This thesis concerns the metaphysics of scale. It investigates the implications of a physical determinable being dimensionful. In particular, it considers the case study of mass, as it features within Newtonian Gravity. Nevertheless, most of the terminology, methodology and arguments developed should be relatively straightforwardly applicable to other determinables and theories. Weak Absolutism about mass holds that mass ratios obtain in virtue of absolute masses. Weak Comparativism denies this. In the first five chapters I argue in favour of Weak Absolutism over Weak Comparativism. The sixth chapter argues against reducing mass to other non-mass facts. The overall conclusion is Strong Absolutism about mass within Newtonian Gravity: mass ratios obtain in virtue of absolute masses, which themselves are fundamental (i.e. they do not require anything further in order to obtain). Comparativism promises to recover all the virtues of absolutism, in particular its empirical adequacy, but at a lower 'metaphysical cost'. Special attention is given to Dasgupta's recent comparativist proposal. Dasgupta interprets the requirement of empirical adequacy in terms of the undetectability of the absolute mass scale. I argue that undetectability is an unsuitable way of understanding empirical adequacy and that we would do better to understand it in terms of a theory's ability to correctly generate the set of empirically possible worlds (or at least the actual world). I refute Dasgupta's comparativism both on my terms and on his own terms. I subsequently develop and strongly criticise alternative versions of comparativism. Chapter five sheds doubt on the supposed 'metaphysical parsimony' of comparativism. This debate should be of particular interest to readers who engage with the substantivalism-relationalism debate. These debates are much more entwined than previously acknowledged, which provides a significant source of mutual inspiration, although I do also draw out some important disanalogies.

Nesta dissertação, uma revisão dos modelos cosmológicos newtonianos e neo-newtonianos baseados na formulação da hidrodinâmica clássica é apresentada, com especial ênfase para os resultados básicos e as limitações mais importantes dessas abordagens. Em seguida, mostramos que a descrição Lagrangiana clássica proposta por Lima, Moreira e Santos (1998) para fluidos simples, pode ser generalizada para incluir modelos com misturas de fluidos, e portanto, cosmologias mais realísticas contendo bárions, matéria escura e energia escura, bem como qualquer forma de interação entre essas componentes. Neste trabalho propomos uma descrição lagrangiana clássica para modelos relativísticos do tipo FRW. Nesta descrição, o comportamento dinâmico do fator de escala a(t), como previsto pelas cosmologias relativísticas, é substituído pelo movimento unidimensional de uma partícula teste de massa m sob a ação de um potencial clássico, V(x), onde x é a coordenada unidimensional da partícula. O tratamento pode ser aplicado para os mais diversos cenários de energia escura. Para exemplificar, discutimos com detalhe os seguintes modelos contendo matéria escura e energia escura: XCDM, X(z)CDM, Lambda CDM, Lambda(t) e gás de Chaplygin. Por completeza, modelos multidimensionais do tipo FRW também são considerados. Em todos esses modelos, o parâmetro de curvatura k das seções espaciais das cosmologias determina a energia total da partícula teste pela relação, E=-mk/2, tal como ocorre nos modelos de fluidos simples. As propriedades dinâmicas associadas com o presente estágio de aceleração do universo são univocamente descritas em termos da função potencial do sistema. Finalmente, utilizando os dados da distância de luminosidade provenientes das supernovas do tipo Ia, discutimos como o potencial unidimensional pode ser reconstruído a partir das observações. / In this dissertation, a review of the Newtonian and neo-Newtonian cosmological models based on the classical hydrodynamics formulation is presented with special emphasis to the basic results and the main limitations of such approaches. Next, we show that the classical Lagrangian description as proposed by Lima, Moreira & Santos (1998) for simple fluids, can be generalized to include fluid mixtures, and, therefore, more realistic cosmologies containing baryons, dark matter and dark energy, as well as, any kind of interaction among such components. In the lagrangian description, the dynamic behavior of the scale factor a(t), as predicted by the relativistic cosmologies, is replaced by the unidimensional motion of a test particle with mass m under the action of a classical potential, V(x), where x(t) is the coordinate of the particle. The treatment can be applied for many different scenarios of dark energy. In order to exemplify, we discuss with detail the following models containing dark matter and dark energy: XCDM, X(z)CDM, Lambda(t)CDM and the Chaplygin gas. For completeness, FRW type multidimensional models are also considered. For all these models, the curvature parameter k of the spatial sections in the relativistic cosmologies determines the total energy by the relation, E=-mk/2, as occurs in the simple fluid models. The dynamic property associated with the present accelerating stage of the Universe are univocally described in terms of the potential function of the system. Finally, by using the data from luminosity distance of supernovae type Ia, we discuss how the unidimensional potential can be reconstructed from the observations.

