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.

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.

We use a combination of Density Functional Theory and Dynamical Mean Field Theory (DFT+DMFT) to study electronic correlations in unconventional superconductors, with a focus on nickelate analogs of cuprate superconductors. We study the infinite layer nickelate superconductor NdNiO₂ in parallel with the isostructural CaCuO₂. Our results point to superconductivity in the nickelate being cupratelike, with correlations dominated by a hybrid Ni-𝑑_{𝑥²-𝑦²} and O-𝑝 band, and with the extra bands not contributing substantially to the superconducting state. We find that the infinite layer nickelate NdNiO₂ and the trilayer nickelate Pr₄Ni₃O₈ are virtually identical in terms of correlation physics when compared at the same chemical doping, despite the differences in Fermiology, indicating that the number of layers can stand in for chemical doping for some properties related to electronic correlations. We find that as opposed to in narrow window DFT+DMFT, in wide window DFT+DMFT the choice of downfolding procedure leads to very different results. This is an important ambiguity in the method that must be resolved or the method is incomplete by itself. We also study Sr₂MoO₄ in parallel with the Hund's superconductor Sr₂RuO₄, and find that Sr₂MoO₄ is a particle-hole dual of Sr₂RuO₄ but without the van Hove singularity at the Fermi level, which disentangles the influence of the van Hove singularity from Hund's physics. We show that Sr₂MoO₄ has a characteristic Hund's peak on the occupied of the spectral function, indicating that the peak should be observable by photoemission experiments.

A complex arrangement of electronic states within materials can manifest exotic quantum-mechanical effects. These systems are often referred to as quantum materials. Increased understanding of quantum materials has historically lead to the development of new technologies. It is therefore extremely important to develop and test precise methods for calculating the behaviour of electronic states within a material. For decades, the workhorse of electronic structure calculations has been density functional theory (DFT). DFT is often referred to as a first-principles method because it allows for the calculation of the distribution of electrons throughout a material with only specification of the lattice geometry and atomic components. From the results of a DFT calculation, it is possible to study the orbital character of electronic wavefunctions, topology of electronic band structure, and some aspects of superconductivity. This provides insight into many quantum properties of a system which may otherwise be difficult or impossible to ascertain from experiments. DFT is, however, sometimes limited by the approximations necessary for practical implementation. Further methods have been developed to systematically correct the limitations of DFT. In particular, the combination of DFT with dynamical mean-field theory (DFT+DMFT) is among the most widely accepted methods for correcting the inadequacy of DFT in handling strong electron-electron correlations. In this thesis, I use methods from DFT and DFT+DMFT to study the quantum properties of materials. / Thesis / Master of Science (MSc)

The origin of cosmic magnetic fields is a important area of astrophysics. The process by which they are created falls under the heading of dynamo theory, and is the topic of this thesis. Our focus for the location of where these magnetic fields operate is one the most ubiquitous objects in the universe, the accretion disk. By studying the accretion disk and the dynamo process that occurs there we wish to better understand both the accretion process and the dynamo process in stars and galaxies as well. We analyse the output from a stratified zero net flux shearing box simulation performed using the ATHENA MHD code in collaboration with Shane Davis. The simulation has turbulence which is naturally forced by the presence of a linear instability called the magnetorotational instability (MRI). We utilise Fourier filtering and the tools of mean field dynamo theory to establish a connection between the calculated EMF and the model predictions of the dynamically quenched alpha model. We find a positive correlation for both components parallel to the large scale magnetic field and the azimuthal components. We have explored many aspects of the theory including additional contributions from magnetic buoyancy and an effect arising from the large scale shear and the current density. We also directly measure the turbulent correlation time for the velocity and magnetic fields both large scale and small. We can also observe the effects of the dynamo cycle, with the azimuthal component of the large scale magnetic field flipping sign in this analysis. We find a positive correlation between the divergence of the eddy scale magnetic helicity flux and the component of the electromotive force parallel to the large scale magnetic field. This correlation directly links the transfer of magnetic helicity to the dynamo process in a system with naturally driven turbulence. This highlights the importance of magnetic helicity and its conservation even in a system with triply periodic boundary conditions. / Thesis / Doctor of Philosophy (PhD)

published_or_final_version / abstract / Physics / Doctoral / Doctor of Philosophy

No description available.

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

In this dissertation, we consider a complex biological system known as cortical microtubule (CMT) system, where stochastic dynamics of the components (i.e., the CMTs) are defined in both space and time. CMTs have an inherent spatial dimension of their own, as their length changes over time in addition to their location. As a result of their dynamics in a confined space, they run into and interact with each other according to simple stochastic rules. Over time, CMTs acquire an ordered structure that is achieved without any centralized control beginning with a completely disorganized system. It is also observed that this organization might be distorted, when parameters of dynamicity and interactions change due to genetic mutation or environmental conditions. The main question of interest is to explore the characteristics of this system and the drivers of its self-organization, which is not feasible relying solely on biological experiments. For this, we replicate the system dynamics and interactions using computer simulations. As the simulations successfully mimic the organization seen in plant cells, we conduct an extensive analysis to discover the effects of dynamics and interactions on system characteristics by experimenting with different input parameters. To compare simulation results, we characterize system properties and quantify organization level using metrics based on entropy, average length and number of CMTs in the system. Based on our findings and conjectures from simulations, we develop analytical models for more generalized conclusions and efficient computation of system metrics. As a fist step, we formulate a mean-field model, which we use to derive sufficient conditions for organization to occur in terms of input parameters. Next, considering the parameter ranges that satisfy these conditions, we develop predictive methodologies for estimation of expected average length and number of CMTs over time, using a fluid model, transient analysis, and approximation algorithms tailored to our problem. Overall, we build a comprehensive framework for analysis and control of microtubule organization in plant cells using a wide range of models and methodologies in conjunction. This research also has broader impacts related to the fields of bio-energy, healthcare, and nanotechnology; in addition to its methodological contribution to stochastic modeling of systems with high-level spatial and temporal complexity.

El CMC, tamaño y forma de micelas son características importantes en la determinación de sus principales propiedades y campos de aplicación. Esta tesis tiene dos partes, las transiciones de forma de las micelas que se trata con "Single chain Field Theory, /SCMFT)" y simulaciones de Monte Carlo. El SCMFT reveló todas las características esenciales de las transiciones de forma esférica a cilíndrica y esférica a disco de las micelas. MC muestra que las transiciones esfera a cilindro se produce a través de una región en que esferas y cilindros coexisten junto con otras formas intermedias.