Universiẗat, Diss., 2000--München.

Techn. University, Diss., 2002--Berlin.

Techn. Hochsch., Diss., 2002--Aachen.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 43-45). Also available in electronic version.

Techn. University, Diss., 2004--Berlin.

The magnetic behaviour of thin films of (111) FCC structures and (0001) corundum structured materials were studied by the mean field analysis and some Monte Carlo simulation. These models were conditioned on a mapping from first principles calculations to the Ising model. The effect of the suggested octopolar reconstruction for the polar (111) surfaces of FCC was also examined.

Monocamadas insolúveis localizadas sobre a superfície de um líquido são sistemas conhecidos e estudados há mais de 100 anos. Elas são formadas quando moléculas anfifílicas são depositadas sobre algum solvente em condições especiais. Quando sofrem compressão isotérmica, tais sistemas exibem um comportamento muito complexo podendo sofrer várias transições de fase nesse processo. Embora, com o surgimento na década de 1990 de técnicas experimentais que proporcionaram um maior ?insight? no entendimento das referidas transições, há muitas questões que permanecem em aberto, principalmente no que diz respeito à influência exercida: pelas conformações intramoleculares; pelas interações entre as moléculas anfifílicas; pelas interações entre as moléculas anfifílicas e as moléculas do solvente sobre as referidas transições. Para ajudar a preencher esta lacuna são necessários modelos moleculares que auxiliem a obtenção da resposta destas questões. É neste contexto que se insere este trabalho, onde três diferentes modelos de campo médio são empregados a fim de se descrever o comportamento das transições de fase sofridas pelas monocamadas no que se refere aos aspectos acima mencionados. Cada modelo é diferente no que diz respeito ao comportamento das caudas hidrofóbicas erguidas em direção ao ar. O emprego de tais modelos proporcionou, em linhas gerais, um melhor entendimento das transições de fase nestes sistemas. / Insoluble monolayers lying on a liquid surface are known for about one century. They are formed when amphiphilic molecules are deposited on some solvent under special conditions. Under isothermal compression, these systems may exhibit a complex behavior suffering several phase transitions. Although with recent experimental development on the area new insights on the phase transitions were obtained, many questions remain unanswered. Some of these questions are related with the influence of some variables like the intramolecular conformations and the interaction between the amphiphilic molecules and the solvent molecules. In order to fill this gap molecular models are a useful and valuable tool. So, it was employed three different mean-field models in order to describe phase transitions of the molecules. The difference between the models relies on the behavior of the hydrophobic tails lifted on the air. Such models proportioned some insight on the phase transitions of the system.

Dans cette thèse, nous aborderons l'approximation de champ moyen pour des particules bosoniques. Pour un certain nombre d'états quantiques, la dérivation de la limite de champ moyen est connue, et il semble naturel d'étendre ces travaux à un cadre général d'états quantiques quelconques. L'approximation de champ moyen consiste à remplacer le problème à N corps quantique par un problème non linéaire, dit de Hartree, quand le nombre de particules est grand. Nous prouverons un résultat général pour un système de particules, confinées ou non, interagissant au travers d'un potentiel singulier. La méthode utilisée repose sur les mesures de Wigner. Notre contribution consiste en l'extension de la méthode des caractéristiques au cadre de champ de vitesse singulier associé à l'équation de Hartree. Cela complète les travaux d'Ammari et Nier et permet de prouver des résultats pour des potentiels critiques pour les équations de Hartree. En particulier, on s'intéressera à un système de bosons interagissant au travers d'un potentiel à plusieurs corps et nous démontrerons l'approximation de champ moyen sous une hypothèse de compacité forte sur ce dernier. Les résultats s’appuient en grande partie sur la flexibilité des mesures de Wigner, ce qui permet également de proposer une preuve alternative à l'approximation de champ moyen dans un cadre variationnel. / In this thesis, we justify the mean field approximation in a general framework for bosonic systems. The derivation of mean field dynamics is known for some specific quantum states. Therefore it is natural to expect the extension of these results for a general family of normal states. The mean field approximation for bosons consists in replacing the many-body quantum problem by a non linear one, so-called Hartree problem, when the number of particles tends to infinity. We establish a general result for bosons confined or not, interacting through a singular potential. The method used is based on Wigner measures. Our contribution consists in extending the characteristics method when the velocity field associated to the Hartree equation is subcritical or critical. It complements the work of Ammari and Nier and provides a result for critical potential for the Hartree equation. We also focus on bosonic systems interacting through a multi-body potential and we prove the mean field approximation under a strong assumption on this potential. All these results essentially rely on the flexibility of Wigner measures and we can give an alternative proof of the variational mean field approximation.

