La dynamique de particules colloïdales à l'interface entre deux fluides joue un rôle central dans la micro-rhéologie, l'encapsulation, l'émulsification, la formation de biofilms, la décontamination de l'eau. En outre, ce sujet est également stimulant d'un point de vue théorique en raison de la complexité de l'hydrodynamique à l'interface et du rôle de la ligne de contact. Malgré ce grand intérêt, le comportement d'une particule à une interface fluide n'a jamais été caractérisé directement. Dans cette thèse, nous étudions le mouvement brownien de billes micrométriques de silice et de sphéroïdes de polystyrène à une interface eau-air. Nous contrôlons expérimentalement tous les paramètres d'intérêt. L'angle de contact des billes est finement ajusté dans la gamme 30°-140° par des traitements chimiques de surface et mesuré in situ par interférométrie. Le rapport d'aspect de particules sphéroïdales varie dans la gamme 1 -10 par étirage de billes sphériques commerciales. Les dynamiques de translation et de rotation sont suivies par particle tracking. Contre intuitivement et contre tous les modèles hydrodynamiques la diffusion est beaucoup plus lente que prévu. Pour expliquer cette dissipation supplémentaire nous concevons un modèle tenant compte de la contribution des fluctuations thermiques de l'interface à la ligne de contact. Les fluctuations donnent origine à des forces aléatoires qui s'ajoutent à celles dues aux chocs de molécules. Le théorème de fluctuation-dissipation permet d'obtenir la friction supplémentaire associée à ces forces flottantes. La friction totale est discutée en termes d'hétérogénéités de la surface des particules et d'ondes capillaires à l'interface. / The dynamics of colloidal particles at the interface between two fluids plays a central role in micro-rheology, encapsulation, emulsification, biofilms formation and water remediation. Moreover, this subject is also challenging from a theoretical point of view because of the complexity of hydrodynamics at the interface and of the role of the contact line. Despite this great interest, the behavior of a single particle at a fluid interface was never directly characterized.In this thesis, we study the Brownian motion of micrometric spherical silica beads and anisotropic polystyrene spheroids at a flat air-water interface. We fully characterize and control all the experimentally relevant parameters. The bead contact angle is finely tuned in the range 30-140° by surface treatments and measured in situ by a homemade Vertical Scanning Interferometer. The spheroid aspect ratio varies in the range 1 – 10 by stretching of commercial beads. The translational and the rotational dynamics are followed by particle tracking.Counter-intuitively, and against all hydrodynamic models, the diffusion is much slower than expected. To explain this extra dissipation we devised a model considering the contribution of thermally activated fluctuations of the interface at the triple line. Such fluctuations couple with the lateral movement of the particle via random forces that add to the ones due to the shocks of surroundings molecules. Fluctuation-dissipation theorem allows obtaining the extra friction associated to this additional mechanism. The fitting values of the total friction are discussed in term of the typical scales of particle surface heterogeneities and of surface capillary waves.

>Magister Scientiae - MSc / The problem of optimal investment has been extensively studied by numerous researchers in order to generalize the original framework. Those generalizations have been made in different directions and using different techniques. For example, Perera [Optimal consumption, investment and insurance with insurable risk for an investor in a Levy market, Insurance: Mathematics and Economics, 46 (3) (2010) 479-484] applied the martingale approach to obtain a closed form solution for the optimal investment, consumption and insurance strategies of an individual in the presence of an insurable risk when the insurable risk and risky asset returns are described by Levy processes and the utility is a constant absolute risk aversion. In another work, Sattinger [The Markov consumption problem, Journal of Mathematical Economics, 47 (4-5) (2011) 409-416] gave a model of consumption behavior under uncertainty as the solution to a continuous-time dynamic control problem in which an individual moves between employment and unemployment according to a Markov process. In this thesis, we will review the consumption models in the above framework and will simulate some of them using an infinite series expansion method − a key focus of this research. Several numerical results obtained by using MATLAB are presented with detailed explanations.

