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.

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.

A 2D [FeII-bistetrazole] coordination polymer exhibiting spin-crossover properties

The reaction of 1,3-bis(tetrazol-1-yl)-2-propanol (btzpol) with Fe(BF4)2 · 6H2O in acetonitrile yields the remarkable 2D coordination polymer [FeII(btzpol)1.8(btzpol-OBF3)1.2](BF4)0.8 · (H2O)0.8(CH3CN) (1). This compound has been structurally characterized using an X-ray single-crystal synchrotron radiation source. The iron(II) centers are bridged by means of double btzpol bridges along the c direction, and by single btzpol bridges along the b direction. The reaction of part of the ligand with the counterion has forced the compound to crystallize in this extended two dimensional structure. The compound shows spin-transition properties, both induced by temperature and light, with T½ = 112 K and T(LIESST) = 46 K, respectively. The relaxation of the metastable high-spin state created by irradiation is exponential, following an Arrhenius type behavior at high temperature, and dominated by a temperature independent tunneling process at lower temperatures.

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.

Toward the discovery of vaccine adjuvants:coupling in silico screening and in vitro analysis of antagonist binding to human and mouse CCR4 receptors

Background Adjuvants enhance or modify an immune response that is made to an antigen. An antagonist of the chemokine CCR4 receptor can display adjuvant-like properties by diminishing the ability of CD4+CD25+ regulatory T cells (Tregs) to down-regulate immune responses. Methodology Here, we have used protein modelling to create a plausible chemokine receptor model with the aim of using virtual screening to identify potential small molecule chemokine antagonists. A combination of homology modelling and molecular docking was used to create a model of the CCR4 receptor in order to investigate potential lead compounds that display antagonistic properties. Three-dimensional structure-based virtual screening of the CCR4 receptor identified 116 small molecules that were calculated to have a high affinity for the receptor; these were tested experimentally for CCR4 antagonism. Fifteen of these small molecules were shown to inhibit specifically CCR4-mediated cell migration, including that of CCR4+ Tregs. Significance Our CCR4 antagonists act as adjuvants augmenting human T cell proliferation in an in vitro immune response model and compound SP50 increases T cell and antibody responses in vivo when combined with vaccine antigens of Mycobacterium tuberculosis and Plasmodium yoelii in mice.

Purification and crystallization of the hydroxylase component of the methanesulfonate monooxygenase from Methylosulfonomonas methylovora strain M2

The aim of the work described in this paper was two-fold: (1) the purification of the hydroxylase component of the MSAMO to electrophoretic homogeneity using a four-step chromatographic strategy and (2) the crystallization of the two-component hydroxylase of the MSAMO in order to enhance our understanding of the precise three-dimensional structure of the MSAMO, thus yielding an insight into the nature of the active site of this enzyme. Optimised crystallization conditions were identified allowing growth of crystals of the hydroxylase component of the MSAMO within five days. Crystals exhibited a brown colour suggesting the presence on an intact Rieske-iron sulfur centre and diffracted to 7.0 Å when a few degrees of data were evaluated on a beam line X11. © 2006 Elsevier Inc. All rights reserved.

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.

Analysis of population dispersion in histological sections

Stereology and other image analysis methods have enabled rapid and objective quantitative measurements to be made on histological sections. These mesurements may include total volumes, surfaces, lengths and numbers of cells and blood vessels or pathological lesions. Histological features, however, may not be randomly distributed across a section but exhibit 'dispersion', a departure from randomness either towards regularity or aggregation. Information of population dispersion may be valuable not only in understanding the two-or three-dimensional structure but also in elucidating the pathogenesis of lesions in pathological conditions. This article reviews some of the statistical methods available for studying dispersion. These range from simple tests of whether the distribution of a histological faeture departs significantly from random to more complex methods which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters.

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.

Analytical techniques for the study of soft contact lens spoilation

Soft contact lens wear has become a common phenomenon in recent times. The contact lens when placed in the eye rapidly undergoes change. A film of biological material builds up on and in the lens matrix. The long term wear characteristics of the lens ultimately depend on this process. With time distinct structures made up of biological material have been found to build up on the lens. A fuller understanding of this process and how it relates to the lens chemistry could lead to contact lenses that are better tolerated by the eye. The tear film is a complex biological fluid, it is this fluid that bathes the lens during wear. It is reasonable to suppose that it is material derived from this source that accumulates on the lens. To understand this phenomenon it was decided to investigate the make up and conformation of the protein species that are found on and in the lens. As inter individual variations in tear fluid composition have been found it is important to be able to study the proteins on a single lens. Many of the analytical techniques used in bio research are not suitable for this study because of the lack of sensitivity. Work with poly acrylamide electrophoresis showed the possibility of analyzing the proteins extracted from a single lens. The development of a biotin avidin electro-blot and an enzyme linked aniibody electro-blot, lead to the high sensitivity detection and identification of the proteins present. The extraction of proteins from a lens is always incomplete. A method that analyses the proteins in situ would be a great advancement. Fourier transform infra red microscopy was developed to a point where a thin section of a contact lens could yield information about the proteins present and their conformation. The three dimensional structure of the gross macroscopic structures termed white spots was investigated using confocal laser microscopy.

Studies on the chromosomal bets-lactamase of pseudomonas aeruginosa

The chromosomal ß-lactamase of Pseudomonas aeruginosa SAlconst (a derepressed laboratory strain) was isolated and purified. Two peaks of activity were observed on gel permeation chromatography (one major peak mol. wt. 45 kD and one minor peak of 54 kD). Preparations from 12 clinical derepressed strains showed identical results. Chromosomal ß-lactamase production in both normal and derepressed P. aeruginosa strains was induced both by iron restricted growth conditions and by penicillin G. The majority of the enzyme (80-90%) was found in the periplasm and cytoplasm but a significant amount (2-20%) was associated with the outer membrane (OM). The growth conditions did not affect the distribution of the enzyme between subcellular fractions although higher activity was found in the cells grown under iron limitation and/ or in the presence of ß-lactams. The penicillanate sulphone inhibitor, tazobactam, displayed irreversible kinetics whilst cloxacillin, cefotaxime, ampicillin and penicillin G were all competitive inhibitors of the enzyme. Similar results were obtained for the Enterobacter cloacae P99 [ß-lactamase, but tazobactam displayed a non-classical kinetic pattern for the Staphylococcus aureus PC1 ß-lactamase. The residues involved in ß-lactam hydrolysis by the P aeruginosa SAlconst enzyme were detennined by affinity labelling with tazobactam. A tryptic digestion fragment of the inhibited enzyme contained the amino acids D, T, S, E, P, G, A, C, V, M, I, Y, F, H, K, R. This suggests the involvement of the conserved SVSK, DAE and KTG motifs found in all penicillin sensitive proteins. A model of the 3-D structure of the active site of the P aeruginosa SAlconst chromosomal ß-!actamase was constructed from the published amino acid sequence of P aeruginosa chromosomal ß-lactamase and the a-carbon coordinates of the S. aureus PCI ß-lactamase by homology modelling and energy minimisation. The crystal structure of tazobactam was determined and energy minimised. Computer graphics docking identified Ser 72 as a possible residue involved in a secondary attack on the C5 position of tazobactam after initial ß-lactam hydrolysis by serine 70. The enhanced activity of tazobactam over sulbactam might be explained by the triazole substituent which might participate in favourable hydrogen bonding between N3 and active site residues.