We investigate local properties of the Green function of the complement of a compact set E. First we consider the case E ⊂ [0, 1] in the extended complex plane. We extend a result of V. Andrievskii which claims that if the Green function satisfies the Hölder1/2 condition locally at the origin, then the density of E at 0, in terms of logarithmic capacity, is the same as that of the whole interval [0, 1]. We give an integral estimate on the density in terms of the Green function, which also provides a necessary condition for the optimal smoothness. Then we extend the results to the case E ⊂ [−1, 1]. In this case the maximal smoothness of the Green function is H¨older-1 and a similar integral estimate and necessary condition hold as well. In the second part of the paper we consider the case when E is a compact set in Rd , d > 2. We give a Wiener type characterization for the Hölder continuity of the Green function, thus extending a result of L. Carleson and V. Totik. The obtained density condition is necessary, and it is sufficient as well, provided E satisfies the cone condition. It is also shown that the Hölder condition for the Green function at a boundary point can be equivalently stated in terms of the equilibrium measure and the solution to the corresponding Dirichlet problem. The results solve a long standing open problem - raised by Maz’ja in the 1960’s - under the simple cone condition.

The aim of this study is to investigate the fluid-structural response to pulsatile Newtonian and non-Newtonian blood flow through an axisymmetric stenosed vessel using FLOTRAN and ANSYS. This is to provide a basic understanding of atherosclerosis. The flow was set to be laminar and follows a sinusoidal waveform. The solid model was set to have isotropic elastic properties. The Fluid-Structural Interaction (FSI) coupling was two-way and iterative. Rigid and Newtonian cases were investigated to provide an understanding on the effects of incorporating FSI into the model. The wall expansion was found to decrease the axial velocity and increase the recirculation effects of the flow. To validate the models and methods used, the results were compared with the study by Lee and Xu [2002] and Ohja et al [1989]. Close comparisons were achieved, suggesting the models used were valid. Two non-Newtonian models were investigated with FSI: Carreau and Power Law models. The Carreau model fluid behaviour was very close to the Newtonian model. The Power Law model produced significant difference in viscosity, velocity and wall shear stress distributions. Pressure distribution for all models was similar. In order to quantify the changes, Importance Factor (IG) was introduced to determine the overall non-Newtonian effects at two regions: the entire flow model and about the vessel wall. The Carreau model showed reasonable values of IG whereas the Power Law model showed excessive values. Transient and geometrical effects were found to affect the Importance Factor. The stress distributions for all models were found to be similar. Highest stress occurred at the shoulders of the stenosis where a stress concentration occurred due to sharp corners of the geometry and large bending moments. The highest stresses were in the axial direction. Notable circumferential stress was found at the ends of the vessel. Carreau model produced slightly higher stresses than the other models. Wall stresses were found to be primarily influenced by internal pressure, rather than wall shear stresses.

