Thesis (Ph.D.) - University of Queensland, 2003. / Includes bibliography.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 171-180).

Thesis (Ph. D.)--Oregon State University, 2008. / Printout. Includes bibliographical references (leaves 88-95). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 96-107).

After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure theory, we explore the notion of a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, we find that Hausdorff dimension can be computed through a counting argument rather than the traditional way. This formulation is then applied to obtain simple proofs of some of the dimensional properties of Brownian motion, such as the doubling of the dimension of a set of dimension smaller than 1/2 under Brownian motion, by utilising Anderson's formulation of Brownian motion as a hyperfinite random walk. We also use the technique to refine a theorem of Orey and Taylor's on the Hausdorff dimension of the rapid points of Brownian motion. The result is somewhat stronger than the original. Lastly, we give a corrected proof of Kaufman's result that the rapid points of Brownian motion have similar Hausdorff and Fourier dimensions, implying that they constitute a Salem set. / Mathematical Sciences / D. Phil. (Mathematical Sciences)

>Magister Scientiae - MSc / The industry of pension funds has become one of the drivers of today’s economic activity by its important volume of contribution in the financial market and by creating wealth. The increasing importance that pension funds have acquired in today’s economy and financial market, raises special attention from investors, financial actors and pundits in the sector. Regarding this economic weight of pension funds, a thorough analysis of the performance of different pension funds plans in order to optimise benefits need to be undertaken. The research explores criteria and invariants that make it possible to compare the performance of different pension fund products. Pension fund companies currently do measure their performances with those of others. Likewise, the individual investing in a pension plan compares different products available in the market. There exist different ways of measuring the performance of a pension fund according to their different schemes. Generally, there exist two main pension funds plans. The defined benefit (DB) pension funds plan which is mostly preferred by pension members due to his ability to hold the risk to the pension fund manager. The defined contributions (DC) pension fund plan on the other hand, is more popularly preferred by the pension fund managers due to its ability to transfer the risk to the pension fund members. One of the reasons that motivate pension fund members’ choices of entering into a certain programme is that their expectations of maintaining their living lifestyle after retirement are met by the pension fund strategies. This dissertation investigates the various properties and characteristics of the defined contribution pension fund plan with a minimum guarantee and benchmark in order to mitigate the risk that pension fund members are subject to. For the pension fund manager the aim is to find the optimal asset allocation strategy which optimises its retribution which is in fact a part of the surplus (the difference between the pension fund value and the guarantee) (2004) [19] and to analyse the effect of sharing between the contributor and the pension fund. From the pension fund members’ perspective it is to define a optimal guarantee as a solution to the contributor’s optimisation programme. In particular, we consider a case of a pension fund company which invests in a bond, stocks and a money market account. The uncertainty in the financial market is driven by Brownian motions. Numerical simulations were performed to compare the different models.

xvi, 127 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / Brownian ratchets generate transport at the micron scale with the help of thermal motion. The Brownian ratchet studied here is the flashing ratchet which transports particles by switching on and off a spatially asymmetric, periodic potential. Experimental work in the literature indicates that interdigitated electrode arrays can been used to create such potentials in solution, but no detailed study of particle trajectories has accompanied such experiments. Here, interdigitated electrode array devices were fabricated. Analysis of the trajectories of individual particles moving in response to a switching voltage revealed that the transport is likely due to electroosmotically driven fluid flow, not the Brownian ratchet effect. Simulation work in the literature predicts that polymers in a ratchet potential will exhibit qualitatively different transport from the particle case. Here, polymer transport was tested experimentally using interdigitated electrode array devices, collecting images of individual à à à à à à » DNA molecules and applying a flashing voltage. The DNA was observed to move in response to the applied potential and the resulting images contain DNA trajectories and also information about its conformations and dynamics. Conformations were analyzed using principal components analysis, extracting the normal modes of the variations amongst large sets of polymer images. These results iv show no conformational changes indicative of the polymer ratchet mechanism, despite the polymer motion. This result and detailed analysis of the DNA trajectories, suggest that the observed motion was driven by bulk flow generated through electroosmosis, in agreement with results from experiments using particles in similar devices. Deterministic Lateral Displacement (DLD) uses an array of obstacles in a microfluidic channel to sort micron-scale objects with à à à à à ¢ à à à à à ¼10nm precision. However, very little work has been done to quantitatively address the role of diffusion in DLD sorting. Here, modeling of transport in DLD arrays has shown that using arrays of obstacles that are small compared to their separation can create sorting that is robust against changes in flow velocity. Also, novel sorting modes were revealed when the model was applied to unconventional array geometries that have not been discussed in the literature. / Adviser: Heiner Linke

