 fluidised bed reactor is modelled. Three char particles of sizes 500 µm, 250 µm, and 100 µm are injected into the fluidised bed and the momentum transport from the fluidising gas and fluidised sand is modelled. Due to the fluidising conditions and reactor design the char particles will either be entrained from the reactor or remain inside the bubbling bed. The particle size is the factor that differentiates the particle motion inside the reactor and their efficient entrainment out of it. A 3-Dimensional simulation has been performed with a completele revised momentum transport model for bubble three-phase flow according to the literature as an extension to the commercial finite volume code FLUENT 6.2.

Myopia: structural and functional correlates

Ocular dimensions are widely recognised as key variants of refractive error. Previously, accurate depiction of eye shape in vivo was largely restricted by limitations in the imaging techniques available. This thesis describes unique applications of the recently introduced 3-dimensional magnetic resonance imaging (MRI) approach to evaluate human eye shape in a group of young adult subjects (n=76) with a range of ametropia (MSE= -19.76 to +4.38D). Specific MRI derived parameters of ocular shape are then correlated with measures of visual function. Key findings include the significant homogeneity of ocular volume in the anterior eye for a range of refractive errors, whilst significant volume changes occur in the posterior eye as a function of ametropia. Anterior vs. posterior eye differences have also been shown through evaluations of equivalent spherical radius; the posterior 25% cap of the eye was shown to be relatively steeper in myopes compared to emmetropes. Further analyses showed differences in retinal quadrant profiles; assessments of the maximum distance from the retinal surface to the presumed visual axes showed exaggerated growth of the temporal quadrant in myopic eyes. Comparisons of retinal contour values derived from transformation of peripheral refraction data were made with MRI; flatter retinal curvature values were noted when using the MRI technique. A distinctive feature of this work is the evaluation of the relationship between ocular structure and visual function. Multiple aspects of visual function were evaluated through several vehicles: multifocal electroretinogram testing, visual field sensitivity testing, and the use of psychophysical methods to determine ganglion cell density. The results show that many quadrantic structural and functional variations exist. In general, the data could not demonstrate a significant correlation between visual function and associated measures of ocular conformation either within or between myopic and emmetropic groups.

Future of contact lens usage

I was recently part of a small committee looking at higher qualifications in contact lens practice and the discussion turned to future technologies. There was mention of different materials and different applications of contact lenses. Drug delivery with contact lenses was discussed as this has been talked about in the literature for a while. The first paper I could find that talked about using contact lenses for drug delivery dates back over 40 years. There was a review paper in CLAE in 2008 that looked specifically at this too [1]. However, where are these products? Why are we not seeing them in the market place? Maybe the technology is not quite there yet, or maybe patents are prohibiting usage or maybe the market is not big enough to develop such products? We do have lenses on the market with slow release of lubricating agents but not therapeutic agents used for ocular or systemic conditions. Contact lenses with pathogen detectors may be part of our contact lens armoury of the future and again we can already see papers in the literature that have trialled this technology for glucose monitoring in diabetics or lactate concentration in the tear film. Future contact lenses may incorporate better optics based on aberration control and we see this starting to emerge with aspheric designs designed to minimise spherical aberration. Irregular corneas can be fitted with topography based designs and again this technology exists and is being used by some manufacturers in their designs already. Moreover, the topography based fitting of irregular corneas is certainly something we see a lot of today and CLAE has seen many articles related to this over the last decade or so. What about further into the future? Well one interesting area must the 3-dimensional contact lenses, or contact lenses with electronic devices built in that simulate a display screen. A little like the virtual display spectacles that are already sold by electronics companies. It does not take much of a stretch of the imagination to see a large electronic company taking this technology on and making it viable. Will we see people on the train watching movies on these electronic virtual reality contact lenses? I think we will, but when is harder to know.

