Visible Light Communications (VLC) has recently emerged as a viable solution for solving the spectrum shortage problem. The idea is to use artificial light sources as medium to communicate with portable devices. In particular, the light sources can be switched on and off with a very high-frequency corresponding to 1s and 0s of digital communication. The high-frequency on-off switching can be detected by electronic devices but not the human eyes, and hence will not affect the light sources' illumination functions. In VLC, if a receiver is equipped with photodiodes that count the number of arriving photons, the channels can be modeled as Poisson channels. Unlike Gaussian channels that are suitable for radio spectrum and have been intensively investigated, Poisson channels are more challenging and are not that well understood. The goal of this thesis is to characterize the fundamental limits of various Poisson channels that models different scenarios in VLC. We first focus on single user Poisson fading channels with time-varying background lights. Our model is motivated by indoor optical wireless communication systems, in which the noise level is affected by the strength of the background light. We study both the single-input single-output (SISO) and the multiple-input and multiple-output (MIMO) channels. For each channel, we consider scenarios with and without delay constraints. For the case without a delay constraint, we characterize the optimal power allocation scheme that maximizes the ergodic capacity. For the case with a strict delay constraint, we characterize the optimal power allocation scheme that minimizes the outage probability. We then extend the study to the multi-user Poisson channels and analyze the sum-rate capacity of two-user Poisson multiple access channels (MAC). We first characterize the sum-rate capacity of the non-symmetric Poisson MAC when each transmitter has a single antenna. We show that, for certain channel parameters, it is optimal for a single-user to transmit to achieve the sum-rate capacity. This is in sharp contrast to the Gaussian MAC, in which both users must transmit, either simultaneously or at different times, in order to achieve the sum-rate capacity. We then characterize the sum-rate capacity of the Poisson MAC with multiple antennas at each transmitter. By converting a non-convex optimization problem with a large number of variables into a non-convex optimization problem with two variables, we show that the sum-rate capacity of the Poisson MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter. We further analyze the sum-rate capacity of two-user Poisson MIMO multiple-access channels (MAC), when both the transmitters and the receiver are equipped with multiple antennas. We first characterize the sum-rate capacity of the Poisson MAC when each transmitter has a single antenna and the receiver has multiple antennas. We show that similar to Poisson MISO-MAC channels, for certain channel parameters, it is optimal for a single user to transmit to achieve the sum-rate capacity, and for certain channel parameters, it is optimal for both users to transmit. We then characterize the sum-rate capacity of the channel where both the transmitters and the receiver are equipped with multiple antennas. We show that the sum-rate capacity of the Poisson MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter.

The implicit-solvent model uses continuum electrostatic theory to represent the salt solution around dissolved biomolecules, leading to a coupled system of the Poisson-Boltzmann and Poisson equations. This thesis uses the implicit-solvent model to study solvation, binding and adsorption of proteins. We developed an implicit-solvent model solver that uses the boundary element method (BEM), called PyGBe. BEM numerically solves integral equations along the biomolecule-solvent interface only, therefore, it does not need to discretize the entire domain. PyGBe accelerates the BEM with a treecode algorithm and runs on graphic processing units. We performed extensive verification and validation of the code, comparing it with experimental observations, analytical solutions, and other numerical tools. Our results suggest that a BEM approach is more appropriate than volumetric based methods, like finite-difference or finite-element, for high accuracy calculations. We also discussed the effect of features like solvent-filled cavities and Stern layers in the implicit-solvent model, and realized that they become relevant in binding energy calculations. The application that drove this work was nano-scale biosensors-- devices designed to detect biomolecules. Biosensors are built with a functionalized layer of ligand molecules, to which the target molecule binds when it is detected. With our code, we performed a study of the orientation of proteins near charged surfaces, and investigated the ideal conditions for ligand molecule adsorption. Using immunoglobulin G as a test case, we found out that low salt concentration in the solvent and high positive surface charge density leads to favorable orientations of the ligand molecule for biosensing applications. We also studied the plasmonic response of localized surface plasmon resonance (LSPR) biosensors. LSPR biosensors monitor the plasmon resonance frequency of metallic nanoparticles, which shifts when a target molecule binds to a ligand molecule. Electrostatics is a valid approximation to the LSPR biosensor optical phenomenon in the long-wavelength limit, and BEM was able to reproduce the shift in the plasmon resonance frequency as proteins approach the nanoparticle.