Extraction processes employing emulsion liquid membranes (ELMs), water-in-oil emulsions dispersed in aqueous phase, have been shown to be highly efficient in removing a variety of organic and inorganic contaminants from industrial wastewaters. As a result, they have been considered as alternative technologies to other more common separation processes such as pressure-driven membrane processes. Unfortunately, a widespread use of the ELM process has been limited due to the instability of emulsion globules against fluid shear. Breakup of emulsions and subsequent release of the internal receptor phase to the external donor phase would nullify the extraction process. Numerous studies have been, therefore, made in the past to enhance the stability of ELMs. Examples include adding more surfactants into the membrane phase and increasing the membrane viscosity. However, increased stability has been unfortunately accompanied by loss in extraction efficiency and rate in most reported attempts. The primary objective of this research is to apply the ELMs in a unique contacting device, a Taylor-Couette column, which provides a relatively low and uniform fluid shear that helps maintaining the stability of emulsion without compromising the extraction efficiency of a target compound. The ELM used in this study is made of membrane phase converted into non-Newtonian fluid by polymer addition, which provides additional uncommon remedy for the problem. This innovative ELM process was optimized to treat various types of simulated industrial wastewaters containing selected phenolic compounds and heavy metals. Experiments performed in this study suggested that the newly developed ELM process achieved exceptionally high overall removal efficiencies for the removal of these target compounds in relatively short contact time. Mechanistic predictive models were further developed and verified with the experimental data. Combined with the experimental data and novel mathematical predictive models, this study is expected to have a high impact on immediate practices of emulsion liquid membrane technologies in relevant industries.

Through past research, it is known that carbon nanotubes have the potential of enhancing the thermal performance of heat transfer fluids. The research is of importance in electronics cooling, defense, space, transportation applications and any other area where small and highly efficient heat transfer systems are needed. However, most of the past work discusses the experimental results by focusing on the effect of varying concentration of carbon nanotubes (CNTs) on the thermal performance of CNT nanofluids. Not much work has been done on studying the effect of processing variables. In the current experimental work, accurate measurements were carried out in an effort to understand the impact of several key variables on laminar flow convective heat transfer. The impact of ultrasonication energy on CNT nanofluids processing, and the corresponding effects on flow and thermal properties were studied in detail. The properties measured were viscosity, thermal conductivity and the convective heat transfer under laminar conditions. Four samples of 1 wt % multi walled carbon nanotubes (MWCNT) aqueous suspensions with different ultrasonication times were prepared for the study. Direct imaging was done using a newly developed wet-TEM technique to assess the dispersion characteristics of CNT nanofluid samples. The results obtained were discussed in the context of the CNT nanofluid preparation by ultrasonication and its indirect effect on each of the properties. It was found that the changes in viscosity and enhancements in thermal conductivity and convective heat transfer are affected by ultrasonication time. The maximum enhancements in thermal conductivity and convective heat transfer were found to be 20 % and 32 %, respectively, in the sample processed for 40 minutes. The thermal conductivity enhancement increased considerably at temperatures greater than 24 °C. The percentage enhancement in convective heat transfer was found to increase with the axial distance in the heat transfer section. Additionally, the suspensions were found to exhibit a shear thinning behavior, which followed the Power Law viscosity model.

Mixing is a crucial process for many large scale and small scale applications from food industry to cosmetics, from drug industry to petrochemical processes, etc. Changes in parameters (temperature, viscosity, velocity distribution, etc.) during the mixing affect the production process and the end product quality and the cost. Thus, these parameters, mostly the hydrodynamic parameters, should be monitored closely during the process. In order to ensure good and efficient mixing in the solution, high degree of turbulence is maintained while dead zones in the tank should be avoided. In chemical industry, the mixing processes generally involve complex solutions that exhibit non-Newtonian flow behavior that merits a study on the agitation hydrodynamics and mixing time. Thus, in this study agitation of carboxymethyl cellulose (CMC) solution in a laboratory scale mixing tank is investigated. The effects of CMC concentration and agitation speed on the hydrodynamics of the solution and mixing time are studied in detail. CMC concentrations studied are 0.5 wt%, 1 wt% and 2 wt%. Impeller speeds, on the other hand, are set as 150 rpm, 300 rpm and 600 rpm. The hydrodynamics of mixing can be studied easily by Ultrasound Doppler Velocimetry (UDV) which is a fast, non-invasive measuring technique in fluid dynamics. Also, the mixing time measurements were carried out through electrical conductivity of the agitated solution. UDV results show that the flow field has a typical pattern produced by the Rushton turbine. The main characteristics of the flow are that, in the impeller region radial components of the flow dominate. Near the wall flow occurs mainly in the axial direction towards the top and bottom of the tank. Mixing time measurements reveal that mixing time increases with decreasing impeller speed and with increasing solution concentration (i.e. viscosity). Typical mixing time values are in the range of 250-2600 seconds for different impeller speeds and CMC concentrations.

