Dimensionality reduction methods allow for the study of high-dimensional systems by producing low-dimensional descriptions that preserve the relevant structure and features of interest. For dynamical systems, attractors are particularly important examples of such features, as they govern the long-term dynamics of the system, and are typically low-dimensional even if the state space is high- or infinite-dimensional. Methods for reduction need to be able to determine a suitable reduced state space in which to describe the attractor, and to produce a reduced description of the corresponding dynamics. In the presence of a parameter space, a system can possess a family of attractors. Parameters are important quantities that represent aspects of the physical system not directly modelled in the dynamics, and may take different values in different instances of the system. Therefore, including the parameter dependence in the reduced system is desirable, in order to capture the model's full range of behaviour. Existing methods typically involve algebraically manipulating the original differential equation, either by applying a projection, or by making local approximations around a fixed-point. In this work, we take more of a geometric approach, both for the reduction process and for determining the dynamics in the reduced space. For the reduction, we make use of an existing secant-based projection method, which has properties that make it well-suited to the reduction of attractors. We also regard the system to be a manifold and vector field, consider the attractor's normal and tangent spaces, and the derivatives of the vector field, in order to determine the desired properties of the reduced system. We introduce a secant culling procedure that allows for the number of secants to be greatly reduced in the case that the generating set explores a low-dimensional space. This reduces the computational cost of the secant-based method without sacrificing the detail captured in the data set. This makes it feasible to use secant-based methods with larger examples. We investigate a geometric formulation of the problem of dimensionality reduction of attractors, and identify and resolve the complications that arise. The benefit of this approach is that it is compatible with a wider range of examples than conventional approaches, particularly those with angular state variables. In turn this allows for application to non-autonomous systems with periodic time-dependence. We also adapt secant-based projection for use in this more general setting, which provides a concrete method of reduction. We then extend the geometric approach to include a parameter space, resulting in a family of vector fields and a corresponding family of attractors. Both the secant-based projection and the reproduction of dynamics are extended to produce a reduced model that correctly responds to the parameter dependence. The method is compatible with multiple parameters within a given region of parameter space. This is illustrated by a variety of examples.

The use of H2O as an additive in SmI2-mediated reductive processes provides access to new transformations and previously inaccessible chemical space. The cyclisation of radicals derived from the selective mono-reduction of Meldrum’s acid derivatives was further investigated and the scope of the methodology expanded to cyclisation cascades. The first general methodology for the reduction of amide-type carbonyls under single electron transfer conditions was developed and applied to the mono-reduction of barbituric acid derivatives, providing an unprecedented direct access to the corresponding hemiaminals with a good degree of stereocontrol. The intermediate acyl-type radicals were in addition successfully exploited in stereoselective radical cyclisations. The hemiaminals derived from mono-reduction and cyclisation of barbituric acid derivatives have been exploited as N-acyliminium equivalents, affording hydrouracils with an excellent degree of regio- and stereoselectivity. Efforts towards the synthesis of the azulene framework of pseudolaric acid B using a model substrate are also described.

A global legacy of radioactively contaminated land exists as a result of nuclear fuel cycle operations. Demonstration of the safe management of the UK nuclear legacy, including contaminated land, is important whilst the long term fate of legacy waste remains uncertain and the UK is moves towards new nuclear power. One aspect of nuclear contaminated land research focuses on the immobilisation of intermediate and long lived radionuclides that are mobile in groundwater and are migrating in the environment. At Sellafield nuclear facility, UK, strontium-90 and technetium-99 are found as co-contaminants in groundwater alongside the most abundant non radioactive contaminant, nitrate. Their differing radiochemical behaviour and the presence of nitrate presents a challenge for remediation strategies. Bioremediation has the potential for in-situ immobilization of 99Tc via reduction from mobile Tc(VII) to less mobile Tc(IV) concurrent with Fe(III) reduction. In this project bioreduction processes were investigated in sediment microcosms and model systems under variable pH and nitrate conditions and using microorganisms representative of the Sellafield site. Sediment bioreduction occurred via stimulation of the natural microbial community. Denitrification resulted a delay in the onset of metal reduction followed by a raised pH. At the mildly acidic pH of the natural sediments, a nitrate concentration of 100 mM caused bioreduction to stall. However, at pH 7, reduction of 100 mM nitrate resulted in a final pH > 9 and alkaline Fe(III) reduction. In bioreduced sediments, the microbial ecology was dominated by nitrate reducing microorganisms and Fe(III) reducing enrichment cultures were necessary to identify relevant alkaline Fe(III) reducing bacteria. Enrichment cultures isolated a novel alkali tolerant Fe(III) reducing Serratia sp. with a growth range of pH 4 to 9. Increased pH resulting from denitrification decreased the mobility of Sr2+ via increased sorption to mineral surfaces. X-ray absorption spectroscopy confirmed Sr2+ incorporation into carbonate mineral phases above pH 8.5. Model systems showed reductive removal of 99Tc from solution by an Fe(II) bearing mineral assemblage at both pH 7 and 9. In contrast Sr2+ remained in solution at pH 7 and precipitated as SrCO3 at pH > 8.5. This study for the first time demonstrates the effects of high nitrate on pH in Sellafield type sediments, alkaline Fe(III) reduction by a Serratia sp, the incorporation behaviour of Sr2+ during sediment bioreduction and the behaviour of Sr2+ and 99Tc in novel Fe(II) mineral bearing model systems. These findings improve the understanding of radionuclide migration at contaminated sites and inform possible engineered bioremediation scenarios.