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Dans la première partie de ma thèse, je fournis un programme informatique qui permet aux utilisateurs de déterminer dans quelles circonstances ils doivent mesurer le mouvement des particules. J’explique comment ces mesures peuvent être effectuées et fournissent un programme pour analyser ce type de données. La partie principale de ma thèse comprend des expériences portant sur l'impact de l'exposition répétée au bruit du trafic, la source anthropique la plus courante de bruit dans l'environnement marin, sur les poissons et les invertébrés pendant leur développement. Je démontre qu’une variété de comportements a été touchée par le bruit. J’ai aussi trouvé que le bruit prévisible peut conduire à des impacts différents sur le développement par rapport au bruit imprévisible, mais que certaines espèces de poissons peuvent être en mesure de s'habituer au bruit du trafic, tandis que d'autres non. En outre, je trouve que le développement et la survie des limaces de mer peuvent être impactés négativement par le bruit des bateaux. Les poissons et les invertébrés constituent une source de nourriture vitale pour des millions de personnes et constituent des liens essentiels dans de nombreux réseaux trophiques. L'étude de leur comportement, de développement et de remise en forme peut nous donner un aperçu des impacts de la population et le niveau de bruit de la communauté qui sont pertinents pour la survie des espèces et l'évolution. Le développement de certaines des nouvelles idées et techniques abordées dans cette thèse nous permettra de faire progresser ce domaine vital de la recherche. / As the first part of my thesis, I provide a computer program which allows users to determine under what circumstances they should measure particle motion; I explain how these measurements can be made and provide a program for analysing this type of data. The main part of my thesis comprises experiments investigating the impact of repeated exposure to traffic noise, the most common anthropogenic source of noise in the marine environment, on fishes and invertebrates during development. In all three chapters involving experiments on fish in tanks and in the field, I found that a variety of behaviours were impacted by traffic noise playback. I also found that predictable noise can lead to different impacts on development compared to unpredictable noise, but that some species of fish may be able to habituate to traffic noise, while others suffer lower survival. Further, I found that the development and survival of seahares can be negatively impacted by traffic-noise playback. Fishes and invertebrates provide a vital food source to millions of people and form crucial links in many food webs; studying their behaviour, development and fitness can give us an insight into population and community level impacts of noise that are relevant to species survival and evolution. Developing some of the novel ideas and techniques discussed in this thesis will enable us to advance this vital area of research.

Orientador: Cássio Machiaveli Oishi / Banca: Messias Meneguette Júnior / Banca: Fabrício Simeoni de Souza / Resumo: Neste trabalho, analisamos métodos de diferenças finitas para solução numérica da equação de Poisson em domínios irregulares com condições do tipo Dirichlet, fazendo um estudo detalhado de cada um desses métodos numéricos. Em particular, analisamos o Método das Interfaces Imersas (MII), Métodos Clássicos usando interpolações linear (MCL) e quadrática (MCQ) e um Método do tipo Fronteiras Imersas modificado (MFIM). Inicialmente, comparamos os resultados obtidos por esses métodos na solução numérica de uma equação elíptica unidimensional, envolvendo uma interface localizada em um ponto que não coincide com a malha. No caso unidimensional provamos que o MCL e o MFIM são equivalentes. Posteriormente, analisamos os resultados obtidos por esses métodos na solução numérica de problemas elípticos bidimensionais, com condições de contorno definida sobre geometrias irregulares. Em geral, os métodos foram consistentes com a solução exata. No caso unidimensional o MII e o MCQ apresentaram resultados semelhantes, com ordem de precisão quadrática, enquanto que o MCL e o MFIM são menos precisos para esses testes. Após isso, realizamos testes preliminares envolvendo geometrias bidimensionais irregulares. Os resultados apontam que o MFIM