Dissertations / Theses on the topic 'Matter models'

Revealing the nature of the dark matter is among the most puzzling issues of today particle physics, astrophysics and cosmology. Given the striking evidences for dark matter at all astrophysical scales, starting from galactic and going to cosmological scales, a widespread and well motivated assumption on the nature of the dark matter is that it is made by a new particle that extends the Standard Models of Particle Physics. Indirect detection of dark matter, which annihilates in over-dense regions like the galactic centre, is an important probe of a possible dark matter interaction with the Standard Model particles. It could provide insights both to the underlying production mechanism of dark matter in the early Universe, on the annihilation properties at present time in galactic halos and on the underlying particle physics model. In this master thesis project we will focus on simplified leptophilic models for dark matter. These models feature an massive boson, called for instance Z', and a Dirac dark matter candidate, that complement the Standard Model of particle physics. We will study the annihilation of dark matter into leptons, focusing in particular on neutrino lines and box-shaped energy spectra. These tow signals are smoking gun signature to discover the dark matter properties. We will perform a numerical analysis using the dark matter software MadDM to predict the expected flux from the galactic centre, by performing scans in the model parameter space. We will implement the constrains from the Fermi-LAT telescope and the XENON1T experiment. Finally we will use the predictions of those models to assess the reach of the future KM3NeT neutrino telescope.

Diffusion-weighted MRI (DW-MRI) is a powerful in vivo imaging technique that is particularly sensitive to the underlying microstructure of white matter tissue in the brain. Many models of the DW-MRI signal exist that allow us to relate the signals we measure to various aspects of the tissue structure, including measures of diffusivity, cellularity and even axon size. From histology, we know that many of these microstructure measures display distinct patterns of variation on length scales greater than the average voxel size. However very few methods exist that use this spatial coherence to inform and guide parameter estimation. Instead, most techniques treat each voxel of data independently. This is particularly problematic when estimating parameters such as axon radius which only weakly influence the signal, as the resulting estimates are noisy. Several methods have been proposed that spatially smooth parameter estimates after fitting the model in each voxel. However if the parameter estimates are very noisy, the underlying trend is likely to be obscured. These methods are also unable to account for spatial coupling that may exist between the various parameters. This thesis introduces a novel framework, the Regional Variation Model (RVM), which exploits the underlying spatial coherence within white matter tracts to estimate trends of microstructure variation across large regions of interest. We fit curves describing parameter variation directly to the diffusion-weighted signals which should capture spatial changes in a more natural way as well as reducing the effects of noise. This allows for more precise estimates of a range of microstructure indices, including axon radius. The resulting curves, which show how microstructure parameters vary spatially through white matter regions, can also be used to detect groupwise differences with potentially greater power than traditional methods.

Una enorme quantità di evidenze sperimentali sulla esistenza di una forma di materia non luminosa nell'Universo, si sono accumulate nel corso di circa un secolo. Chiarire la sua natura è diventata una delle sfide più eccitanti ed urgenti negli sforzi per capire il nostro Universo. In questo lavoro presento uno studio su un approccio per scoprire la Materia Oscura interpretata come particella elementare e sulla possibilità di produrla e rilevarla negli acceleratori. Nella parte introduttiva presento una breve storia delle evidenze astrofisiche e astronomiche che hanno portato alla ipotesi della esistenza di Materia Oscura. Assumendo che la Materia Oscura sia costituita da una particella elementare ulteriore a quelle predette dal Modello Standard, delineo poi i tre principali metodi di rilevazione utilizzati attualmente per identificarla. Nella seconda parte discuto come si possono costruire teorie nelle quali sia possibile interpretare le ricerche attuali ed i risultati corrispondenti. Eseguo un confronto tra approcci diversi, partendo da modelli completi fino a quelli che utilizzano teorie di campo effettive. In particolare, discuto i loro lati positivi e negativi, motivando l'utilizzo di uno schema intermedio, il cosiddetto approccio con modelli semplificati, caratterizzati da un numero limitato di nuovi stati e parametri e che supera le limitazioni intrinseche delle teorie effettive nel contesto delle ricerche negli acceleratori. Nell'ultima parte fornisco una esaustiva classificazione dei modelli semplificati nel canale t, che non sono ancora stati analizzati sistematicamente nella letteratura. Per ciascuno di essi presento un possibile completamento UV e i segnali più promettenti ad LHC. Per questa ragione tutti i modelli considerati sono stati implementati in strumenti Monte Carlo, validati nel confronto con risultati analitici, studiati in dettaglio e resi pronti per un rilascio pubblico per la comunità fenomenologica e sperimentale di LHC.

