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.

Novel biodegradable fibres for applications in tissue engineering and drug delivery

The preparation and characterisation of novel biodegradable polymer fibres for application in tissue engineering and drug delivery are reported. Poly(e-caprolactone) (PCL) fibres were produced by wet spinning from solutions in acetone under low shear (gravity flow) conditions. The tensile strength and stiffness of as-spun fibres were highly dependent on the concentration of the spinning solution. Use of a 6% w/v solution resulted in fibres having strength and stiffness of 1.8 MPa and 0.01 GPa respectively, whereas these values increased to 9.9 MPa and 0.1 GPa when fibres were produced from 20% w/v solutions. Cold drawing to an extension of 500% resulted in further increases in fibre strength (up to 50 MPa) and stiffness (0.3 GPa). Hot drawing to 500% further increased the fibre strength (up to 81 MPa) and stiffness (0.5 GPa). The surface morphology of as-spun fibres was modified, to yield a directional grooved pattern by drying in contact with a mandrel having a machined topography characterised by a peak-peak separation of 91 mm and a peak height of 30 mm. Differential scanning calorimetery (DSC) analysis of as-spun fibres revealed the characteristic melting point of PCL at around 58°C and a % crystallinity of approximately 60%. The biocompatibility of as-spun fibres was assessed using cell culture. The number of attached 3T3 Swiss mouse fibroblasts, C2C12 mouse myoblasts and human umbilical vein endothelial cells (HUVECs) on as-spun, 500% cold drawn, and gelatin coated PCL fibres were observed. The results showed that the fibres promoted cell proliferation for 9 days in cell culture and was slightly lower than on tissue culture plastic. The morphology of all cell lines was assessed on the various PCL fibres using scanning electron microscopy. The cell function of HUVECs growing on the as-spun PCL fibres was evaluated. The ability HUVECs to induce an immune response when stimulated with lipopolysaccaride (LPS) and thereby to increase the amount of cell surface receptors was assessed by flow cytometry and reverse transcription-polymerase chain reaction (RT-PCR). The results showed that PCL fibres did not inhibit this function compared to TCP. As-spun PCL fibres were loaded with 1 % ovine albumin (OVA) powder, 1% OVA nanoparticles and 5% OVA nanoparticles by weight and the protein release was assessed in vitro. PCL fibres loaded with 1 % OVA powder released 70%, 1% OVA nanoparticle released 60% and the 5% OVA nanoparticle released 25% of their protein content over 28 days. These release figures did not alter when the fibres were subjected to lipase enzymatic degradation. The OVA released was examined for structural integrity by SDS-PAGE. This showed that the protein molecular weight was not altered after incorporation into the fibres. The bioactivity of progesterone was assessed following incorporation into PCL fibres. Results showed that the progesterone released had a pronounced effect on MCF-7 breast epithelial cells, inhibiting their proliferation. The PCL fibres display high fibre compliance, a potential for controlling the fibre surface architecture to promote contact guidance effects, favorable proliferation rate of fibroblasts, myoblasts and HUVECs and the ability to release pharmaceuticals. These properties recommended their use for 3-D scaffold production in soft tissue engineering and the fibres could also be exploited for controlled presentation and release of biopharmaceuticals such as growth factors.

Applications of Reissner's principle to structural dynamics

The analysis and prediction of the dynamic behaviour of s7ructural components plays an important role in modern engineering design. :n this work, the so-called "mixed" finite element models based on Reissnen's variational principle are applied to the solution of free and forced vibration problems, for beam and :late structures. The mixed beam models are obtained by using elements of various shape functions ranging from simple linear to complex cubic and quadratic functions. The elements were in general capable of predicting the natural frequencies and dynamic responses with good accuracy. An isoparametric quadrilateral element with 8-nodes was developed for application to thin plate problems. The element has 32 degrees of freedom (one deflection, two bending and one twisting moment per node) which is suitable for discretization of plates with arbitrary geometry. A linear isoparametric element and two non-conforming displacement elements (4-node and 8-node quadrilateral) were extended to the solution of dynamic problems. An auto-mesh generation program was used to facilitate the preparation of input data required by the 8-node quadrilateral elements of mixed and displacement type. Numerical examples were solved using both the mixed beam and plate elements for predicting a structure's natural frequencies and dynamic response to a variety of forcing functions. The solutions were compared with the available analytical and displacement model solutions. The mixed elements developed have been found to have significant advantages over the conventional displacement elements in the solution of plate type problems. A dramatic saving in computational time is possible without any loss in solution accuracy. With beam type problems, there appears to be no significant advantages in using mixed models.