e o MII são mais acurados e possuem ordem de convergência quadrática / Abstract: In this work, we study finite difference methods for the numerical solution of PoissonŠs equation on irregular domains with Dirichlet-type boundary conditions, performing a detailed study of these schemes. In particular, we analyze the Immersed Interfaces method (IIM), the classical method with linear (CML) and quadratic (CMQ) interpolation and the modified immersed boundary method (MIBM). Firstly, we compare the results obtained from these methods for solving a one-dimensional elliptic equation. In this equation, an interface is located at an irregular grid point. In general, all methods have been found consistent to the exact solution. In the one-dimensional case, IIM and CMQ have showed similar results, with second-order accuracy while MBIM and CML have presented less accurate results. Finally, we conduct preliminary results for two-dimensional irregular geometries. The results show that IIM and MIBM are more accurate than the classical method with linear interpolation / Mestre

This dissertation examines the translation of paintings and drawings by François Boucher (1703–1770) into luxury media. Eighteenth-century collectors expended small fortunes on precious objects that reproduced Boucher’s work: cameos, intaglios, enamel-painted porcelain vessels, gold boxes, biscuit porcelain figurines, wool and silk tapestries, and furniture upholstery. Existing studies of eighteenth-century reproduction have tended to focus on innovations in printmaking that enabled the production of inexpensive and extremely faithful facsimiles of works of art. Luxury reproductions, by contrast, were expensive, scarce, and materially assertive, often calling attention to their mediums, and to the act of mediation itself. Through an investigation of the morphological, material, and temporal stakes of these intermedial translations, I show that luxury copies were not derivative substitutes for absent originals, but rather were generative tools of social, artistic, and political identity construction. A central figure in this story is the royal mistress Madame de Pompadour (1721–1764), who was an avid collector of Boucher’s work (and of reproductions after his work), and who reproduced his cameos and intaglios in a limited-edition set of engravings. Through her engravings and decorative installations, Pompadour demonstrated a keen interest in the material processes of transmission and the agency of media. I examine Pompadour’s work and patronage in relation to her political identity as a mediator between the court and the king. Boucher was the perfect collaborator in Pompadour’s project; the material processes of intermedial translation often became the very subject of his work. Boucher’s and Pompadour’s deep investment in the materiality of mediation demands that we revise our understanding of the Rococo “unity of the arts,” which too often is attributed to a dematerialized mobility.

L’identité des cellules souches et des progéniteurs neuraux, comme celle de tout type cellulaire, est caractérisée par des signatures moléculaires spécifiques qui dépendent de l’environnement dans lesquelles les cellules se trouvent. Ainsi, il est primordial d’étudier ces cellules dans un contexte in vivo. Le toit optique du poisson zèbre est un modèle idéal pour ce type d’étude. En effet, c’est une large partie du cerveau moyen localisée en position dorsale et qui présente la particularité de croitre de manière orientée tout au long de la vie de l’animal grâce aux cellules neuroépitheliales présentes à sa périphérie (dans la « peripheral midbrain layer », PML). De plus, les progéniteurs neuroépithéliaux, les progéniteurs lents et les cellules post-mitotiques sont localisées dans des domaines adjacents du toit, conséquence de sa croissance orientée. Chaque population cellulaire est marquée par des profils d’expression particuliers. Ainsi, une recherche dans la base de données ZFIN nous a permis d’identifier environ 50 gènes ayant une forte expression dans les cellules de la PML (progéniteurs neuroépithéliaux). De façon intéressante, beaucoup de « gènes PML » codent pour des facteurs de la biogenèse des ribosomes. L’accumulation de ce type de transcrits dans les progéniteurs lents était surprenante. Ainsi, au cours de mon doctorat, j’ai étudié le rôle spécifique des facteurs de la biogenèse des ribosomes dans le maintien des cellules neuroepithéliales de la PML. En effet, bien qu’il soit généralement admis que la biogenèse des ribosomes est un processus essentiel dans toutes les cellules, il a été récemment démontré que plusieurs facteurs nécessaires à la synthèse des ribosomes ont un rôle tissu-spécifique. Par exemple, Notchless est requis pour la survie de la masse cellulaire interne de l’embryon préimplantatoire de souris. Récemment, des expériences de knock-out conditionnel chez la souris ont montré que Notchless était nécessaire au maintien des cellules souches hématopoïétiques et intestinales, mais