xiv, 171 p. ; ill. (some col.) A print copy of this title is available through the UO Libraries. Search the library catalog for the location and call number. / Biological molecular motors, which use chemical energy from ATP hydrolysis to generate mechanical force, are involved in a variety of important mechanical processes in eukaryotic cells, such as intracellular transport, cell division and muscle contraction. These motors, which produce motion on the nanoscale, operate in the presence of substantial thermal noise. In this dissertation, two approaches are used to model the physics of nanoscale motors: (1) A theoretically established type of Brownian motor called the "flashing ratchet" is studied. This motor transports diffusive particles in a preferred direction. (2) A coarse-grained mechanical model for the biological molecular motor myosin-V is developed, and used to study the role of Brownian diffusion, and the interaction between chemical and mechanical degrees of freedom, in the transport mechanism of this motor. In chapter III, Brownian dynamics simulations and analytical calculations demonstrate that the average velocity of rigid chains of particles in a flashing ratchet reverses direction in response to changing the size of the chain or the temperature of the heat bath. Recent studies have introduced policies for "closed-loop" control of a flashing ratchet, in which the system is controlled based on information about its internal state (such as the positional distribution of particles). In chapter IV, the effect of time delay on the implementation of closed-loop control of a flashing ratchet is investigated. For a large ensemble, a well-chosen delay time improves the ratchet performance (increasing the velocity) by synchronizing into a quasi-stable mode that takes advantage of the semi-deterministic nature of the time development of average quantities for a large ensemble. I n chapter V, a coarse-grained mechanical model is presented for the transport mechanism of myosin-V, which walks along intracellular filaments. The model is well constrained by experimental data on the mechanical properties of myosin V and on the kinetic cycle. An experimentally motivated model for the intramolecular coordination of the motor's steps is proposed and tested. / Adviser: Heiner Linke

Orientador: Roberto E. Lagos Monaco / Banca: José Antonio Roversi / Banca: Bernardo Laks / Resumo: Neste trabalho estudamos o modelo do movimento Browniano de uma partícula carregada sob a ação de campos elétrico e magnético, externos e homogêneos, no formalismo de Langevin. Calculamos a energia cinética média através do teorema da flutuação-dissipação e obtivemos uma expressão para a temperatura efetiva das partículas Brownianas em função da temperatura do reservatório e dos campos externos. Esta temperatura efetiva mostrou-se sempre maior que a temperatura do reservatório, o que explica a expressão "portadores quentes". Estudamos essa temperatura efetiva no regime assintótico, ou seja, no estado estacionário atingido em tempos muito longos (quando comparado com o tempo de colisão) e a utilizamos para escrever as equações de transporte em semicondutores, denominadas equações de Shockley generalizadas sendo que incluem nesse caso também a ação do campo magnético. Uma aplicação direta e relevante foi a modelagem para o já conhecido efeito Gunn para portadores assumidos como Brownianos. A temperatura efetiva calculada por nós no regime transiente permitiu estudar também os efeitos do reservatório na relaxação da temperatura efetiva à temperatura terminal (de não equilíbrio e estacionária). Nossos resultados no que diz respeito ao efeito Gunn, embora seja o modelo mais simples de um portador Browniano, mostrou uma surpreendente concordância com resultados experimentais, sugerindo que modelos mais sofisticados devam incluir os elementos apresentados neste estudo / Abstract: We present a Brownian model for a charged particle in a field of forces, in particular, electric and magnetic external homogeneous fields, within the Langevin formalism. We compute the average kinetic energy via the fluctuation dissipation and obtain an expression for the Brownian particle's effective temperature. The latter is a function of the heat bath temperature and both external fields. This effective temperature is always greater than the heat bath temperature, therefore the expression "hot carriers". This effective temperature, in the asymptotic regime, the stationary state at long times (greater than the collision time), is used to write down the transport equations for semiconductors, namely the generalized Shockley equations, now incorporating the magnetic field effect. A direct and relevant application follows: a model for the well known Gunn effect, assuming a Brownian scheme. In the transient regime the computed effective temperature also allow us to probe some features of the heat bath, as the effective temperature relaxes to its terminal stationary value. As for our results in the Gunn effect model, the simplest of all in a Brownian scheme, we obtain a surprisingly good agreement with experimental data, suggesting that more involved models should include our minimal assumptions / Mestre