Condensed matter physics is the study of the macroscopic and microscopic properties of condensed phases of matter. For quite some time, Landau’s symmetry breaking theory was believed to describe and explain the nature of any phase transition. However, since the late 1980s, it has become apparent that it is necessary to introduce some new kind of order, named topological order, that transcends the traditional symmetry description. In this thesis we will study the Kitaev model, which is a Hamiltonian lattice model that allows one to incorporate the concept of topological order, as well as the corresponding operators and algebras. First, we consider the model on an infinite lattice, and show how to relate local and global degrees of freedom of the anyons/quasi-particles living on sites to the ribbon operators. Afterwards, we introduce holes and an external boundary to the lattice, and examine the ramifications of this generalization in terms of the ground state degeneracy. Lastly, we verify that the algebra formed by boundary site operators has the structure of a quasi-Hopf algebra.

This thesis uses theory and simulation to elucidate the principles and mechanisms that govern the thermodynamics, material science, and rheology of biological anisotropic soft matter that are involved in growth/self-assembly/material processing in plant cell walls, a multi-functional biological fibrous composite. The plant cell wall can be considered as a reinforced biological membrane consisting of cellulose microfibrils (CMFs) of high tensile strength embedded in a polysaccharide matrix. These CMFs in the extracellular matrix are oriented instrategic directions and generate commonly observed textures such as line, ring, helix, crossed helix and helicoids. The orientation of CMFs governs the physical properties of wood, controls the shape of the cell and contributes to themorphology at the tissue and organ level. Two models are used in this thesis, depending on the concentration of CMFs.At concentration of CMFs below Onsager critical limit, we develop an integrated mechanical model that describes nematic liquid crystalline self-assembly of rigid fibers on an arbitrarily curved 2D fluid membrane to demonstrate the possibility of the CMF orientation imparted by the interaction between membrane curvature and embedded fiber order. This curvature driven planar self assembly model can predict and explain the observed line, ring and helical cell wall textures. These predictions are partially validated through available experimental observations. An integrated shape and nematic order equation developed in this thesis gives a complete model whose solution describes the coupled membraneshape and fiber order state. The validated model is then used to analyze the structure and mechanics of biological and biomimetic fiber-laden membranes of variable curvature. The statics of anisotropic fiber-laden membranes developed inthis model is integrated with the planar nematodynamics of fibers and the dynamics of isotropic membranes to formulate a viscoelastic model to study dynamic remodeling of plant cell wall during growth and morphogenesis. The novel coupling between in-plane fiber orientation and order and membrane curvature formulated this thesis has the potential to open up a novel venue to control two dimensional anisotropic soft matter with tailored functionalities. When the concentration of the CMFs exceeds Onsager's critical fiber concentration threshold, the interaction between these CMFs results in theiralignment in a specific direction as an attempt to minimize the excluded volume of the CMFs. A mathematical model based on the Landau–de Gennes theory of liquid crystals is used to simulate defect textures arising in the domain of chiralself-assembly due to the presence of secondary phases such as pit canal and cell lumens. In addition to providing information on material properties and length scales that cannot be experimentally measured in vivo, the simulated transient defect pattern confirms for first time the long postulated formation mechanism of helicoidal plywoods through liquid crystalline self-assembly. The model is further extended to investigate defect textures and liquid crystalline (LC) phases observed in polygonal arrangement of cylindrical particles embedded in a cholesteric liquid crystal matrix. These validated findings provide a comprehensive set of trends and mechanisms that contribute to the evolving understanding of biological plywoods and serve as a platform for future biomimetic applications.The integration of soft matter physics theories and models with actual biological data for plant cell walls provides a foundation for understanding growth, form, and function and a platform for biomimetic innovation.