pas à celui des cellules différenciées. En effet, en absence de Notchless dans les cellules souches, la grosse sous-unité ribosomique (60S) ne peut pas être exportée hors du noyau et s’accumule. Au contraire, dans les cellules différenciées, où Notchless n’est pas indispensable, cette accumulation n’est pas observée. J’ai commencé une étude fonctionnelle basée sur la surexpression conditionnelle de la forme dominante-négative du gène notchless homolog 1 (nle1, homologue poisson zèbre du gène Notchless mammifère). Selon mon hypothèse, les progéniteurs lents de la PML (Slow amplifying progenitors, SAPs) pourraient avoir besoin de Notchless pour la maturation de la sous-unité 60S, contrairement aux cellules différenciées qui pourraient survivre après la délétion de ce gène. Des expériences sont encore en cours, mais nous avons déjà pu démontrer que nle1 joue un rôle crucial dans la survie des progénitéurs neuroépithéliaux de la PML. En parallèle, j’ai étudié des lignées de poisson-zèbre mutantes pour des gènes codants pour des composants du complexe de snoRNP (box C/D small nucleolar ribonucleoprotein : Fibrillarine, Nop56, Nop58). Les trois mutants présentent des phénotypes similaires, en particulier une apoptose massive et une dérégulation du cycle cellulaire dans l’ensemble du toit optique à 48 heures de développement. Étonnamment, ces résultats sont en faveur d’un arrêt du cycle cellulaire à la transition G2/M. Ainsi, cette étude pourrait permettre de mettre en évidence de nouveaux mécanismes d’arrêt du cycle cellulaire lors de défauts de biogenèse des ribosomes. L’ensemble de ces résultats montrent comment les facteurs de la biogenèse des ribosomes (tout comme le processus) contribue à la régulation fine de l’homéostasie cellulaire, et donc à la détermination de l’identité des cellules progénitrices. / In neural stem cells (NSCs) and neural progenitors (NPs), as in other cell types, cell identity is characterized by specific molecular signatures that depend on the environment provided by neighboring cells. Thus, it is important to study progenitor cells in vivo. The zebrafish optic tectum (OT) is a suitable model for that purpose. Indeed, this large structure of the dorsal midbrain displays life-long oriented growth supported by neuroepithelial cells present at its periphery (in the peripheral midbrain layer, PML). Moreover, neuroepithelial progenitors, fast-amplifying progenitors and post-mitotic cells are found in adjacent domains of the OT, as a consequence of its oriented growth. Each cell population is marked by concentric gene expression patterns. Interestingly, a datamining of the ZFIN gene expression database allowed us to identify around 50 genes displaying biased expression in PML cells (neuroepithelial progenitors). Interestingly, many “PML genes” code for ribosome biogenesis factors. The accumulation of transcripts for such ubiquitously expressed genes in SAPs was very surprising so during my thesis I examined whether ribosome biogenesis may have specific roles in these neuroepithelial cells, while improving our knowledge. Indeed, although it is generally admitted that ribosome biogenesis is essential in all cells, it has been shown quite recently that several components of the ribosome biogenesis have tissue restricted roles. For example, Notchless is required for the survival of the inner cell mass in the preimplantation mouse embryo. More recently, conditional knock-out experiments in mice showed that Notchless is necessary for the maintenance of hematopoietic stem cells and intestinal stem cells, but not for committed progenitors and differentiated cells. Indeed in the absence of Notchless in stem cells, the immature 60S subunit cannot be exported from the nucleus and accumulates. This does not happen in differentiated cells where Notchless is dispensable. I started a functional study based on the conditional overexpression of a dominant-negative form of the gene notchless homolog 1 (nle1, the zebrafish homolog of the mammalian gene Notchless). My hypothesis was that the PML slow-amplifying progenitors (SAPs) may require Notchless for the maturation of the 60S subunit, but not the differentiated cells which could survive also after the deletion of this gene. Experiments are still underway. So far we could demonstrate that nle1 has a crucial role in SAPs. I studied zebrafish mutants for genes coding for the components of the box C/D small nucleolar ribonucleoprotein (snoRNP) complex (Fibrillarin, Nop56, Nop58). Mutants displayed a similar phenotype with massive apoptosis and a deregulation of the cell cycle in the whole tectum at 48hpf. Our data suggest a cell cycle arrest at the G2/M transition, highlighting novel possible mechanisms of cell cycle arrest upon impaired ribosome biogenesis. All together, these data highlight how ribosome biogenesis factors and the whole ribosome biogenesis contribute to the fine regulation of cell homeostasis thereby contributing to the determination of progenitor cell identity.

