The vibrational spectra of rectangular plates

The wire drive pulse-echo system has been extensively used to excite and measure modes of vibration of thin rectangular plates. The frequency spectra of different modes have been investigated as a function of the material elastic moduli and the plate geometry. Most of the work was carried out on isotropic materials. For square plates a wide selection of materials were used. These were made isotropic in their in-plane dimensions where the displacements are taking place. The range of rnaterials enabled the dependence on Poisson's ratio to be investigated. A method of determining the value of Poisson's ratio resulted from this investigation. Certain modes are controlled principally by the shear modulus. Of these the fundamental has two nodal lines across the plate surface. One of them, which has nodes at the corners, (the Lame mode) is uniquely a pure shear mode where the diagonal is a full wave length. One controlled by the Young's modulus has been found. The precise harmonic relationship of the Lame mode series in square and rectangular plates was established. Use of the Rayleigh-Lamb equation has extended the theoretical support. The low order modes were followed over a wide range of sides ratios. Two fundamental types of modes have been recognised; These are the longitudinal modes where the frequency is controlled by the length of the plate only and the 2~f product has an asymptotic value approaching the rod velocity. The other type is the in-plane flexural modes (in effect a flexurally vibrating bar where the -2/w is the geometrical parameter). Where possible the experimental work was related to theory. Other modes controlled by the width dimension of the plate were followed. Anisotropic materials having rolled sheet elastic symmetry were investigated in terms of the appropriate theory. The work has been extended to examine materials from welds in steel plates.

Enzymatic stabilization of gelatin-based scaffolds

The definitive goal of this research is to develop protein-based scaffolds for use in soft tissue regeneration, particularly in the field of dermal healing. The premise of this investigation was to characterize the mechanical properties of gelatin cross-linked with microbial transglutaminase (mTGase) and to investigate the cytocompatibility of mTGase cross-linked gelatin. Dynamic rheological analysis revealed a significant increase in the storage modulus and thermal stability of gelatin after cross-linking with mTGase. Static, unconfined compression tests showed an increase in Young's modulus of gelatin gels after mTGase cross-linking. A comparable increase in gel strength was observed with 0.03% mTGase and 0.25% glutaraldehyde cross-linked gelatin gels. In vitro studies using 3T3 fibroblasts indicated cytotoxicity at a concentration of 0.05% mTGase after 72 h. However, no significant inhibition of cell proliferation was seen with cells grown on lower concentrations of mTGase cross-linked gelatin substrates. The mechanical improvement and cytocompatibility of mTGase cross-linked gelatin suggests mTGase has potential for use in stabilizing gelatin gels for tissue-engineering applications.

Theoretical studies of the mid-latitude ionosphere

Following a brief description of the atmosphere and ionosphere in Chapter I we describe how the equations of continuity and momentum for 0+, H+, He+, 0++ are derived from the formulations of St-Maurice and Schunk(1977) and Quegan et al.(1981) in Chapter II. In Chapter III we investigate the nature of the downward flow of protons in a collapsing post-sunset ionosphere. We derive an analytical form for the limiting temperature, we also note the importance of the polarization field term and concluded that the flow will remain subsonic for realistic conditions. The time-dependent behaviour of He+ under sunspot minimum conditions is investigated in Chapter IV. This is achieved by numerical solution of the 0+, H+ and,He+ continuity and momentum equations, treating He+ as a minor ion with 0+ , H+ as major ions. We found that He+ flows upwards during the day-time and downwards during the nighttime. He+ flux tube content reached a maximum on the 8th day of the integration period and started to decreasing. This is due to the large amount of H+ present at the late stages of the integration period which makes He+ unable to diffuse through the H+ layer away from the loss region. In Chapter V we investigate the behaviour of 0++ using sunspot maximum parameters. Although our results support the findings of Geis and Young (1981) that the large amounts of 0++ at the equator are caused mainly by thermal diffusion, the model used by Geis and Young overemphesizes the effect of thermal diffusion. The importance of 0++ - 0+ collision frequency is also noted. In Chapter VI we extend the work of Chapter IV, presenting a comparative study of H and He at sunspot minimum and sunspot maximum.In this last Chapter all three ions, O+ ,H+ and He+ , are treated theoretically as major ions and we concentrate mainly on light ion contents and fluxes. The results of this Chapter indicate that by assuming He+ as a minor ion we under-estimate He+ and over-estimate. H+. Some interesting features concerning the day to day behaviour of the light ion fluxes arise. In particular the day-time H+ fluxes decrease from day to day in contrast to the work of Murphy et al.(1976). In appendix.A we derive some analytical forms for the optical depth so that the models can include a realistic description of photoionization.