Cette thèse utilise la théorie et la simulation pour élucider les principes et mécanismes qui gouverne la hermodynamique, la science des matériaux, et la rhéologie de la matière biologique molle anisotropique qui est impliquée dans ledéveloppement/auto-assemblage/la transformation des parois cellulaires de plantes, un composite biologique fibreux multifonctionnel. Les parois cellulaires de plantes peuvent être considérées comme des membranes biologiques renforcées consistant en des microfibres de cellulose (CMFs) de hautes ténacités contenues dans une matrice de polysaccaride. Ces CMFs dans la matrice extracellulaire sont orientés dans une direction stratégique hélices et des hélicoïdes. L'orientation des CMFs gouverne les propriétés physiques du bois et contrôle la forme des cellules. Deux modèles sont employés dans cette thèse dépendamment de la concentration en CMFs. A la concentration de CMFs dessous la limite critique de Onsager, nous développons un modèle mécanique intégré qui décrit un auto-assemblage de fibres rigides de type cristal liquide nématique sur une membrane courbée bidimensionnelle arbitraire afin de démontrer la possibilité de l'orientation des CMFs indue par les interactions entre la courbature de la membrane et l'organisation fibrillaire intrinsèque. Cette auto-assemblage planaire indus par la courbature peut prédire et expliquer les lignes, annaux et textures hélicoïdales observées dans les parois cellulaires. Ces prédictions sont partiellement validées au travers d'observations expérimentales publiés. Une équation décrivant l'ordre nématique et la forme intégrée qui a été développé dans cette thèse fournis un modèle complet dont la solution décrit le couplage entre l'alignement des fibres et la forme de la membrane. Le model validé est par la suite utilisé à fin d'analyser la structure et la mécanique de membrane fibreuses biologiques et biomimétiques de courbatures variables. La statique des membranes fibreuses anisotropes développés dans ce modèle est intégrée avec la némato-dynamique planaire des fibres et la dynamique des membranes isotropes afin de formuler un modèle viscoélastique pour étudier le remodelage dynamique des CMF durant leur développement et morphogénèse. Le nouveau couplage entre l'orientation fibrillaire planaire et l'ordre ainsi que la courbature de la membrane formulé dans cette thèse à le potentiel d'ouvrir de nouvelles avenues pour contrôler l'ordre bidimensionnel de matière molle selon des propriétés bien définies. Quand la concentration en CMFs excède la limite critique en fibre de Onsager, l'interaction entre les CMFs résulte en un alignement dans une direction spécifique qui tente de minimiser le volume exclu de CMFs. Un modèle mathématique basé sur la théorie de Landau de Gennes des cristaux liquides est utilisé pour simuler les textures de défauts survenant dans un chirale d'auto assemblage du à la présence de phases secondaires tel que les lumens cellulaires. En plus de fournir de l'information sur les propriétés matériels et les ordres de grandeurs qui ne peuvent être mesuré expérimentalement in vivo, les motifs des défauts transitoires simulés confirment pour la première fois le mécanisme de formation des assemblages hélicoïdaux. Le modèle est de plus étendu pour investiguer les textures de défauts et les phases liquides cristallines (LC) observées dans les arrangements polygonaux de particules cylindriques inclus dans des matrices de cristaux liquide cholestériques. Ces découvertes validées fournissent un ensemble de mécanismes qui contribues à faire évoluer la compréhension des assemblages lamellaires biologiques et servent de plateforme pour de futur développement d'applications biomimétiques. L'intégration des théories et des modèles de la matière molle avec des données biologique concrète pour les parois cellulaires fournissent des fondement pour la compréhension du développement, de formation et fonctionnalité ainsi qu'une plateforme pour l'innovation biomimétique

We investigate models of composite dark matter in which the dark matter candidate arises naturally as an accidentally stable bound state of a confining dynamics and with observable signatures in a wide variety of experiments. In the first part of the thesis we introduce and explore a new class of models with dark fermions in the adjoint repre- sentation of the confining gauge group. The low energy dynamics and the cosmological history are peculiar and provide a dark matter candidate with properties much different from that of a canonical WIMP. The dark matter is heavy but has a large interaction range and can be tested primarily with indirect searches. In the second part of the thesis we classify and study models of composite dark matter with a strongly interacting chiral dark sector, in which all the mass scales are generated dynamically. In this case the candidate is a SM singlet dark pion with a thermal abundance whose low energy phenomenology can be thoroughly studied through chiral lagrangian techniques. We present an analysis of the low energy phenomenology, compute the radiatively generated masses of the light states and study the cosmological history of the model. The presence of partner states interacting with the SM offers the opportunity to test the model at colliders. In the last part of the thesis we present the phenomenological signatures of the models previously introduced and determine the current bounds. In doing so we also present a strategy to derive a limit on the lifetime of dark matter particles in generic models of particle dark matter from the observation of the 21 cm cosmological signal.

