Following trauma, such as an impact injury or stroke, brain tissue can swell. Swelling is the result of water accumulation in the tissue that is driven by pathological changes, such as increased permeability of the capillary walls and osmotic pressure changes within the tissue. Swelling causes increased intracranial pressure and mechanical deformation of the brain tissue, exacerbating the original injury. Furthermore, prolonged local swelling can lead to the spread of damage to the (initially undamaged) surrounding tissue, since compression and increased intracranial pressure may restrict blood flow in this tissue. In this thesis, we develop mathematical models to examine the consequences of pathophysiological damage mechanisms on the swelling, and associated stress and strain, experienced by brain tissue. Mixture theory is used to represent brain tissue as a mixture of elastic solid, fluid and solutes. This modelling approach allows elastic deformations to be coupled with hydrodynamic pressure and osmotic gradients; the consequences of different mechanisms of damage may then be quantified. We consider three particular problems motivated by experimental observations of swelling brain tissue. Firstly, we investigate the swelling of isolated, damaged, brain tissue slices; we show that mechanisms leading to an osmotic pressure difference between the tissue slice and its surroundings can explain experimental observations for swollen tissue slices. Secondly, we use our modelling approach to demonstrate that local changes in capillary permeability can cause significant stresses and strains in the surrounding tissue. Thirdly, we investigate the conditions under which a locally swollen, damaged, region can cause compression of the vasculature within the surrounding tissue, and potentially result in damage propagation. To do this, we propose a coupled model for the oxygen concentration within, and mechanical deformation of, brain tissue. We use our model to assess the impact of treatment strategies on damage propagation through the tissue, and show that performing a craniectomy reduces the extent of propagation.

Biological tissue differs from other materials in many ways. Perhaps the most crucial difference is its ability to grow. Growth processes may give rise to stresses that exist in a body in the absence of applied loads and these are known as residual stresses. Residual stress is present in many biological systems and can have important consequences on the mechanical response of a body. Mathematical models of biological structures must therefore be able to capture accurately the effects of differential growth and residual stress, since greater understanding of the roles of these phenomena may have applications in many fields. In addition to residual stresses, biological structures often have a complex morphology. The theory of 3-D elasticity is analytically tractable in modelling mechanical properties in simple geometries such as a cylinder. On the other hand, rod theory is well-suited for geometrically-complex deformations, but is unable to account for residual stress. In this thesis, we aim to develop a map between the two frameworks. Firstly, we use 3-D elasticity to determine effective mechanical properties of a growing cylinder and map them into an effective rod. Secondly, we consider a growing filament embedded in an elastic foundation. Here, we estimate the degree of transverse reinforcement the foundation confers on the filament in terms of its material properties. Finally, to gain a greater understanding of the role of residual stress in biological structures, we consider a case study: the chameleon's tongue. In particular we consider the role of residual stress and anisotropy in aiding the rapid projection of the tongue during prey capture. We construct a mechanical model of the tongue and use it to investigate a proposed mechanism of projection by means of an energy balance argument.

The application of techniques from nonlinear analysis to materials science has seen great developments in the recent years and it has really been a driving force for substantial mathematical research in the area of partial differential equations and the multi-dimensional calculus of variations. This thesis has been motivated by two recent and remarkable experimental observations of H. Seiner in shape-memory alloys which we attempt to interpret mathematically. Much of the work is original and has given rise to deep problems in the calculus of variations. Firstly, we study the formation of non-classical austenite-martensite interfaces. Ball & Carstensen (1997, 1999) theoretically investigated the possibility of the occurrence of such interfaces and studied the cubic-to-tetragonal case extensively. In this thesis, we present an analysis of non-classical austenite-martensite interfaces recently observed by Seiner et al.~in a single crystal of a CuAlNi shape-memory alloy, undergoing a cubic-to-orthorhombic transition. We show that these can be described by the general nonlinear elasticity model and we make some predictions regarding the admissible volume fractions of the martensitic variants involved, as well as the habit plane normals. Interestingly, in the above experimental observations, the interface between the austenite and the martensitic configuration is never exactly planar, but rather slightly curved, resulting from the pattern of martensite not being exactly homogeneous. However, it is not clear how one can reconstruct the inhomogeneous configuration as a stress-free microstructure and, instead, a theoretical approach is followed. In this approach, a general method is provided for the construction of a compatible curved austenite-martensite interface and, by exploiting the structure of quasiconvex hulls, the existence of curved interfaces is shown in two and three dimensions. As far as the author is aware of, this is the first construction of such a curved austenite-martensite interface. Secondly, we study the nucleation of austenite in a single crystal of a CuAlNi shape-memory alloy consisting of a single variant of stabilized 2H martensite. The nucleation process is induced by localized heating and it is observed that, regardless of where the localized heating is applied, the nucleation points are always located at one of the corners of the sample - a rectangular parallelepiped in the austenite. Using a simplified nonlinear elasticity model, we propose an explanation for the location of the nucleation points by showing that the martensite is a local minimizer of the energy with respect to localized variations in the interior, on faces and edges of the sample, but not at some corners, where a localized microstructure can lower the energy. The result for the interior, faces and edges is established by showing that the free-energy function satisfies a set of quasiconvexity conditions at the stabilized variant throughout the specimen, provided this is suitably cut. The proofs of quasiconvexity are based on a rigidity argument and are specific to the change of symmetry in the phase transformation. To the best of the author's knowledge, quasiconvexity conditions at edges and corners have not been considered before.

