Neste trabalho estudamos o comportamento crítico do modelo de Potts p-estados na árvore de Cayley, através das propriedades do conjunto de zeros de Yang-Lee da função de partição. Tratando a transformação do grupo de renormalização como um mapeamento racional na esfera de Riemann utiliza-se alguns resultados da teoria de Julia e Fatou para obter-se uma descrição geométrica do comportamento crítico do modelo. Mostra-se de que forma o conjunto de zeros de Yang-Lee se relaciona com o conjunto de Julia do mapa do grupo de renormalização, e calculam-se alguns parâmetros geométricos desse conjunto que descrevem o comportamento não universal do modelo. / We study the critical behavior of the p-state Potts model on a Cayley tree, looking for the properties of the Yang-Lee zeros set of the partition function. We treated the renormalization group transformation as a rational mapping on the Riemann sphere, and use some results from the Julia and Fatou theory to obtain a geometrical description of the critical properties of the model. We show how the Yang-Lee zeros set is associated with the Julia set of the renormalization group map, and we also calculate some geometrical parameters of this set which describes the non-universal behavior of the model.

L’affabulation homodiégétique et la métafiction étant souvent utilisées, quand il s’agit de migrants narrateurs, cette recherche porte sur l’étude de la figure du migrant narrateur dans les romans italiens publiés entre 2001 et 2014 et adopte une approche comparative par rapport aux techniques, symboles et connexions historiques liés à l’utilisation de la métafiction. En comparant la multitude de techniques narratives qu’entraîne la métafiction ainsi que les thématiques véhiculées par ces techniques, il s’agira d’établir les points communs dans la façon dont ces romans utilisent les outils stylistiques et exploitent les thèmes liés à la métafiction afin de déterminer, le cas échéant, la cohérence de l’utilisation de la métafiction dans ces romans. / Since homodiegetic narration and metafiction are often used when there are migrant narrators in Italian contemporary novels, my PhD project focuses on migrant narrators characters in the Italian novels published between 2001 and 2014 and proposes a comparative study of technics, symboles and historical connections connected to metafiction. The aim is to compare the various narrative metafictional technics and their themes in order to find common ways in which these novels use stylistic elements and develop themes connected to metafiction to confirm a coherent use of metafiction in these novels.

Density functional theory (DFT) is not only an accurate but also a widely used theory for describing the quantum-mechanical electronic structure of matter. In this approach, the intractable problem of interacting electrons is simplified to a tractable problem of non-interacting electrons moving in an effective potential. Even with this simplification, DFT remains extremely computationally expensive. In particular, DFT scales cubically with respect to the number of atoms, which restricts the size of systems that can be studied. Orbital free density functional theory (OF-DFT) represents a simplification of DFT applicable to metallic systems that behave like a free-electron gas. Current implementations of OF-DFT employ the plane-wave basis, the global nature of the basis prevents the efficient use of modern high-performance computer archi- tectures. We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a gener- alized framework suitable for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we develop a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In doing so, we make the calculation of the electronic ground-state and forces on the nuclei amenable to computations that altogether scale linearly with the number of atoms. We develop a parallel implementation of our method using Portable, Extensible Toolkit for scientific computations (PETSc) suite of data structures and routines. The communication between processors is handled via the Message Passing Interface(MPI). We implement this formulation using the finite-difference discretization, us- ing which we demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson mixing. We verify the accuracy of our results by comparing the energies and forces with plane-wave methods for selected examples, one of which is the vacancy formation energy in Aluminum. Overall, we demonstrate that the proposed formulation and implementation is an attractive choice for performing OF-DFT calculations.

Neste trabalho estudamos o comportamento crítico do modelo de Potts p-estados na árvore de Cayley, através das propriedades do conjunto de zeros de Yang-Lee da função de partição. Tratando a transformação do grupo de renormalização como um mapeamento racional na esfera de Riemann utiliza-se alguns resultados da teoria de Julia e Fatou para obter-se uma descrição geométrica do comportamento crítico do modelo. Mostra-se de que forma o conjunto de zeros de Yang-Lee se relaciona com o conjunto de Julia do mapa do grupo de renormalização, e calculam-se alguns parâmetros geométricos desse conjunto que descrevem o comportamento não universal do modelo. / We study the critical behavior of the p-state Potts model on a Cayley tree, looking for the properties of the Yang-Lee zeros set of the partition function. We treated the renormalization group transformation as a rational mapping on the Riemann sphere, and use some results from the Julia and Fatou theory to obtain a geometrical description of the critical properties of the model. We show how the Yang-Lee zeros set is associated with the Julia set of the renormalization group map, and we also calculate some geometrical parameters of this set which describes the non-universal behavior of the model.