In this dissertation, I study critical phenomena and phase transitions in systems with long-range interactions, in particular, the ferromagnetic Ising model with quenched site dilution and the asset exchange model with growth. In the site-diluted Ising model, I focus on the effects of quenched disorder on both critical phenomena and nucleation. For critical phenomena, I generalize the Harris criterion for the mean-field critical point and the spinodal, and find that they are not affected by dilution, whereas pseudospinodals are smeared out. For nucleation, I find that dilution reduces the lifetime of the metastable state. I also investigate the structure of nucleating droplets in both nearest-neighbor and long-range Ising models. In both cases, nucleating droplets are more likely to occur in spatially more dilute regions. I also modify the asset exchange model to include different types of economic growth, such as constant growth and geometric growth. For constant growth, one agent eventually gets almost all the wealth regardless of the growth rate. For geometric growth, the wealth distribution depends on the way that the growth is distributed among agents, which is represented by the parameter 𝛾. For the evenly distributed growth, 𝛾=0, and as 𝛾 increases, the growth in the total wealth is distributed preferentially to richer agents. For 𝛾=1, the wealth of every agent grows at a rate that is linearly proportional to his/her wealth. I find a phase transition at 𝛾=1. For 𝛾<1, there is an rescaled steady state wealth distribution and the system is effectively ergodic. In this state, the wealth at all ranks grows exponentially in time and inequality stays constant. For 𝛾>1, one agent eventually obtains almost all the wealth, and the system is not ergodic. For 𝛾=1$, the dynamics of the poor agents' wealth is similar to that of a geometric random walk. In addition, I elucidate the effects of unfair trading, inhomogeneity in agents, modified growth which only depends on richest $1% agents' wealth, and a finite range of wealth exchange.

abstract: This dissertation studies the scheduling in two stochastic networks, a co-located wireless network and an outpatient healthcare network, both of which have a cyclic planning horizon and a deadline-related performance metric. For the co-located wireless network, a time-slotted system is considered. A cycle of planning horizon is called a frame, which consists of a fixed number of time slots. The size of the frame is determined by the upper-layer applications. Packets with deadlines arrive at the beginning of each frame and will be discarded if missing their deadlines, which are in the same frame. Each link of the network is associated with a quality of service constraint and an average transmit power constraint. For this system, a MaxWeight-type problem for which the solutions achieve the throughput optimality is formulated. Since the computational complexity of solving the MaxWeight-type problem with exhaustive search is exponential even for a single-link system, a greedy algorithm with complexity O(nlog(n)) is proposed, which is also throughput optimal. The outpatient healthcare network is modeled as a discrete-time queueing network, in which patients receive diagnosis and treatment planning that involves collaboration between multiple service stations. For each patient, only the root (first) appointment can be scheduled as the following appointments evolve stochastically. The cyclic planing horizon is a week. The root appointment is optimized to maximize the proportion of patients that can complete their care by a class-dependent deadline. In the optimization algorithm, the sojourn time of patients in the healthcare network is approximated with a doubly-stochastic phase-type distribution. To address the computational intractability, a mean-field model with convergence guarantees is proposed. A linear programming-based policy improvement framework is developed, which can approximately solve the original large-scale stochastic optimization in queueing networks of realistic sizes. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020