The general objective of this thesis is to conduct experiments on sphere free-falling in liquid that advance our understanding of the drag reduction on solids moving in liquid by means of lubricating gas layers and attached streamlined air cavities. Part I of the thesis investigates the effect of thin air layers, naturally sustained on superhydrophobic surfaces, on the terminal velocity and drag force of metallic spheres free- falling in water. The surface of 20 mm to 60 mm steel or tungsten-carbide spheres is rendered superhydrophobic by a simple coating process that uses a commercially available hydrophobic agent. By comparing the free-fall of unmodified spheres and superhydrophobic spheres, in a 2.5 meters tall water tank, it is demonstrated that even a very thin air layer (~ 1 – 2 μm) that covers the freshly dipped superhydrophobic sphere, can reduce the drag force on the spheres by up to 80 %, at Reynolds numbers 105 to 3×105, owing to an early drag crisis transition. Part II of the thesis investigates the drag reduction by means of the dynamic Leidenfrost vapor-layer sustained on the surface of heated metallic spheres free-falling in a fluorocarbon liquid, FC-72 (perfluorohexane). In these experiments we employed two tall liquid tanks: a 3 meter tall 14 cm wide tank and a 2 meter tall 20 × 20 cm cross-section tank with a heater device. These tanks are significantly larger than the tanks used in prior studies and allow us to track the extended fall trajectories and to compare the drag on room-temperature no-vapor-layer spheres to that of heated Leidenfrost vapor-layer spheres. Analysis of the extended free-fall trajectories and acceleration, based on the sphere dynamic equation of motion, enables the accurate evaluation of the vapor-layer-induced drag reduction, without the need for extrapolation. We demonstrate that the drag on the Leidenfrost sphere in FC-72, can be as low as CD = 0.04 ± 0.01, or an order of magnitude lower than the values for the no-vapor-layer spheres in the subcritical Reynolds number range. This drag reduction extends into the supercritical Reynolds number range. The analysis method developed herein, to describe the sphere trajectories, can be applied in other related studies. Part III of the thesis examines a recently demonstrated phenomenon of the formation of stable-streamlined gas cavity following the impact of a heated Leidenfrost sphere on a liquid surface or a superhydrophobic sphere on water. The sphere encapsulated in a teardrop-shaped gas cavity was found to have near-zero hydrodynamic drag due to the self-adjusting streamlined shape and the free-slip boundary condition on the cavity interface. Here it is shown that such cavities can be formed following the water impact from a sufficient height of non-superhydrophobic spheres with water contact angles between 30° and 120°. In this case the streamlined cavity is attached just above the sphere’s equator, instead of entirely wrapping the sphere. Nevertheless, this sphere with attached cavity has near-zero drag and predetermined free-fall velocity in compliance with the Bernoulli law of potential flow. Last, the effect of surfactant addition to the water solution is investigated. The shape and fall velocity of the sphere with streamlined cavity formation were unaffected by the addition of low-surface-modulus synthetic surfactants, but was destabilised when a solution containing high-surface-modulus surfactants, such as soaps were used.