The structural properties of glassfibre reinforced plastics

The research work described in this thesis is concerned with the development of glassfibre reinforced plastics for structural uses in Civil Engineering construction. The first stage was primarily concerned with the design of GRP lamintes with structura1 properties and method of manufacture suitable for use with relatively large structural components. A cold setting, pressure moulding technique was developed which proved to be efficient in reducing the void content in the composite and minimising the exothermic effect due to curing. The effect of fibre content and fibre arrangement on strength and stiffness of the cornposite was studied and the maximum amount of' fibre content that could be reached by the adopted type of moulding technique was determined. The second stage of the project was concerned with the introduction of steel-wire "sheets" into the GRP cornposites, to take advantage of the high modulus of steel wire to improve the GRP stiffness and to reduce deformation. The experimental observations agreed reasonably well with theoretical predictions in both first and second stages of the work. The third stage was concerned with studying the stability of GRP flat rectangular plates subjected to uniaxial compression or pure shear, to simulate compression flanges or shear webs respectively. The investigation was concentrated on the effect of fibre arrangement in the plate on buckling load. The effect of the introduction of steel-wire sheets on the plate stability in compression was also investigated. The boundary conditions were chosen to be close to those usually assumed in built-up box-sections for both compression flanges and webs. The orthotropic plate and the mid-plane symmetric were used successfully in predicting the buckling load theoretically. In determining the buckling load experimentally, two methods were used. The Southwell plot method and electrical strain gauge method. The latter proved to be more reliable in predicting the buckling load than the former, especially for plates under uniaxial compression. Sample design charts for GRP plates that yield and buckle simultaneously under compression are also presented in the thesis. The final stage of the work dealt with the design and test of GRP beams. The investigation began by finding the optimum cross-section for a GRP beam. The cross-section which was developed was a thin walled corrugated section which showed higher stiffness than other cross-sections for the same cross-sectional area (i.e. box, I, and rectangular sections). A cold setting, hand layings technique was used in manufacturing these beams wbich were of nine types depending on the type of glass reinforcement employed and the arrangement of layers in the beam. The simple bending theory was used in the beam design and proved to be satisfactory in predicting the stresses and deflections. A factor of safety of 4 was chosen for design purposes and considered to be suitable for long term use under static load. Because of its relatively low modulus, GRP beams allowable deflection was limited to 1/120th of the span which was found to be adequate for design purposes. A general discussion of the behaviour of GRP composites and their place relative to the more conventional structural material was also presented in the thesis.

Structural characterisation of hypoxia-mimicking bioactive glasses

Nickel and cobalt are both known to stimulate the hypoxia-inducible factor-1 (HIF-1a), thus significantly improving blood vessel formation in tissue engineering applications. We have manufactured nickel and cobalt doped bioactive glasses to act as a controlled delivery mechanism of these ions. The resultant structural consequences have been investigated using the methods of isotopic and isomorphic substitution applied to neutron diffraction. The structural sites present will be intimately related to their release properties in physiological fluids such as plasma and saliva, and hence the bioactivity of the material. Detailed structural knowledge is therefore a prerequisite for optimising material design. Results show that nickel and cobalt adopt a mixed structural role within these bioactive glasses occupying both network-forming (tetrahedral) and network-modifying (5-fold) geometries. Two thirds of the Ni (or Co) occupies a five-fold geometry with the remaining third in a tetrahedral environment. A direct comparison of the primary structural correlations (e.g. Si-O, Ca-O, Na-O and O-Si-O) between the archetypal 45S5 Bioglass® and the Ni and Co glasses studied here reveal no significant differences. This indicates that the addition of Ni (or Co) will have no adverse effects on the existing structure, and thus on in vitro/in vivo dissolution rates and therefore bioactivity of these glasses.

Using genetic programming and decision trees for generating structural descriptions of four bar mechanisms

Four bar mechanisms are basic components of many important mechanical devices. The kinematic synthesis of four bar mechanisms is a difficult design problem. A novel method that combines the genetic programming and decision tree learning methods is presented. We give a structural description for the class of mechanisms that produce desired coupler curves. Constructive induction is used to find and characterize feasible regions of the design space. Decision trees constitute the learning engine, and the new features are created by genetic programming.

Dispersion engineering of highly nonlinear chalcogenide suspended-core fibers

Chalcogenide optical fibers are currently undergoing intensive investigation with the aim of exploiting the excellent glass transmission and nonlinear characteristics in the near- and mid-infrared for several applications. Further enhancement of these properties can be obtained, for a particular application, with optical fibers specifically designed that are capable of providing low effective area together with a properly tailored dispersion, matching the characteristics of the laser sources used to excite nonlinear effects. Suspended-core photonic crystal fibers are ideal candidates for nonlinear applications, providing small-core waveguides with large index contrast and tunable dispersion. In this paper, the dispersion properties of As2S3 suspended-core fibers are numerically analyzed, taking into account, for the first time, all the structural parameters, including the size and the number of the glass bridges. The results show that a proper design of the cladding struts can be exploited to significantly change the fiber properties, altering the maximum value of the dispersion parameter and shifting the zero-dispersion wavelengths over a range of 400 nm.