At present, the best model for the Universe as a whole is given by the so called ``Hot Big Bang'', which describes an expanding universe in which the density and temperature of matter and radiation are followed in time. The value of the parameters characterizing the observed universe is summarized by the concordance $\Lambda$CDM model, where CDM stands for Cold Dark Matter (the main matter component), and $\Lambda$ is the cosmological constant (some kind of unknown energy, with an anti-gravitational effect). According to this model, the universe is spatially flat (i.e. the density parameter $\Omega$ equals one), and 75\% of its energy balance is assigned to dark energy, about 20\% to dark matter and about 5\% to ordinary (baryonic) matter; the expansion speed assumes a value $H_{0}=70.5$ Km/s/Mpc (the Hubble parameter). The present dissertation focuses on the distribution of dark matter into virialized structures, called dark matter haloes. According to structure formation theory, cosmic structures originates from the amplification of quantum fluctuations during an early stage of accelerated expansion (cosmic inflation); these perturbations grow by self-gravity until they collapse and originate virialized structures. In the linear regime (when fluctuations are small), this process is well understood by the Jeans' theory. The non linear regime is much harder to describe; erlier attempts assumed a simple spherical simmetry, where the collapse is driven only by the internal density (e.g. Peebles, 1980); more recently (White \& Silk 1979; Bond \& Myers 1996) this hypothesis has been relaxed, and a more complex model was proposed in which proto-structures are described by triaxial ellipsoids, governed by their internal density and shape. Using the results coming from the dynamical analysis of the spherical collapse, and exploiting the statistical ``excursion sets formalism'', it is possible to obtain analytical information about the mass distribution of dark matter haloes. In this approach, for each particle in the universe, the trajectory describing the density evolution of a sphere of matter built around that particle is modeled as a random walk as a function of the mass $M$ within that sphere. When a trajectory crosses some pre-defined threshold, one assumes that a virialized structure of mass $M$ has formed. By considering all the particles in the universe one obtains analytical forms for the global mass function, and for the progenitor and descendant mass functions. From these it is possible to calculate other quantities, like the (instantaneous and integrated) rates of creation and destruction of dark matter haloes. In the 1990's the ellipsoidal collapse was first tried in order to find a better match with numerical simulations. However, partly due to the analytical complexity of the model, until now one can still not find in the literature analytical forms for e.g. the descendant and merger rate distributions (see Table \ref{tab:scec}). The main goal of this work is to provide such expressions for a number of statistics related to the mass distributions of dark matter haloes, striving to obtain simple and accurate formulas. In order to do so, we start from the statistical considerations by Sheth, Mo e Tormen (2001), who introduced the dynamical effects of the ellipsoidal collapse into the excursion sets formalism just by modifying the shape of the density threshold. Sheth and Tormen (2002) further suggested an new expression for the ellipsoidal global mass function, using a Taylor expansion series for the barrier: this expression allows one to also derive analytical formulas for the conditional mass functions. We obtain a set of models changing the order of this Taylor expansion, and considering the normalization of the distribution as a free parameter; we then compare these equations with the results of the cosmological simulation Gif2 (Gao et al. 2004) and, in some cases, with the Millennium Simulation (Springel et al. 2005). For the global and conditional mass functions the match between models and simulations is estimated using a $\chi ^2$-method. For the merger rates we compare the results qualitatively, whereas for the creation rates we only derived analytical results. We especially focus on the cases providing the simplest analytical expressions: the zero-order and the infinite-orders Taylor series. In the last part of the dissertation we propose a new statistical method that can overcome two inconvenients of $\chi ^2$-methods: (i) data binning and (ii) neglect of field particles (dust) in simulations. Concerning point (i), different bin-sizes can lead to small differences in the $\chi ^2$-results. As for point (ii), particles that are not bound to haloes are usually considered only for computing the normalization. By using a maximum likelihood analysis we can treat unbinned data, as well as take into account dust in the determination of the best parameters of the mass function. Our tests are performed by comparing a two-parameter mass function with results of Monte Carlo simulations. Our work naturally settles within the systematic search of analytical expressions associated to the ellipsoidal collapse of dark matter haloes. Since haloes are thought to be the sites where baryons can condense and form stars, galaxies and other luminous objects, the expression we derive can be used for a number of applications, ranging from unveiling the nature of dark matter through self-annihilation, to the understanding of the mechanisms leading to galaxy formation. Furthermore, the description of galaxy evolution requires knowledge on the hosting haloes: semi-analytical models of galaxy formation depend on the global mass function of the dark matter haloes, and the corrisponding merger-trees are based on the progenitor mass functions. The rates of creation and destruction are useful to compute the abundances of objects like Active Galactic Nuclei (AGNs) and Super Massive Black Holes (SMBHs). Many other examples can be found in the literature for the use of dark matter distributions in studies of galaxy formation. The structure of the dissertation is as follows: {\bf Chapters 1} justifies the need of dark matter. In {\bf Chapters 2} we present the concordance cosmological model, its geometry and thermal history. We also introduce the linear and non-linear models for the formation of dark matter haloes. {\bf Chapter 3} describes the excursion sets approach in the framework of the spherical collapse. The extension of this method to the ellipsoidal collapse is given in {\bf Chapter 4}, where the firsts analytical results are derived. In {\bf Chapter 5} we compare our analytical predictions to a number of results from numerical simulations. {\bf Chapter 6} is devoted to the new maximum likelihood tests with unbinned data and dust particles. We finally draw our {\bf Conclusions}, followed by one {\bf Appendix} where the numerical simulations are described.