Esse é um trabalho teórico e experimental em que princípios básicos de mecânica estatística são utilizados para entender a dinâmica de micro e nano esferas acopladas direta e indiretamente a células aderentes vivas, objetivando a caracterização mecânica das mesmas. Dentre esses princípios básicos estão inclusos, principalmente, conceitos relacionados à difusão. Na difusão clássica, tem-se uma dependência linear do deslocamento quadrático médio com o tempo. Caso contrário, quando o expoente é diferente de um, tem-se o que se chama de difusão anômala. Caso seja maior que um, o processo é superdifusivo, e se menor que um, subdifusivo. Para se estudar o comportamento mecânico de sistemas complexos pode-se usar micro e nanoesferas como elementos de análise. Essas esferas são dispostas no material a ser estudado, e observando a sua dinâmica é possível caracterizar o processo que conduziu essa dinâmica e consequentemente inferir propriedades físicas do material. Nesse trabalho aplicam-se técnicas de rastreamento de partículas, microscópicas e nanoscópicas, para estudar propriedades dinâmica de células, especialmente difusibilidade, remodelação da estrutura celular e campos de força. Para isso foram utilizadas duas técnicas experimentais de rastreamento de micro e nanoesferas e modelos fenomenológicos e de mecânica estatística. Essas propriedades dinâmicas tem uma grande semelhança com materiais vítreos moles. Nesse contexto, certas funções celulares, como divisão, contração, difusão, requerem que as células apresentem fluidez similarmente a um líquido, enquanto que para outras funções, como manter a sua estrutura celular, elas devam ter uma aparência mais rígida. Essas características assemelham-se a um material vítreo, onde desordem e metastabilidade são características subjacentes de suas funções mecânicas. Os resultados experimentais apresentados aqui evidenciam essa metaestabilidade na forma de anomalias e correlações temporais dos vários dados coletados. Também explicamos os dados experimentais encontrados em termos das atividades metabólicas e a remodelação ativa do citoesqueleto. Mostra-se também os dados obtidos para músculo cardíaco em plena atividade pulsátil. Os resultados aqui obtidos têm aplicações diretas em pesquisa básica e clínica. / This is a theoretical and experimental work in which basic principles of statistical mechanics are used to understand the dynamics of micro and nano spheres attached directly or indirectly to living adherent cells, with the aim of the mechanical characterization of them. Among these basic principles, mainly concepts related to diffusion are included. In classical diffusion, there is a linear dependence of the mean squared displacement in time. Otherwise, when the exponent is diferent than one , there is what is called anomalous diffusion. If it is bigger than one, the process is superdiffusive, and if it is smaller than one, subdiffusive. To study the mechanical behavior of complex systems,micro and nanospheres can be used as analysis elements. These spheres are arranged in the material to be studied, and from observation of the dynamics is possible to characterize the leading process of this dynamic and therefore infer physical properties of the material. In this work, particle tracking techniques, for microscopic and nanoscopic spheres, are applied to study dynamic properties of cells, especially diffusivity, remodeling of the cell structure and force fields. For that we used two experimental techniques of tracking of micro and nanospheres, and phenomenological and statistical mechanics models. These dynamic properties have a great similarity to soft glassy materials. In this context, certain cellular functions such as division, contraction, diffusion, require that cells present fluidity similarly to a liquid, while for other functions, such as keeping the cellular structure, they should have a stiffer appearance. These characteristics resemble a glassy material, where disorder and metastability are underlying characteristics of their mechanical functions. The experimental results presented here show this metastability as anomalies and temporal correlations of the various data collected. We also explain the experimental data found in terms of metabolic activity and the active remodeling of the cytoskeleton. Also data obtained for heart muscle in full pulsatile activity is showed. The results obtained have direct applications in basic and clinical research.