C’est chez un téléostéen qu’il a été démontré pour la première fois que le contrôle stimulateur de l’axe gonadotrope par la GnRH peut être contrebalancé par un contrôle inhibiteur assuré par la dopamine (DA). Ce contrôle dopaminergique inhibiteur a été retrouvé par la suite chez diverses espèces de vertébrés. Cependant l’importance fonctionnelle de cette voie inhibitrice de régulation varie beaucoup d’une espèce à l’autre. Pour approfondir nos connaissances sur ce système dopaminergique inhibiteur de la reproduction, nous avons utilisé le poisson zèbre (Danio rerio), un modèle de vertébrés pour lequel de nombreux outils moléculaires sont disponibles.Nous avons d’abord démontré qu’il existait bien un contrôle dopaminergique de la fonction gonadotrope dans cette espèce: en injectant un antagoniste dopaminergique en même temps qu’un analogue de la GnRH, nous avons pu stimuler l’expression de la LH dans l’hypophyse et réactiver les cycles de ponte chez des femelles âgées sexuellement régressées, un effet qui n’est pas produit par l’agoniste de la GnRH seul. Nous avons ensuite étudié le substrat neuroanatomique de cette action inhibitrice. Après avoir observé l’expression par les cellules à LH des sous-Types de récepteurs D2 qui existent chez le poisson-Zèbre, nous avons mis en évidence de nombreuses terminaisons dopaminergiques sur- ou à proximité- de ces cellules gonadotropes. Nous avons ensuite localisé, par des expériences de traçage rétrograde chez l’adulte, les corps cellulaires des neurones dopaminergiques qui émettent ces projections, dans la partie la plus antéro-Ventrale de l'aire préoptique. Nous avons appelé ces neurones hypophysiotropes: les neurones dopaminergiques préoptico-Hypophysaires (POHDA). Nous nous sommes aussi intéressés au développement des neurones POHDA. Grâce à des repères anatomiques précoces, nous avons pu les répérer précisément au sein de l’aire préoptique et suivre leur apparition sur des embryons de plus en plus jeunes. Nous avons ainsi mis en évidence que les tout premiers neurones POHDA n’apparaissent qu’à partir de 72 heures post-Fécondation (hpf), soit plus de 24 h après les neurones dopaminergiques du noyau suprachiasmatique (SCDA) voisin. Cette différenciation tardive explique probablement pourquoi les neurones POHDA ont jusque-Là été ignorés dans toutes les études de développement. En outre, nous avons montré que contrairement au nombre des neurones SCDA qui reste constant tout au long de la vie du poisson-Zèbre, celui des neurones POHDA continue d’augmenter tant que le poisson continue à grandir de manière allométrique, grâce à une neurogenèse continue. Enfin, nous avons examiné les profils d'expression de plusieurs gènes en relation avec la régionalisation du cerveau antérieur. Cette étude a permis de montrer que les réseaux génétiques impliqués dans le développement des populations SCDA et POHDA sont au moins en partie différents.Ces travaux démontrent pour la première fois l’existence d’un contrôle dopaminergique inhibiteur de la fonction gonadotrope chez le poisson-Zèbre. Ils décrivent l’anatomie de ce système dopaminergique chez l’adulte, sa mise en place au cours du développement et ses capacités de neurogenèse continue. Ils apportent chez le poisson-Zèbre des bases génétiques sur l’identité régionale de l’aire préoptique qui vont permettre d’aborder des études fonctionnelles sur le développement de ces neurones neuroendocrines mal connus. / It was first demonstrated in a teleost fish that the stimulatory control of the gonadotrope axis by GnRH can be counterbalanced by an inhibitory control exerted by dopamine (DA). Later on, this inhibitory dopaminergic control was found in various vertebrate species. However the functional importance of this regulatory pathway varies according to the species. To deepen our knowledge on this inhibitory dopaminergic system, we used the zebrafish (Danio rerio) as a model, in which numerous molecular tools are available.First we demonstrated that DA indeed plays a role in the neuroendocrine control of zebrafish reproduction. By injecting a dopamine receptor antagonist together with an agonist of the GnRH (GnRHa), we were able to stimulate LH expression in the pituitary, and to reactivate the spawning cycles in sexually regressed old females, an effect of which was not produced by the GnRHa alone.We then studied the neuroanatomical basis of this inhibitory control. After observing the expression of the D2-DA receptors subtypes in LH cells, we highlighted numerous dopaminergic terminals on- or in the vicinity of- these cells. We then localized, by DiI retrograde tracing experiments in adult zebrafish, the dopaminergic cell bodies giving rise to these projections in the most antero-Ventral part of the preoptic area. We have called these hypophysiotropic neurons the preoptico-Hypophysial (POH) DA neurons.We next studied the development of POHDA neurons. Taking advantage of early anatomical landmarks, we followed the embryonic development of these cells. We showed that the first POHDA neurons arise at around 72 hours post fertilization (hpf), more than 24 hours later that the DA neurons in the neighbor suprachiasmatic nucleus (SCDA). This late differentiation would explain why POHDA neurons have not been studied in the developing embryo so far. We showed that contrary to the number of the SCDA neurons, which is constant all along the fish life, that of POHDA neurons increases proportionally to the growth of the fish due to continuous neurogenesis. Finally, we examined the expression profiles of developmental genes related to the regionalization of the anterior forebrain. We showed that the genetic networks involved in the development of POHDA and SCDA populations are at least partly different. To summarize, this work demonstrates for the first time the existence of a dopaminergic inhibitory control of gonadotrope function in zebrafish. It describes the anatomy of the preoptico-Hypophyseal dopaminergic system supporting these DA actions and the setting up of these neurons during embryonic development. We show that these neuroendocrine population displays neurogenesis even during adulthood. Our findings also provide the genetic bases for future functional studies on the development of POHDA, a poorly studied neuroendocrine DA population.