La miglior descrizione dell'Universo, di cui si dispone al momento, è il modello del ``Big Bang Caldo'', che contempla un universo in espansione nel quale viene seguita l'evoluzione temporale della densità e della temperatura della materia e della radiazione. I parametri che caratterizzano l'Universo osservato sono riassunti in un modello chiamato $\Lambda$CDM di concordanza: CDM sta per Cold Dark Matter (la componente dominante della materia), e $\Lambda$ è la costante cosmologica (una sorta di energia oscura, con effetto anti-gravitazionale). Secondo questo modello, l'universo è spazialmente piatto (cioè il parametro di densità $\Omega$ è uguale a uno), e il $75\%$ del suo bilancio energetico è assegnato all'energia oscura, circa il $20\%$ alla materia oscura e circa il $5\%$ alla materia ordinaria (barioni); la velocità dell'espansione assume il valore $70.5$ Km/s/Mpc (parametro di Hubble). Questa tesi si sofferma sulla distribuzione della materia oscura in strutture virializzate, chiamate aloni di materia oscura. Secondo la teoria di formazione delle strutture, le strutture cosmiche hanno origine dall'amplificazione di fluttuazione quantistiche durante un periodo iniziale di espansione accelerata (inflazione cosmica); queste perturbazioni crescono per effetto dell'autogravità fino al collasso, creando delle strutture virializzate. Durante il regime lineare (quando le fluttuazioni sono piccole), questo processo è ben descritto dalla teoria di Jeans. Il regime non lineare è molto più difficile da descrivere; i primi tentativi assumono una simmetria sferica, per la quale il collasso è descritto solo dalla densità interna (es. Peebles, 1980); più recentemente (White \& Silk 1979; Bond \& Myers 1996) questa ipotesi è stata rilassata, ed è stato proposto un modello più complesso nel quale le protostrutture sono descritte da ellissoidi triassiali, regolati dalla loro densità interna e dalla loro forma. Utilizzando i risultati ottenuti dall'analisi dinamica del collasso sferico e sfruttando il formalismo statistico degli ``excursion set'', è possibile ottenere informazioni analitiche in merito alla distribuzione di massa degli aloni di materia oscura. In questo approccio, per ogni particella nell'universo, la traiettoria che descrive l'evoluzione della densità della sfera di materia costruita attorno a quella particella viene modellata come un cammino browniano come funzione della massa $M$ all'interno della sfera. Quando una traiettoria interseca una pre-definita soglia, si assume che venga a formarsi una struttura virializzata di massa $M$. Considerando tutte le particelle dell'universo, si ottengono forme analitiche per la funzione di massa globale, e per le funzioni di massa dei progenitori e dei figli. Da queste, è possibile calcolare altre quantità, come i tassi di creazione e distruzione (istantanei e integrati). Negli anni '90, il collasso ellissoidale è stato utilizzato per trovare un miglior accordo con le simulazioni numeriche. Tuttavia, in parte a causa della complessità analitica del modello, fino ad ora non è stato ancora possibile trovare in letteratura forme analitiche per esempio per la funzione dei figli o per i tassi di distruzione (vedi Tabella \ref{tab:scec}). l'obiettivo principale di questo lavoro è di fornire tali espressioni per una serie di funzioni legate alle distribuzione di massa degli aloni di materia oscura, aspirando ad ottenere delle formule semplici ed accurate. Per farlo, siamo partiti dalle considerazioni statistiche di Sheth, Mo e Tormen (2001) che introducono gli effetti dinamici del collasso ellissoidale nel formalismo excursion sets, modificando la forma della soglia di densità. Sheth e Tormen (2002), inoltre, propongono una nuova espressione per la funzione di massa globale ellissoidale, usando uno sviluppo in serie di Taylor