Improving the solubility and dissolution of poorly soluble drugs by salt formation and the consequent effect on mechanical properties

The bioavailability of BCS II compounds may be improved by an enhanced solubility and dissolution rate. Four carboxylic acid drugs were selected, which were flurbiprofen, etodolac, ibuprofen and gemfibrozil. The drugs were chosen because they are weak acids with poor aqueous solubility and should readily form salts. The counterions used for salt formation were: butylamine, pentylamine, hexylamine, octylamine, benzylamine, cyclohexylamine, tert-butylamine, 2-amino-2-methylpropan­2-ol, 2-amino-2-methyl propan-1,3-ol and tromethamine. Solubility was partially controlled by the saturated solution pH with the butylamine counterion increasing the solution pH and solubility and dissolution to the greatest extent. As the chain length increased, solubility was reduced due to the increasing lipophilic nature of the counterion. The benzylamine and cyclohexylamine counterions produced crystalline, stable salts but did not improve solubility and dissolution significantly compared to the parent compound. The substitution of hydroxyl groups to tert-butylamine counterions produced an increase in solubility and dissolution. AMP2 resulted in the most enhanced solubility and dissolution compared to the parent drug but using the tris salt did not further improve solubility due to a very stable crystal lattice structure. The parent drugs were very difficult to compress due to orientation effects and lamination. Compacts were prepared of each parent drug and salt and their modulus of elasticity values were measured using a three-point bend (Young’s modulus, E0) were extrapolated to zero porosity and compared. Compressibility and E0 were improved with the butylamine, tert-butylamine, cyclohexylamine and AMP2 counterions. The most significant improvement in compression and E0 was with the AMP2 salts. Mechanical properties were related to the hydrogen bonding within the crystal lattice structure for the gemfibrozil salt series.

Local and systemic delivery of a novel group of inhibitors of transglutaminase enzyme: A potential approach for treating of catheter-related complications and liver fibrosis