微生物から人類まで、地球上のすべての生命体は、非平衡開放条件下で生命活動を維持している。生物が織りなすさまざまな生命現象の基礎となり、生物を生物たらしめている本質的なものは、非平衡開放条件下での「自己組織化現象」や 「時間発展的な自己秩序化現象」と言える。本論文は、生命体そのものではなく、その自己組織や自己秩序化についての実空間の簡単なモデル系を取り上げて、研究を行った結果をまとめたものである。 / From microorganisms to human beings, all living organisms on the earth maintain life activities under non-equilibrium open conditions. "Self-organizing phenomena" or "time-evolving self-ordering phenomena" under non-equilibrium open conditions are essential things that serve as the foundation of various life phenomena woven by living things and that keep living things as creatures. By taking a simple model system of real space about its self-organization and self-ordering, this paper summarized the results of research processed. / 博士(工学) / Doctor of Philosophy in Engineering / 同志社大学 / Doshisha University

In dieser Arbeit werden Algorithmen für die Berechnung elektronischer Korrelations- und Anregungsenergien mittels der Coupled-Cluster Methode auf adaptiven Gittern entwickelt und implementiert. Die jeweiligen Funktionen und Operatoren werden adaptiv durch Multiskalenanalyse dargestellt, was eine Basissatz unabängige Beschreibung mit kontrollierter numerischer Genauigkeit ermöglicht. Gleichungen für die Coupled-Cluster Methode werden in einem verallgemeinerten Rahmen, unabhängig von virtuellen Orbitalen und globalen Basissätzen, neu formuliert. Hierzu werden die amplitudengewichteten Anregungen in virtuelle Orbitale ersetzt durch Anregungen in n-Elektronenfunktionen, welche durch Gleichungen im n-Elektronen Ortsraum bestimmt sind. Die erhaltenen Gleichungen können, analog zur Basissatz abh¨angigen Form, mit leicht angepasster Interpretation diagrammatisch dargestellt werden. Aufgrund des singulären Coulomb Potentials werden die Arbeitsgleichungen mit einem explizit korrelierten Ansatz regularisiert. Coupled-Cluster singles mit genäherten doubles (CC2) und ähnliche Modelle werden, für geschlossenschalige Systeme und in regularisierter Form, in die MADNESS Bibliothek (eine allgemeine Bibliothek zur Darstellung von Funktionen und Operatoren mittels Multiskalenanalyse) implementiert. Mit der vorgestellten Methode können elektronische CC2 Paarkorrelationsenergien und Anregungsenergien mit bestimmter numerischer Genauigkeit unabhängig von globalen Basissätzen berechnet werden, was anhand von kleinen Molekülen verifiziert wird / In this work algorithms for the computation of electronic correlation and excitation energies with the Coupled-Cluster method on adaptive grids are developed and implemented. The corresponding functions and operators are adaptively represented with multiresolution analysis allowing a basis-set independent description with controlled numerical accuracy. Equations for the coupled-cluster model are reformulated in a generalized framework independent of virtual orbitals and global basis-sets. For this, the amplitude weighted excitations into virtuals are replaced by excitations into n-electron functions which are determined by projected equations in the n-electron position space. The resulting equations can be represented diagrammatically analogous to basis-set dependent approaches with slightly adjusted rules of interpretation. Due to the singular Coulomb potential, the working equations are regularized with an explicitly correlated ansatz. Coupled-cluster singles with approximate doubles (CC2) and similar models are implemented for closed-shell systems and in regularized form into the MADNESS library (a general library for the representation of functions and operators with multiresolution analysis). With the presented approach electronic CC2 pair-correlation energies and excitation energies can be computed with definite numerical accuracy and without dependence on global basis sets, which is verified on small molecules.