per la barriera: questa espressione permette di derivare forme analitiche anche per le funzioni di massa condizionali. Abbiamo ottenuto un set di modelli cambiando l'ordine di questo sviluppo di Taylo, e considerando la normalizzazione delle distribuzioni come un parametro libero; abbiamo poi confrontato queste equazioni con i risultati della simulazione cosmologica Gif2 (Gao et al. 2004) e, in alcuni casi, con la Millennium Simulation (Springel et al. 2005). Per le funzioni di massa globale e condizionali, l'accordo tra modelli e simulazioni è stimato usando un metodo $\chi ^2$. Per i merger rates abbiamo confronti qualitativi, mentre per i tassi di creazione abbiamo derivato le sole equazioni analitiche. Ci siamo soffermati specialmente sui casi che forniscono le espressioni analiticamente più semplici: le serie di Taylor con zero ordini e con infiniti ordini. Nell'ultima parte della tesi, proponiamo un nuovo metodo statistico che può scartare gli inconvenienti dei metodi $\chi ^2$: (i) la divisione in intervalli dei dati e (ii) il trascurare le particelle di campo (polvere) delle simulazioni. Per quanto riguarda il punto (i), differenti ampiezze degli internalli di massa possono portare a piccole differenze nei risultati del $\chi^2$. Il punto (ii) si riferisce al fatto che le particelle che non sono legate in aloni sono di solito considerate solo per il calcolo della normalizzazione. Usando un'analisi di massima verosimiglianza, possiamo trattare dati non raggruppati in intervalli e considerare la polvere nella determinazione dei parametri migliori per la funzione di massa. I nostri tests sono condotti confrontando una funzione di massa a due parametri con i risultati di simulazioni Monte Carlo. Il nostro lavoro si inserisce naturalmente nella ricerca sistematica delle espressioni analitiche associate al collasso ellissoidale degli aloni di materia oscura. Poichè si pensa che gli aloni siano i siti ove i barioni possono concentrarsi e formare stelle, galassie ed altri oggetti luminosi, le espressioni che otteniamo possono essere usate in varie applicazioni, dallo svelare la natura della materia oscura attraverso l'auto annichilazione, fino alla comprensione dei meccanismi che portano alla formazione galattica. Inoltre, la descrizione dell'evoluzione galattica richiede la conoscenza dell'alone correlato: i modelli semi-analitici di formazione galattica dipendono dalla funzione di massa globale degli aloni di materia oscura, e i corrispondenti merger-trees sono basati sulle funzioni di massa dei progenitori. I tassi di creazione e distruzione sono utili per calcolare le abbondanze di oggetti come Nuclei Galattici Attivi (AGN) e Buchi Neri Super Massicci (SMBH). Altri esempi dell'utilizzo delle distribuzioni della materia oscura in studi di formazione galattica si possono trovare copiosi in letteratura.\\ L'elaborato si articola in questo modo: il {\bf Capitoli 1} giustifica la necessità della materia oscura. Nel {\bf Capitolo 2} presentiamo il modello cosmologico di concordanza, la sua geometria e la storia termica. Inoltre, introduciamo i modelli, lineare e non lineare, di formazione degli aloni di materia oscura. Il {\bf Capitolo 3} descrive l'approccio degli excursion sets nel contesto del collasso sferico. L'estensione di questo metodo al collasso ellissoidale è proposto nel {\bf Capitolo 4}, ove vengono esposti i primi risultati analitici. Nel {\bf Capitolo 5} confrontiamo le nostre predizioni analitiche con i risultati di due simulazioni numeriche. Il {\bf Capitolo 6} è dedicato all'esposizione dei test di un nuovo metodo di massima verosimiglianza con l'utilizzo di dati non raggruppati in intervalli e con le particelle di polvere. Infine tracciamo le nostre {\bf Conclusioni}, seguite da un'{\bf Appendice} ove sono descritte le simulazioni numeriche.