A number of advanced pre-treatment techniques and methods have been evaluated for the sole purpose of improving digestibility of waste activated sludge. The pre-treatment of waste activated sludge (WAS) offers the benefit of releasing solubilized substrates, making them readily available to be utilized in the anaerobic digestion process. Other potential benefits include: reducing shock loading to the digester, improving overall digestibility and potentially providing filament / foaming control. Chlorine dioxide, a well-known disinfectant and oxidizing agent has been utilized in many drinking water processes around the world. Its use in wastewater treatment processes however is limited; especially in Canada where legislation has prevented its use for final effluent disinfection. As an oxidizing agent, chlorine dioxide induces cell rupture resulting in the release of soluble material, which when fed into the digester, may serve as readily available substrate for active microorganisms. This mode of action creates the potential for chlorine dioxide to be used as a sludge pre-treatment agent to improve digester performance and in alleviating pre-existing filamentous sludge bulking. This study was conducted using waste activated sludge obtained from the City of Winnipeg’s South End Water Pollution Control Centre (SEWPCC), with the following objectives: 1. Determine the efficacy of chlorine dioxide in alleviating pre-existing filamentous sludge bulking; 2. Determine chlorine dioxide ability to increase WAS solubilization; and 3. Define impact of chlorine dioxide on anaerobic digester performance. WAS pre-treatment using chlorine dioxide was found to be effective in alleviating filamentous bulking. This is significant as filamentous bulking in the activated sludge may lead several problems downstream. Following pre-treatment, sludge bulking was determined to be alleviated as observed by photomicrographic evidence and as measured by a 57% decrease in the stirred sludge volume index (sSVI). Particulate COD solubilization increased by 60%, 76%, and 74% over the untreated sludge for WAS pre-treated with 25, 50, and 100 mg ClO2/L (v/v), respectively. The pre-treatment of sludge using chlorine dioxide did not have any negative impact on digester performance although it also did not lead to improved performance. The volatile solids destruction and COD removal remained unchanged for both untreated and pre-treated sludge. Chlorine dioxide pre-treatment did not affect anaerobic digestion even at the lowest SRT evaluated; it is possible to decrease the digester SRT to as low as 6 days while maintaining the solids destruction and COD removal capability. Biogas production did not improve with increasing chlorine dioxide dosage during pre-treatment but also was not hindered by the pre-treatment agent. Chlorine dioxide was shown to alleviate filamentous bulking and improve solubility and has the potential to improve digester performance without negative impacts to the digester. However, the full benefit of the pre-treatment method may only be realized for complex “difficult to disintegrate” sludge types. / October 2016

Three suspended solids types containing a range of physicochemical characteristics were used to determine the effect of suspended solids on the bioavailability of acenaphthene, 1,2,4,5-tetrachlorobenzene, zinc, and chlordane to Daphnia magna and Pimephales promelas. Generally, the bioavailability of zinc and chlordane decreased due to interactions with all suspended solids types while bioavailability of acenaphthene and 1,2,4,5-tetrachlorobenzene were not clearly reduced. Partition coefficients and slope of dose-response curves related chemical characteristics and organism sensitivity, respectively, to experimentally determined results. It is believed that the biologically available form of these chemicals to Daphnia magna and Pimephales promelas resides in the aqueous phase.

The frequency shifts and Q changes of a resonant microwave cavity were utilized as a basis for determining microwave properties of solids and liquids. The method employed consisted of varying the depth of penetration of a cylindrical sample of the material into a cavity operating in the TM0 1 0 Mode. The liquid samples were contained in a thin-walled quartz tube. The perturbation of the cavity was achieved by advancing the sample into the cavity along the symmetry axis by employing a micrometer drive appropriately calibrated for depth of penetration of the sample. A differentiation method was used to obtain the half-power points of the cavity resonance profile at each depth of penetration. The perturbation techniques for resonant cavities were used to reduce the experimental data obtained to physical parameters for the samples. The probing frequency employed was near 9 gHz.

This thesis represents one phase of a joint effort of research on the properties of liquids and solids. This work is concerned primarily with the microwave properties of solids. In this investigation the properties exhibited by conductor and semiconductor materials when they are subjected to electromagnetic radiation of microwave frequency are studied. The method utilized in this experiment is the perturbation of a resonant cavity produced by introduction of a cylindrically shaped sample into it.