Computational approaches play an important role in today's materials science owing to the remarkable advances in modern supercomputing architecture and algorithms. Ab initio simulations solely based on a quantum description of matter are now very able to tackle materials problems in which the system contains up to a few thousands atoms. This dissertation aims to address the modern electronic structure calculation methods applied to a range of various materials such as liquid and amorphous phase materials, nanostructures, and small organic molecules. Our simulations were performed within the density functional theory framework, emphasizing the use of real-space ab initio pseudopotentials. On the first part of our study, we performed liquid and amorphous phase simulations by employing a molecular dynamics technique accelerated by a Chebyshev-subspace filtering algorithm. We applied this technique to find l- and a- SiO₂ structural properties that were in a good agreement with experiments. On the second part, we studied nanostructured semiconducting oxide materials, i.e., SnO₂ and TiO₂, focusing on the electronic structures and optical properties. Lastly, we developed an efficient simulation method for non-contact atomic force microscopy. This fast and simple method was found to be a very powerful tool for predicting AFM images for many surface and molecular systems. / text

Many writers have suggested that our capacity to occupy space meaningfully has been undermined by our contemporary ocular-centric culture, which distances us from reality and corrupts our physical and embodied experience of the world. This study challenges these claims within an architectural context, by examining the fundamentally visual nature of architecture and inhabitation as well as the spatio-visual practices, acts and strategies that we use to occupy space. Drawing on theory and practice-based methods from outside the professional limits of architectural practice, the study implements visual acts of occupation to establish a new and expanded conception of architecture as a performative spatio-visual practice – a conception that engages and connects its practice with the purportedly ocular-centric spatial conditions in which it is made and occupied.

Cold bosonic atoms trapped in optical lattices formed by standing wave interference patterns of multiple laser beams constitute excellent emulators of models of strongly correlated quantum systems of bosons. In this thesis, we develop and deploy strong-coupling expansion (i.e., an expansion in terms of the ratio of the inter-site hopping amplitude of the bosons to the strength of their interactions) techniques for studying the properties of three different instances of such systems. In the first instance, we have used strong coupling expansion techniques to calculate the density pro le for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperatures and large on site interaction in the presence of super fluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. Our calculations for the scaled density in the vacuum-to-super fluid transition agree well with the experimental data for appropriate temperatures. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments. Experimental realizations of “atomtronic" Josephson junctions have recently been created in annular traps in relative rotation with respect to potential barriers that generate the weak links. If these devices are additionally subjected to optical lattice potentials, then they can incorporate strong-coupling Mott physics within the design, which can modify the behaviour and can allow for interesting new configurations of system generated barriers and of super fluid ow patterns. we have examined theoretically the behavior of a Bose super fluid in an optical lattice in the presence of an annular trap and a barrier across the annular region which acts as a Josephson junction. As the fluid is rotated relative to the barrier, it generates circulating super-currents until, at larger speeds of rotation, it develops phase slips which are typically accompanied by vortices. We use a finite temperature strong-coupling expansion about the mean- held solution of the Bose Hubbard model to calculate various properties of the device. In addition, we discuss some of the rich behavior that can result when there are Mott regions within the system. Rubidium-Cesium dipolar molecule formation through Feshbach resonance is an area of great current interest, for, the dipolar molecules, once formed, interact via v long range dipolar forces, leading to possibilities of novel phases. Experimentalists currently make such systems mostly using trial and error, and the resulting efficiencies for molecule formation tend to be low. With a goal to assist cold-atom experimentalists to achieve higher e ciencies of molecule formation, we have estimated the trap parameters for Rb and Cs atoms in a 3D optical lattice required to create single occupancy per site Mott phase for both the species in the same regions of the trap. We thus identify the ne tuning of the external magnetic held near Rb-Cs Feshbach resonance required to achieve highest probability for creating single Rb-Cs Feshbach molecules in the system. We have used the Falicov-Kimball model to describe the relevant system and strong-coupling expansions about the mean- held solution to calculate the density pro les for both species and efficiency for molecule formation, determined by overlapping regions of single occupancy for both Rb and Cs, up to second order in the expansion. We also calculate the entropy per particle which serves as an estimation of the temperature in the experimental system

In this thesis, we study the problem of protein side chain assignment (SCA) given multiple sources of experimental and modeling data. In particular, the mechanism of X-ray crystallography (X-ray) is re-examined using Fourier analysis, and a novel probabilistic model of X-ray is proposed for SCA's decision making. The relationship between the measurements in X-ray and the desired structure is reformulated in terms of Discrete Fourier Transform (DFT). The decision making is performed by developing a new resolution-dependent electron density map (EDM) model and applying Maximum Likelihood (ML) estimation, which simply reduces to the Least Squares (LS) solution. Calculation of the condence probability associated with this decision making is also given. One possible extension of this novel model is the real-space refinement when the continuous conformational space is used. Furthermore, we present a data fusion scheme combining multi-sources of data to solve SCA problem. The merit of our framework is the capability of exploiting multi-sources of information to make decisions in a probabilistic perspective based on Bayesian inference. Although our approach aims at SCA problem, it can be easily transplanted to solving for the entire protein structure.