This thesis explores topics related to the formation and development of the large-scale structure in the Universe, with the focus being to compute properties of the evolved non-linear density field in an approximate way. The first three chapters form an introduction: Chapter 1 contains the theoretical basis of modern cosmology, Chapter 2 discusses the role of N-body simulations in the study of structure formation and Chapter 3 considers the phenomenological halo model. In Chapter 4 a novel method of computing the matter power spectrum is developed. This method uses the halo model directly to make accurate predictions for the matter spectrum. This is achieved by fitting parameters of the model to spectra from accurate simulations. The final predictions are good to 5% up to k = 10 hMpc-1 across a range of cosmological models at z = 0, however accuracy degrades at higher redshift and at quasi-linear scales. Chapter 5 is dedicated to a new method of rescaling a halo catalogue that has previously been generated from a simulation of a specific cosmological model to a different model; a gross rescaling of the simulation box size and redshift label takes place, then individual halo positions are modified in accord with the large scale displacement field and their internal structure is altered. The final power spectrum of haloes can be matched at the 5% level up to k = 1 hMpc-1, as can the spectrum of particles within haloes reconstituted directly from the rescaled catalogues. Chapter 6 applies the methods of the previous two chapters to modified gravity models. This is done in as general a way possible but tests are restricted to f(R) type models, which have a scale-dependent linear growth rate as well as having 'chameleon screening' - by which modifications to gravity are screened within some haloes. Taking these effects into account leads to predictions of the matter spectrum at the 5% level and rescaled halo distributions that are accurate to 5% in both real and redshift space. For the spectrum of halo particles it is demonstrated that accurate results may be obtained by taking the enhanced gravity in some haloes into account.

Fine particulate matter (PM2.5) has been associated with a variety of problems that include adverse health effects, reduction in visibility, damage to buildings and crops, and possible interactions with climate. Although stringent air quality regulations are in place, policy makers need efficient tools to test a wide range of control strategies. Sensitivity analysis provides predictions on how the interdependent concentrations of various PM2.5 components and also gaseous pollutant species will respond to specific combinations of precursor emission reductions. The Community Multiscale Air Quality Model (CMAQ) was outfitted with the Decoupled Direct Method in 3D for calculating sensitivities of particulate matter (DDM-3D/PM). This method was evaluated and applied to high PM2.5 episodes in the Southeast United States. Sensitivities of directly emitted particles as well as those formed in the atmosphere through chemical and physical processing of emissions of gaseous precursors such as SO2, NOx, VOCs, and NH3 were calculated. DDM-3D/PM was further extended to calculate receptor oriented sensitivities or the Area of Influence (AOI). AOI analysis determines the geographical extent of relative air pollutant precursor contributions to pollutant levels at a specific receptor of interest. This method was applied to Atlanta and other major cities in Georgia. The tools developed here (DDM-3D/PM and AOI) provide valuable information to those charged with air quality management.

In this thesis we explore two different theories for modelling soft matter systems. We start by discussing density functional theory (DFT) and dynamical density functional theory (DDFT) and consider the thermodynamics underpinning these theories as well as showing how the main results may be derived from the microscopic properties of soft matter. We use this theory to set up a model for the evaporation of the solvent from a thin film of a colloidal suspension. The general background for such systems is discussed and we display some of the striking nanostructures which self-assemble during the evaporation process. We show that our theory successfully reproduces some of these patterns and deduce the various mechanisms and transport processes behind the formation of the different structures. In the second part of this thesis we discuss results for a second model; the phase field crystal (PFC) model. The model equations are discussed, showing how they may be derived from DDFT as well as discussing the general background of PFC models. We present some results for the PFC model in its most commonly used form before going on to introduce a modified PFC model. We show how the changes in the model equations are reflected in the thermodynamics of the model. We then proceed by demonstrating how this modified PFC model may be used to qualitatively describe colloidal systems. A two component generalisation of the modified PFC model is introduced and used to investigate the transition between hexagonal and square ordering in crystalline structures. We conclude by discussing the similarities and connections between the two models presented in the thesis.

In this thesis we studied dark matter models with strong self-interactions, typically known as self-interacting dark matter (SIDM). This kind of models constitute a promising solution to the tension between small scale structure observations and predictions assuming the standard case of collisionless cold dark matter (CDM) while keeping the success of the standard cosmological model, LambdaCDM, at large scales. The presence of strong self-interactions can increase the dark matter capture and annihilation in astrophysical objects like our sun, enhancing the potential of indirect detection signals. We used the high energy neutrinos produced by such annihilations to probe SIDM models. We established strong constraints on SIDM with velocity independent cross section by comparing the expected neutrino signal with the results of the IceCube-79 dark matter search. Also, we determined the sensitivity for the IceCube-DeepCore and PINGU detectors for SIDM with a velocity dependent self-interacting cross section (vdSIDM). Most of its relevant parameter space can be tested with the three years of data already collected by IceCube-DeepCore, complementing results from direct detection experiments and other indirect detection studies.