The present thesis investigates targeted (locally and systemically) delivery of a novel group of inhibitors of enzyme transglutaminases (TGs). TGs are a widely distributed group of enzymes that catalyse the formation of isopeptide bonds between the y-carboxamide group of protein-bound glutamines and the a-amino group of protein-bound lysines or polyamines. The first group of the novel inhibitors tested were the tluorescently labelled inhibitors of Factor XIIIa (FXIIIa). These small, non-toxic inhibitors have the potential to prevent stabilisation of thrombi by FXIIIa and consequently increase the natural rate of thrombolysis, in addition it reduces staphylococcal colonisation of catheters by inhibiting their FXIIIa¬mediated cross-linking to blood clot proteins on the central venous catheter (CVCs) surface. The aim of this work was to incorporate the FXIIIa inhibitor either within coating of polyurethane (PU) catheters or to integrate it into silicone catheters, so as to reduce the incidence of thrombotic occlusion and associated bacterial infection in CVCs. The initial work focused on the incorporation of FXIIIa inhibitors within polymeric coatings of PU catheters. After defining the key characteristics desired for an effective polymeric-coating, polyvinylpyrrolidone (PVP), poly(lactic-co-glycolic acid) (PLGA) or their combination were studies as polymers of choice for coating of the catheters_ The coating was conducted by dip-coating method in a polymer solution containing the inhibitor. Upon incubation of the inhibitor-and polymer-coated strips in buffer, PVP was dissolved instantly, generating fast and significant drug release, whilst PLGA did not dissolve, yielding a slow and an insufficient amount of drug release. Nevertheless, the drug release profile was enhanced upon employing a blend solution of PVP and PLGA. The second part of the study was to incorporate the FXIIIa inhibitor into a silicone elastomer; results demonstrated that FXIIIa inhibitor can be incorporated and released from silicone by using citric acid (CA) and sodium bicarbonate (SB) as additives and the drug release rate can be controlled by the amount of incorporated additives in the silicone matrix. Furthermore, it was deemed that the inhibitor was still biologically active subsequent to being released from the silicone elastomer strips. Morphological analysis confirmed the formation of channels and cracks inside the specimens upon the addition of CA and SB. Nevertheless, the tensile strength, in addition to Young's modulus of silicone elastomer strips, decreased constantly with an increasing amount of amalgamated CA/ SB in the formulations. According to our results, incorporation of FXIIIa inhibitor into catheters and other medical implant devices could offer new perspectives in preventing bio-material associated infections and thrombosis. The use of tissue transglutaminase (T02) inhibitor for treating of liver fibrosis was also investigated. Liver fibrosis is characterized by increased synthesis and decreased degradation of the extracellular matrix (ECM). Transglutaminase-mediated covalent cross-linking is involved in the stabilization of ECM in human liver fibrosis. Thus, TG2 inhibitors may be used to counteract the decreased degradation of the ECM. The potential of a liposome based drug delivery system for site specific delivery of the fluorescent TG2 inhibitor into the liver was investigated; results indicated that the TG2 inhibitor can be successfully integrated into liposomes and delivered to the liver, therefore demonstrating that liposomes can be employed for site-specific delivery of TG2 inhibitors into the liver and TG2 inhibitor incorporating liposomes could offer a new approach in treating liver fibrosis and its end stage disease cirrhosis.

Structural behaviour of glass reinforced plastics

The aim of this research is to promote the use of G.R.P. as a structural material. In the past, the use of G.R.P. has been confined to non-load carrying applications. Such uses are still rapidly increasing but in addition significant changes have been made during the last decade in the development of semi-structural and now even fully structural applications. Glass-reinforced plastic is characterized by a high strength but a relatively low modulus of elasticity. For this reasona G.R.P. structure can expect to show large deformations as a result of which the individual structural members will fail under load due to a loss of stability rather than approaching the ultimate strength of the material. For this reason the selection of the geometrical shapes of G.R.P. structural elements is considered to be an important factor in designing G.R.P. structures. The first chapter of this thesis deals with a general review of the theoretical and experimental methods used to describe the structural properties of G.R.P. The research programme includes five stages dealing with the structural behaviour of G.R.P. The first stage (Chapter 2) begins with selecting and designing an optimum box beam cross-section which gives the maximum flexural and torsional rigidity. The second stage of investigation (Chapter 3) deals with beam to beam connections. A joint was designed and manufactured with different types of fasteners used to connect two beam units. A suitable fastener was selected and the research extended to cover the behaviour of long span beams using multiple joints. The third part of the investigation includes a study of the behaviour of box beams subjected to combined bending, shear and torsion. A special torque rig was developed to perform the tests. Creep deformation of 6 m span G.R.P. was investigated as the fourth stage under a range of loading conditions. As a result of the phenomenon of post buckling behaviour exhibited in the compression flange during testing of box beams during earlier stages of the investigation it was decided to consider this phenomenon in more detail in the final stage of the investigation. G.R.P. plates with different fibre orientation were subjected to uniaxial compression and tested up to failure. In all stages of the investigation theoretical predictions and experimental results were compared and generally good correlation between theory and experimental data was observed.