Thermal processing of miscanthus, sugarcane bagasse, sugarcane trash and their acid hydrolysis residues

The research presented in this thesis was developed as part of DIBANET, an EC funded project aiming to develop an energetically self-sustainable process for the production of diesel miscible biofuels (i.e. ethyl levulinate) via acid hydrolysis of selected biomass feedstocks. Three thermal conversion technologies, pyrolysis, gasification and combustion, were evaluated in the present work with the aim of recovering the energy stored in the acid hydrolysis solid residue (AHR). Mainly consisting of lignin and humins, the AHR can contain up to 80% of the energy in the original feedstock. Pyrolysis of AHR proved unsatisfactory, so attention focussed on gasification and combustion with the aim of producing heat and/or power to supply the energy demanded by the ethyl levulinate production process. A thermal processing rig consisting on a Laminar Entrained Flow Reactor (LEFR) equipped with solid and liquid collection and online gas analysis systems was designed and built to explore pyrolysis, gasification and air-blown combustion of AHR. Maximum liquid yield for pyrolysis of AHR was 30wt% with volatile conversion of 80%. Gas yield for AHR gasification was 78wt%, with 8wt% tar yields and conversion of volatiles close to 100%. 90wt% of the AHR was transformed into gas by combustion, with volatile conversions above 90%. 5volO2%-95vol%N2 gasification resulted in a nitrogen diluted, low heating value gas (2MJ/m3). Steam and oxygen-blown gasification of AHR were additionally investigated in a batch gasifier at KTH in Sweden. Steam promoted the formation of hydrogen (25vol%) and methane (14vol%) improving the gas heating value to 10MJ/m3, below the typical for steam gasification due to equipment limitations. Arrhenius kinetic parameters were calculated using data collected with the LEFR to provide reaction rate information for process design and optimisation. Activation energy (EA) and pre-exponential factor (ko in s-1) for pyrolysis (EA=80kJ/mol, lnko=14), gasification (EA=69kJ/mol, lnko=13) and combustion (EA=42kJ/mol, lnko=8) were calculated after linearly fitting the data using the random pore model. Kinetic parameters for pyrolysis and combustion were also determined by dynamic thermogravimetric analysis (TGA), including studies of the original biomass feedstocks for comparison. Results obtained by differential and integral isoconversional methods for activation energy determination were compared. Activation energy calculated by the Vyazovkin method was 103-204kJ/mol for pyrolysis of untreated feedstocks and 185-387kJ/mol for AHRs. Combustion activation energy was 138-163kJ/mol for biomass and 119-158 for AHRs. The non-linear least squares method was used to determine reaction model and pre-exponential factor. Pyrolysis and combustion of biomass were best modelled by a combination of third order reaction and 3 dimensional diffusion models, while AHR decomposed following the third order reaction for pyrolysis and the 3 dimensional diffusion for combustion.

On the impact of Cu dispersion on CO2 photoreduction over Cu/TiO2

A family of Cu/TiO2 catalysts was prepared using a refined sol–gel method, and tested in the photocatalytic reduction of CO2 by H2O to CH4 using a stirred batch, annular reactor. The resulting photoactivity was benchmarked against pure TiO2 nanoparticles (synthesised by an identical sol–gel route). CO2 photoreduction exhibited a strong volcano dependence on Cu loading, reflecting the transition from 2-dimensional CuOx nanostructures to 3-dimensional crystallites, with optimum CH4 production observed for 0.03 wt.% Cu/TiO2.

3D simulation of the effects of sphericity on char entrainment in fluidised beds

The paper presents a 3-dimensional simulation of the effect of particle shape on char entrainment in a bubbling fluidised bed reactor. Three char particles of 350 μm side length but of different shapes (cube, sphere, and tetrahedron) are injected into the fluidised bed and the momentum transport from the fluidising gas and fluidised sand is modelled. Due to the fluidising conditions, reactor design and particle shape the char particles will either be entrained from the reactor or remain inside the bubbling bed. The sphericity of the particles is the factor that differentiates the particle motion inside the reactor and their efficient entrainment out of it. The simulation has been performed with a completely revised momentum transport model for bubble three-phase flow, taking into account the sphericity factors, and has been applied as an extension to the commercial finite volume code FLUENT 6.3. © 2010 Elsevier B.V.All rights reserved.