Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6455. Adviser: Karl Hess. Includes bibliographical references (leaves 86-88) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6456. Adviser: M. B. Weissman. Includes bibliographical references (leaves 75-78) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6461. Adviser: Eduardo Fradkin. Includes bibliographical references (leaves 110-116) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6463. Adviser: Steve Granick. Includes bibliographical references. Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1058. Adviser: Dale Van Harlingen. Includes bibliographical references (leaves 120-122) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1060. Adviser: S. Lance Cooper. Includes bibliographical references (leaves 107-111) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. / Source: Dissertation Abstracts International, Volume: 69-05, Section: B, page: 3051. Adviser: Richard Martin. Includes bibliographical references (leaves 128-130) Available on microfilm from Pro Quest Information and Learning.

Diffusion is a transport process of great interest as it pertains to many problems in biology, medicine and chemistry. In particular, studies of diffusion taking place in porous systems could help to model processes such as toxins spreading in soils or groundwater, transport of materials through permeable membranes or polyelectrolyte migration in gel electrophoresis. A more thorough understanding of the details of diffusion at the microscopic level could be useful in designing optimized gels for electrophoresis as well as more precise sieving methods. In numerical studies, a common approach is to model diffusion by using a Monte Carlo (MC) algorithm of a random walk on a lattice. In this work, we use methodologies to solve these algorithms exactly and thus efficiently obtain precise results. This thesis consists of two studies, in the form of publishable manuscripts, of the biased and unbiased random walk of small particles on a lattice. First, we model the diffusion of point-like particles in networks of identical periodic square and cubic cavities interconnected by holes. The geometry of these cavities is parameterized in order to study these systems for a variety of different cavity structures. The diffusion inside these systems is modeled by a random walk on a lattice with an algorithm previously developed by the Slater group. In this approach, the MC algorithm can be solved exactly, thereby reducing the time required to obtain precise results which would otherwise require lengthy simulations. We test theoretical predictions and validate analytical results for various asymptotic cases. Additionally, we develop interpolation functions to fit our exact numerical data. In the second study, we develop a new matrix method of exact calculation by expanding and improving a previous model to overcome its limitations. Our new model is capable of treating random walks biased by periodic time-dependent fields. We chose to model the case of particles diffusing in a 2-D network of trap-shaped obstacles in the presence of an external force (of finite frequency and arbitrary strength). In these studies, we examine the effect that varying the frequency of the applied force has on the mean velocities of particles of different sizes. Using this approach, we are able to qualitatively reproduce known experimental results. As in the first project, this new algorithm can be solved exactly and thus provides the same advantages, including a significant reduction in the time required to obtain precise results.

The photoluminescence of quantum dots is studied in a high magnetic field regime where the cyclotron frequency is comparable to the confinement energy. Applying a magnetic field perpendicular to the lateral potential plane lifts the shell degeneracy and magneto-photoluminescence spectroscopy therefore provides a probe to investigate the energy shell structure of quantum dots. By isolating a single quantum dot, the inhomogeneous broadening from a distribution of dot sizes and compositions is eliminated and the fine structure of the spectrum is revealed. The orbital splitting of angular momentum states is shown to follow the Fock-Darwin scheme. However, it is also apparent that each angular momentum branch consists of two distinct lines whose magnetic field evolution cannot be explained by a simple Zeeman spin splitting. The dependence of line splitting on orbital state can be described by the addition of spin-orbit coupling to the Fock-Darwin model. Accordingly, a quantitative measurement of the spin-orbit coupling strength in self-assembled quantum dots is obtained for the first time.

La ferrihydrite est un oxyde de fer abondant dans les milieux marins et lacustres, qui peut influencer la disponibilité de certains nutriments et purifier l'eau de métaux toxiques. Toutefois, les mécanismes entraînant sa formation et les raisons pour lesquelles elle est toujours nanoparticulaire sont encore mal connus. À partir de la théorie classique de la nucléation, je développe dans cette thèse un modèle simple pour la précipitation aqueuse de phases faiblement cristallines. Il s'agit d'un système d'équations différentielles représentant l'évolution temporelle de la distribution de taille des amas précipités. En utilisant les paramètres physico-chimiques connus pour la ferrihydrite, ce modèle produit des distributions dont le rayon moyen correspond aux valeurs attendues. Pour mieux comparer les distributions simulées et réelles, je devrai préciser les paramètres physico-chimiques de la ferrihydrite et avoir accès à des mesures plus précises de la distribution de taille des échantillons expérimentaux.