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.

A three dimensional numerical investigation of hillslope flow processes

Physically based distributed models of catchment hydrology are likely to be made available as engineering tools in the near future. Although these models are based on theoretically acceptable equations of continuity, there are still limitations in the present modelling strategy. Of interest to this thesis are the current modelling assumptions made concerning the effects of soil spatial variability, including formations producing distinct zones of preferential flow. The thesis contains a review of current physically based modelling strategies and a field based assessment of soil spatial variability. In order to investigate the effects of soil nonuniformity a fully three dimensional model of variability saturated flow in porous media is developed. The model is based on a Galerkin finite element approximation to Richards equation. Accessibility to a vector processor permits numerical solutions on grids containing several thousand node points. The model is applied to a single hillslope segment under various degrees of soil spatial variability. Such variability is introduced by generating random fields of saturated hydraulic conductivity using the turning bands method. Similar experiments are performed under conditions of preferred soil moisture movement. The results show that the influence of soil variability on subsurface flow may be less significant than suggested in the literature, due to the integrating effects of three dimensional flow. Under conditions of widespread infiltration excess runoff, the results indicate a greater significance of soil nonuniformity. The recognition of zones of preferential flow is also shown to be an important factor in accurate rainfall-runoff modelling. Using the results of various fields of soil variability, experiments are carried out to assess the validity of the commonly used concept of `effective parameters'. The results of these experiments suggest that such a concept may be valid in modelling subsurface flow. However, the effective parameter is observed to be event dependent when the dominating mechanism is infiltration excess runoff.

Effects of fibre reinforcement on the mechanical properties of brushite cement

In this study the effect of structure and amount of polyglactin fibre incorporation into a brushite forming calcium phosphate cement system and the effect of mechanical compaction on the fibre modified system were investigated. In comparison the effect of resorbable polycaprolactone surface coating of cement specimens was investigated. The results showed that, apart from the mechanical properties of the reinforcing material, the structure of the incorporated fibres, regular or random, is crucial for the resulting flexural strength and modulus of elasticity. Fibre reinforcement could also be combined with mechanical compaction of the cement/fibre composite paste leading to a possible 7-fold increase in flexural strength or an almost 5-fold increase in modulus of elasticity. Reinforcement of the tensile surface of cement grafts may ultimately improve strength where required, especially in conjunction with bone fixation devices. © 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Effect of microstructure upon elastic behaviour of human tooth enamel

Tooth enamel is the stiffest tissue in the human body with a well-organized microstructure. Developmental diseases, such as enamel hypomineralisation, have been reported to cause marked reduction in the elastic modulus of enamel and consequently impair dental function. We produce evidence, using site-specific transmission electron microscopy (TEM), of difference in microstructure between sound and hypomineralised enamel. Built upon that, we develop a mechanical model to explore the relationship of the elastic modulus of the mineral-protein composite structure of enamel with the thickness of protein layers and the direction of mechanical loading. We conclude that when subject to complex mechanical loading conditions, sound enamel exhibits consistently high stiffness, which is essential for dental function. A marked decrease in stiffness of hypomineralised enamel is caused primarily by an increase in the thickness of protein layers between apatite crystals and to a lesser extent by an increase in the effective crystal orientation angle. © 2009 Elsevier Ltd. All rights reserved.

Well-Posedness and Conditioning of Optimization Problems

AMS subject classification: 49K40, 90C31.

Characterization of Schrödinger Processes with Unbounded Potentials

2000 Mathematics Subject Classification: 49L20, 60J60, 93E20

A Characterization Theorem for the K-functional Associated with the Algebraic Version of Trigonometric Jackson Integrals

2000 Mathematics Subject Classification: 41A25, 41A36.

A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.

Convexity around the Unit of a Banach Algebra

2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.