This dissertation focuses on the performance analysis of multiclass open queueing networks using semi-martingale reflecting Brownian motion (SRBM) approximation. It consists of four parts. In the first part, we derive a strong approximation for a multiclass feedforward queueing network, where jobs after service completion can only move to a downstream service station. Job classes are partitioned into groups. Within a group, jobs are served in the order of arrival; that is, a first-in-first-out (FIFO) discipline is in force, and among groups, jobs are served under a pre-assigned preemptive priority discipline. We obtain an SRBM as the result of strong approximation for the network, through an inductive approach. Based on the strong approximation, some procedures are proposed to approximate the stationary distribution of various performance measures of the queueing network. Our work extends and complements the previous work done on the feedforward queueing network. The numeric examples show that the strong approximation provides a better approximation than that suggested by a straightforward interpretation of the heavy traffic limit theorem. In the second part, we develop a Brownian approximation for a general multiclass queueing network with a set of single-server stations that operate under a combination of FIFO (first-in-first-out) and priority service disciplines and are subject to random breakdowns. Our intention here is to illustrate how to approximate a queueing network by an SRBM, not to justify such approximation. We illustrate through numerical examples in comparison against simulation that the SRBM model, while not always supported by a heavy traffic limit theorem, possesses good accuracy in most cases, even when the systems are moderately loaded. Through analyzing special networks, we also discuss the existence of the SRBM approximation in relation to the stability and the heavy traffic limits of the networks. In most queueing network applications, the stationary distributions of queueing networks are of great interest. It becomes natural to approximate these stationary distributions by the stationary distributions of the approximating SRBMs. Although we are able to characterize the stationary distribution of an SRBM, except in few limited cases, it is extremely difficult to obtain the stationary distribution analytically. In the third part of the dissertation, we propose a numerical algorithm, referred to as BNA/FM (Brownian network analyzer with finite element method), for computing the stationary distribution of an SRBM in a hypercube. SRBM in a hypercube serves as an approximate model of queueing networks with finite buffers. Our BNA/FM algorithm is based on finite element method and an extension of a generic algorithm developed in the previous work. It uses piecewise polynomials to form an approximate subspace of an infinite dimensional functional space. The BNA/FM algorithm is shown to produce good estimates for stationary probabilities, in addition to stationary moments. This is in contrast to the BNA/SM (Brownian network analyzer with spectral method) developed in the previous work, where global polynomials are used to form the approximate subspace and they sometime fail to produce meaningful estimates of these stationary probabilities. We also report extensive computational experiences from our implementation that will be useful for future numerical research on SRBMs. A three-station tandem network with finite buffers is presented to illustrate the effectiveness of the Brownian approximation model and our BNA/FM algorithm. In the last part of the dissertation, we extend the BNA/FM algorithm to calculate the stationary distribution of an SRBM in an orthant. This type of SRBM arises as a Brownian approximation model for queueing networks with infinite buffers. We prove the convergence theorems which justify the extension. A three-machine job shop example is presented to illustrate the accuracy of our extended BNA/FM algorithm. In fact, this extended algorithm is also used in the first two parts of this dissertation to analyze the performance of several queueing network examples and it gives fairly good performance estimates in most cases. / Business, Sauder School of / Graduate

Orientador: Amir Ordacgi Caldeira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-14T14:38:31Z (GMT). No. of bitstreams: 1 Valente_DanielMendonca_M.pdf: 3285803 bytes, checksum: ada969db5abe126088faf5bdf5aa0c24 (MD5) Previous issue date: 2009 / Resumo: Este trabalho consiste em um estudo do emaranhamento em sistemas quânticos abertos, modelados como partículas brownianas. O interesse surge da possibilidade de entender como o meio pode criar ou manter emaranhamento entre sistemas quânticos, em vez de somente ocasionar perda de coerência e energia. Primeiramente, revisamos os significados do emaranhamento em mecânica quântica e algumas formas de quantificá-lo. Em seguida, estudamos a literatura de sistemas quânticos abertos para uma partícula, em especial o movimento browniano quântico. Com isso, foi possível calcular o emaranhamento entre uma partícula quântica browniana e seu reservatório. Numa segunda etapa, estudamos o modelo de duas partículas brownianas em um banho comum. Esse modelo permite a introdução não só de uma escala de tempo característica como também uma de comprimento. Um potencial efetivo entre as partículas surge no modelo como consequência das hipóteses assumidas. Na ausência de potencial externo, é preservada a invariância translacional do sistema. Porém, pudemos alcançar nosso principal resultado, que foi calcular a matriz densidade das duas partículas em equilíbrio térmico e, com ela, o emaranhamento entre as partículas / Abstract: This work consists in a study of entanglement in open quantum systems, within the brownian particles model. The interest comes from the possibility of understanding the mechanisms that lead the environment to create or to keep entanglement between quantum systems and not only make them lose energy or coherence. We start by making a review of the meaning of entanglement to quantum mechanics and some ways to quantify it. Then, we study the literature of open quantum systems for one particle, specially the quantum brownian motion. Moreover, it has been possible to calculate the entanglement between the quantum brownian particle and its reservoir. At a second stage, we studied the model of two brownian particles in a common bath. This model permits not only the introduction of a time scale but also of a lenth one. An effective potential between the particles emerges in the model as a consequence of our assumptions. In the absence of an external potential, the system's translational invariance is preserved. The last step was to achieve what became our main result. We have calculated the equilibrium density matrix for the two brownian particles and the entanglement between them / Mestrado / Física Geral / Mestre em Física