In this thesis, a novel framework for dynamic congestion control has been proposed. The study is about the congestion control in broadband communication networks. Congestion results when demand temporarily exceeds capacity and leads to severe degradation of Quality of Service (QoS) and possibly loss of traffic. Since traffic is stochastic in nature, high demand may arise anywhere in a network and possibly causing congestion. There are different ways to mitigate the effects of congestion, by rerouting, by aggregation to take advantage of statistical multiplexing, and by discarding too demanding traffic, which is known as admission control. This thesis will try to accommodate as much traffic as possible, and study the effect of routing and aggregation on a rather general mix of traffic types. Software Defined Networking (SDN) and Network Function Virtualization (NFV) are concepts that allow for dynamic configuration of network resources by decoupling control from payload data and allocation of network functions to the most suitable physical node. This allows implementation of a centralised control that takes the state of the entire network into account and configures nodes dynamically to avoid congestion. Assumes that node controls can be expressed in commands supported by OpenFlow v1.3. Due to state dependencies in space and time, the network dynamics are very complex, and resort to a simulation approach. The load in the network depends on many factors, such as traffic characteristics and the traffic matrix, topology and node capacities. To be able to study the impact of control functions, some parts of the environment is fixed, such as the topology and the node capacities, and statistically average the traffic distribution in the network by randomly generated traffic matrices. The traffic consists of approximately equal intensity of smooth, bursty and long memory traffic. By designing an algorithm that route traffic and configure queue resources so that delay is minimised, this thesis chooses the delay to be the optimisation parameter because it is additive and real-time applications are delay sensitive. The optimisation being studied both with respect to total end-to-end delay and maximum end-to-end delay. The delay is used as link weights and paths are determined by Dijkstra's algorithm. Furthermore, nodes are configured to serve the traffic optimally which in turn depends on the routing. The proposed algorithm is a fixed-point system of equations that iteratively evaluates routing - aggregation - delay until an equilibrium point is found. Three strategies are compared: static node configuration where each queue is allocated 1/3 of the node resources and no aggregation, aggregation of real-time (taken as smooth and bursty) traffic onto the same queue, and dynamic aggregation based on the entropy of the traffic streams and their aggregates. The results of the simulation study show good results, with gains of 10-40% in the QoS parameters. By simulation, the positive effects of the proposed routing and aggregation strategy and the usefulness of the algorithm. The proposed algorithm constitutes the central control logic, and the resulting control actions are realisable through the SDN/NFV architecture.

Neste trabalho abordam-se alguns aspectos numéricos relacionados ao movimento de uma partícula carregada em um fluido ionizado, constituindo assim o fenômeno de eletroforese. A equação de Navier-Stokes governa a hidrodinâmica do sistema, sendo atribuída a esta um termo forçante relacionado a equação de Poisson-Boltzmann que descreve a interação com o campo elétrico. A simulação foi realizada utilizando a linguagem Fortran 90 e as discretizações foram feitas pelo método de diferenças finitas junto as equações governantes. Para descrever a posição da partícula foi usada a técnica de fronteira virtual, onde são criados pontos lagrangeanos sobre,o contorno da partícula formando uma espécie de segunda malha. Foram feitos testes com objetivo de validar as equações governantes e identificar a influencia das condições de contorno direção da partícula. / In this work we study some of the numerical aspects related to the motion of a charged particle in an ionized fluid, known as the phenomenon of electrophoresis. The Navier-Stokes equations models the ,hydrodynamics of the system, with the addition of a forcing term, related to the Poisson-Boltzmann equation, which describes the interaction of the electric field. The simulation was performed using Fortran 90 and discretizations were made by the method of finite differences applied to the governing equations. To describe the position of the particle the technique of virtual boundary is used, where Lagrangean points are created around the circumference of the particle forming a sort of second mesh. Tests were made with the objective of validating the governing equations and to identify the influence of boundary conditions in the direction of the particle.