This work is a collection of solved problems in descriptive geometry, supplemented by elementary theory needed for their solution. The theory includes definitions and elementary properties of polygons and their constructions. Theory about solids, mostly prisms and pyramids, is also included. The second chapter introduces theory of projection, including definitions of projection methods (Monge, center, etc.) and corresponding terms. The second part contains a collection of problems, where each problem is solved in four projection methods (there are problems of construction of a point, line, plane, prism and pyramid). For each problem there is an animation for Lisa Viewer program attached, which makes an integral part of the work. These animations allow to look at figures of the problems interactively and even in three dimensions. There is also a PDF document with problem assignment and solution for each problem, suitable for print. Powered by TCPDF (www.tcpdf.org)

The present thesis deals with geometric lighting and methods of its construction. In particular, it is aimed at parallel and central lighting of objects and groups of objects. The work includes a theoretical part, in which you can learn about the properties, methods and basic concepts related to geometric lighting. Afterwards, there is a practical part, which contains a set of examples in different projections with their solutions and visual pictures. Last chapter is about using computer for modeling of geometric lighting; mainly it is about possibilities of software Rhinoceros. In addition, the chapter contains modeled lighting of the charming Taj Mahal. The project is filled up with a number of pictures to enhance the reader's imagination about the principles and methods of lighting. In the work I emphasized intelligibility and usability of the methods listed there. In general, thesis Geometry of shadows is devoted to everybody who wants to learn more about the geometry of shadows. The thesis could be a useful study material for students and teachers of descriptive geometry. The work also includes the DVD, which contained Rhinoceros files of images, worksheets with examples solved at the work and the thesis in electronic form.

The two dimensional electron gas subjected to a perpendicular magnetic field is a model system that supports a variety of electronic phases. Perhaps the most well-known are the fractional quantum Hall states, but in recent years there has been an upsurge of interest in the charge ordered phases commonly referred to as electron solids. These solids are a consequence of electron-electron interactions in a magnetic field. While some solid phases form in the lowest Landau level, the charged ordered phases are most abundant in the higher Landau levels. Examples of such phases include the Wigner solids, electronic bubble phases and stripe or nematic phases. Open questions surround the exact role of disorder, confinement potential, temperature and the Landau level index in determining the stability and competition of these phases with other ground states. <div>The interface of GaAs/AlGaAs remains the cleanest host for the two-dimensional electron gas due to the extremely high quality of materials available and the advancement in molecular beam epitaxy growth techniques. As a result, exceptionally high electron mobilities in this system have been instrumental in the discovery of numerous electron solids. </div><div>In this Thesis, I discuss the discovery and properties of several electron solids that develop in such state-of-the-art two dimensional electron gases. These electron solids often develop at ultra low temperatures, in the milliKelvin temperature range. After an introduction to the physics of the quantum Hall effect in two dimensions, in chapter 3, I discuss electron solids developing in the N=1 Landau level. While these solids have been known for some time, details of the competition of these phases xiii with the nearby fractional quantum Hall states remains elusive. A number of reports observe new fractional quantum Hall states at filling factors where electron solids are found in other experiments. We undertook a systematic study to answer some of these unsettled questions. We see evidence for incipient fractional quantum Hall states at 2+2/7 and 2+5/7 at intermediate temperatures which are overtaken by the electronic bubble phases at lower temperatures. Several missing fractional states including those at filling factors 2+3/5, 2+3/7, 2+4/9 highlight the relative stability of the electronic solids called the bubble phases in the vicinity in our sample. </div><div>In chapter 4, I discuss a newly seen electron crystal which manifests itself in transport measurements as a reentrant integer quantum Hall state. Reentrant integer behavior is common in high Landau levels, but so far it was not observed in the lowest Landau level in narrow quantum well samples. In contrast to high Landau levels, where such reentrant integer behavior was associated with electronic bubbles, we believe that the same signature in the N=0 Landau level is due to an electronic Wigner crystal. The filling factors at which we observe such reentrance reveal that it is a crystal of holes, rather than electrons. The discovery of this reentrant integer state paints a complex picture of the interplay of the Wigner crystal and fractional quantum Hall states. </div><div>Finally, in chapter 5, I discuss the observation of a novel phenomenon, that of reentrant fractional quantum Hall effect. In the lowest Landau level, we observe a fractional quantum Hall state, but as the field is increased, we see a deviation and then a return to quantization in the Hall resistance. Such a behavior indicates a novel electron solid. In contrast to the collective localization of electrons evidenced by the reentrant integer quantum Hall effect, such reentrance to a fractional Hall resistance clearly points to the involvement of composite fermion quasiparticles. This property thus distinguishes the ground state we observed as a solid formed of composite fermions. Such a solid phase is evidence for exotic electron-electron correlations at play which are clearly different from those in the traditional Wigner solid of electrons.<br></div>