Rheological properties of idealised models which exhibit all the non-Newtonian flow phenomenology commonly seen in dense suspensions are investigated by particulate-dynamics computer-simulations. The objectives of these investigations are: (i) to establish the origins of various aspects of dense suspension rheology such as shear-thinning, shear thickening and dilatancy; (ii) to elucidate the different regions of a typical dense suspension rheogram by examining underlying structures and shear induced anisotropies in kinetic energy, diffusivity and pressure; (iii) to investigate the scaling of the simplest idealised model suspension; i.e. the hard-sphere model in Newtonian media and its relationship to the isokinetic flow curves obtained through non-equilibrium molecular dynamics (NEMD) simulations; (iv) to preliminarily determine the effect of perturbations present in all real colloidal suspensions, namely particle size polydispersity and a slight 'softness' of the interparticle potential. Non-equilibrium isokinetic simulations have been performed upon ;systems of particles interacting through the classical hard-sphere potential and a perturbation thereof, in which the hard-core is surrounded by a 'slightly soft' repulsive skin. The decision to base the present work upon isokinetic studies was made in order to obtain a better under- standing of suspension rheology by making a direct connection with previous NEMD studies of thermal systemst(93). These studies have shown that the non-linear behaviour exhibited by these systems under shear is atttributable to a shear-induced perturbation of the equilibrium phase behaviour. The present study shows this behaviour to correspond to the high shear region of the generalised suspension flow curve.

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This report provides an introduction to geometric mechanics, which seeks to model the behavior of physical mechanical systems using differential geometric objects. In addition to its elegance as a method of representation, this formulation also admits the application of powerful analytical techniques from geometry as an aid to understanding these systems. In particular, it reveals the fundamental role that symplectic geometry plays in mechanics (something which is not at all obvious from the traditional Newtonian formulation), and in the case of systems exhibiting symmetry, leads to an elucidation of conservation and reduction laws which can be used to simplify the analysis of these systems. The contribution here is primarily one of exposition. Geometric mechanics was developed as an aid to understanding physics, and we have endeavored throughout to highlight the physical principles at work behind the mathematical formalism. In particular, we show quite explicitly the entire development of mechanics from first principles, beginning with Newton's laws of motion and culminating in the geometric reformulation of Lagrangian and Hamiltonian mechanics. Self-contained presentations of this entire range of material do not appear to be common in either the physics or the mathematics literature, but we feel very strongly that this is essential in order to understand how the more abstract mathematical developments that follow actually relate to the real world. We have also attempted to make many of the proofs contained herein more explicit than they appear in the standard references, both as an aid in understanding and simply to make them easier to follow, and several of them are original where we feel that their presentation in the literature was unacceptably opaque (this occurs primarily in the presentation of the geometric formulation of Lagrangian mechanics and the appendix on symplectic geometry). Finally, we point out that the fields of geometric mechanics and symplectic geometry are vast, and one could not hope to get more than a fragmentary glimpse of them in a single work, which necessiates some parsimony in the presentation of material. The subject matter covered herein was chosen because it is of particular interest from an applied or engineering perspective in addition to its mathematical appeal. / text