The manifold boundary approximation method, MBAM is a new technique used in approximating systems of equations using parameter reduction. This method and other approximation methods are introduced and described. Several current issues in performing MBAM are discussed in further detail. These issues significantly slow down the process of MBAM and create a barrier of entry for those wishing to use the method without a strong background in mathematics. A solution is proposed to automatically reparameterize models and evaluate specific types of variables approaching limits -- significantly speeding up the process of MBAM. An implementation of the solution is discussed.

This diploma thesis deals with creation of reduction core problem mainly in fired roofing tiles. With those is the emphasis on the impermeability and frost resistance. Black reduction core is reducing frost resistance but depends on firing temperature. At 1060 °C the reduction in frost resistance is not as unfavorable as at 900 °C. This thesis includes overview of research conducted on reduction core topic. There is enough literature focusing on frost resistance, experimental part is focused mainly on the impact of reduction core on impermeability and compares two types of production mixtures used in Czech Republic (calcium-containing type from Hranice and non-calcium type from Stod). It includes comparison of mixtures with fluidized fly ash and dust from grinding masonry elements. It opens discussion if those mixtures can be used for reduction core elimination.

There has been a well-documented and causal relationship between cigarette smoking and disease for over forty years, and at least an implicit concern over tobacco and health for decades, if not centuries prior; however, government policy on how to address tobacco as a public health issue has been erratic. At the turn of the twentieth century, when cigarettes first became a national phenomenon, the federal government imposed few if any regulations, and even encouraged the use of cigarettes. By the 1960s, government, public health entities and the tobacco industry were cooperating to try to fix the problem. Although there was great success in this early, if uneasy alliance, by the 1980s this coalition was fragmented and the search for a pragmatic solution to the tobacco problem came to an abrupt end. This dissertation is an investigation into how policy-makers, tobacco industry executives and public health officials each ignored opportunities to come to a practical solution to the problem which confronted them. The 1960s saw these groups work together to formulate a harm reduction policy approach which would lessen, if not eliminate, the concerns from each constituent group. Despite some significant early successes, this effort was derailed due to partisan positioning, misguided self-interest, and certain individual personalities. This analysis of the safer-cigarette campaign sheds light on a little explored avenue in the tobacco debate, as well as highlights the challenges of policy making in Washington.

The use of alkali and alkaline earth metals as reducing agents in liquid ammonia solvent for aromatic and conjugated systems has been investigated by chemists at least since the early 1900's, e.g., Lebau and Picon (1). By subsequent additions of a proton source, the system yielded the first successful partial reduction of a monobenzenoid system, as reported by Wooster and Godfrey (2), in 1937. As a result of that success a patent was issued to Wooster for the process (3). Little additional work was reported until Birch and his co-workers picked up the investigation in the early 1940's. It was through his vigorous study and development of this reduction system that Birch's name came to be associated with reductions of organic compounds by alkali metals in liquid ammonia, hence, the Birch reduction. In this thesis the Birch reduction of cinnamic acid is investigated.

The thesis deals with speckle suppression in images acquired by optical coherence tomograph. It is divided into four parts. The first part describes basic information about the medical imaging method. It also deals with principle of measurement. The second section discusses the formation of image speckle and selected methods to reduce them. Next part is practical and consists of data acquisition, determination of the evaluation methodology and the implementation of speckle reduction methods. The last part is focused on testing and reviews of algorithms and discussion about their results.

Active noise reduction was first proposed as a solution for environmental noise over fifty years ago. The use of active noise reduction (ANR) systems, however, was not demonstrated until much later. Recent advances in technology have made the use of active noise reduction systems in personal hearing protection devices (HPDs) practical. Through the use of advanced electronics technology, ANR equipped devices offer the potential to provide increased low frequency attenuation for hearing conservation applications. In order to use ANR equipped devices in an Occupational Safety and Health Administration (OSHA) sanctioned hearing conservation program, a testing standard for ANR equipped HPDs needs to be developed. Existing HPD testing standards offer the most promise for developing an acceptable standard for testing ANR-equipped HPDs. The microphone in real ear (MIRE) testing method is one method that offers a practical method for determining the performance of ANR devices for use in hearing conservation programs. A modified version of this method was successfully used in this study to determine the performance profile of an open-back ANR equipped headset. The results of this and other studies that have used a modified MIRE testing method can be used to support the acceptance of this method as the basis of an approved standard for testing ANR-equipped hearing protection devices. / Master of Science