In the mathematical modeling of the classical option pricing models it is assumed that the underlying stock price process follows a geometric Brownian motion, but through statistical analysis persistency was found in the log-returns of some South African stocks and Brownian motion does not have persistency. We suggest the replacement of Brownian motion with fractional Brownian motion which is a Gaussian process that depends on the Hurst parameter that allows for the modeling of autocorrelation in price returns. Three fractional Black-Scholes (Black) models were investigated where the underlying is assumed to follow a fractional Brownian motion. Using South African options on futures and warrant prices these models were compared to the classical models. / Dissertation (MSc)--University of Pretoria, 2012. / Mathematics and Applied Mathematics / unrestricted

The goal of this thesis was to get familiar with the basics of mathematical description of the thermal motion of particles in a given media, and with other possibilities of the software package COMSOL Multiphysics. A model for viscous and viscoelastic environments was created, a uniform and user friendly system for simulation and calculation of MSD and system for data conversion from FCS to MSD. Furthermore, the possibilities of the model for use in microrheology were assessed and another procedure in the implementation of the COMSOL program in the characterization of gels was proposed.

No description available.

In this thesis, I will study the qualitative properties of solutions of stochastic differential equations arising in applications by using the numerical methods. It contains two parts. In the first part, I will first review some of the basic theory of the stochastic calculus and the Ito-Taylor expansion for stochastic differential equations (SDEs). Then I will discuss some numerical schemes that come from the Ito-Taylor expansion including their order of convergence. In the second part, I will use some schemes to solve the stochastic Duffing equation, the stochastic Lorenz equation, the stochastic pendulum equation, and the stochastic equations which model the spread options.

This thesis investigates DNA dynamics and translocation through nanopores using Brownian dynamics (BD) simulations, offering insights into sequencing technologies, DNA marker detection, and accurate barcoding utilizing solid-state nanopore platforms. First, we in silico study the intricate process of capture and translocation in a single nanopore. Our simulation reveals a high probability of hairpin loop formation during the capture process. However, attaching a charged tag to one end of DNA improves multi-scan rates and enhances unidirectional translocations. We use modulating voltage biases to multi-scan a lambda-phage dsDNA with oligonucleotide flap markers (tags) through a single and double nanopore system. Our study shows that the bulkier tags introduce velocity variations along the chain length that lead to potential inaccuracies in genetic distance (barcode) estimations. We introduce an interpolation scheme that incorporates both the tag velocities and the average velocity of the chain to improve barcode precision. Subsequently, we include bead and side-chain tags to explain asymmetric dwell time distributions as observed in double nanopore experiments. Our findings indicate that local charge interactions between tags and the nanopore's electric field introduce dwell time asymmetries that can be used for discriminating tags based on their net charges. Finally, we obtain the current blockades of the molecular motifs attached to a dsDNA using electrokinetic Brownian dynamics (EKBD) simulation. Our simulation demonstrates that divalent salt reduces the translocation speed, facilitating precise measurement of the motif's dwell time. Finally, we formulate a volumetric ansatz to construct current blockade diagrams from the ordinary BD simulation in a computationally efficient way and show that using simple scale factors, these volumetric blockades can be mapped accurately to the ionic current blockades obtained from more expensive EKBD simulation. Our studies present comprehensive explorations of DNA translocation and barcoding methods in solid-state nanopores, demonstrating their utility in nanopore sequencing and nanobiotechnology

No description available.