Nesta tese investigamos modelos de matéria escura com auto-interações fortes, conhecidos tipicamente como matéria escura auto-interagente (SIDM). Este tipo de modelos constituem uma solução promissora à tensão entre as observações de estrutura a pequena escala e as previsões assumindo o caso padrão de matéria escura fria não colisional (CDM), enquanto se mantêm o sucesso do modelo cosmológico padrão, LambdaCDM, a grandes escalas. A presença de auto-interações fortes podem aumentar a captura e a aniquilação da matéria escura em objetos astrofísicos como o nosso sol, aumentando o potencial de sinais de detecção indireta. Usamos o sinal de neutrinos de alta energia produzidos por essas aniquilações para explorar modelos de SIDM. Estabelecemos fortes vínculos em modelos de SIDM com seção de auto-interação independente da velocidade comparando o sinal de neutrinos esperado com os resultados de busca de matéria escura do IceCube-79. Também, determinamos a sensibilidade dos detectores IceCube-DeepCore e PINGU para modelos de SIDM com uma seção de auto-interação dependente da velocidade (vdSIDM). A maior parte do espaço de parâmetros de interesse pode ser testado com os três anos de dados já coletados pelo IceCube-DeepCore, complementando os resultados de experimentos de detecção direta e outras an análises de detecção indireta.

This thesis presents studies of the low energy properties of nseveral frustrated spin-1/2 Heisenberg antiferromagnets using various analytic and computational methods. The models studied include the union jack model, the alternating Heisenberg chain, the Heisenberg bilayer model, and the spin-Peierls model. The union jack model is a Heisenberg antiferromagnetic spin model with frustration, and is analyzed using spin-wave theory. For small values of the frustrating coupling $\alpha$, the system is N{\' e}el ordered, while for large $\alpha$ the frustration is found to induce a canted phase. Spin wave theory with second order corrections finds the critical coupling at $\alpha \simeq 0.645$,which agrees quantitatively with series expansion results. No intermediate spin-liquid phase is found to exist between the two phases. The alternating Heisenberg chain is studied using an alternative triplet-wave expansion formalism for dimerized spin systems, modification of the ??bond operator?? formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace, rather than constraint equations. Comparisons are made with the results of dimer series expansions and exact diagonalization. The S=1/2 Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the S=0 and S=1 channels, and antibound states in the S=2 channel, is predicted with triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N{\' e}el phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series expansion methods and found to conform with theoretical expectations. The Heisenberg spin-Peierls model with dispersive, gapless phonons is studied with Density Matrix Renormalization Group methods. We investigate the zero temperature properties of the model using the crossover method. The calculations were found to converge poorly and no conclusive results could be found using this method. An analysis of the convergence problems and the discovery of an anomalous triplet ground state is presented in this chapter.

We investigate the phenomenon of phase organization in charge density waves. Coppersmith and Littlewood [87] have argued that charge density waves become organized into a "minimally stable" state when subject to a pulsed driving force. They have also proposed that the pulse duration memory effect, observed by Fleming and Schneemeyer [86], is evidence for this self organizing behaviour.
We review the microscopic origins of charge density waves, experimental results, and theoretical models of charge density waves. We also review theories of complex systems, and, in particular, the phase organization theory proposed by Tang et al. [87]. We focus on how the phase organization theory applies to the dynamics of charge density waves.
We investigate phase organization in a model of elastically coupled particles subject to a periodic potential and a pulsed driving force. By numerical simulation of the model, we show that the phase organization behaviour is contingent on the existence of a large number of inequivalent metastable configurations in the model. We also show that this model is equivalent to a purely elastic model of charge density waves interacting with impurities.
We further investigate phase organization in a model of charge density waves that has been proposed by Karttunen et al. [99], in which the dynamical generation of phase slips is naturally accounted for. Based on the results of numerical simulations, we argue that phase slips reduce or eliminate the phase organization behaviour of charge density waves by breaking the elasticity of the system.

In this dissertation, we review the physics associated with surfaces and interfaces in equilibrium and non-equilibrium. Our emphasis will be on interfaces that are driven far away from equilibrium with special interest in the phenomenon of kinetic roughening. Models which describe non-equilibrium interfaces will be introduced and analyzed using techniques such as the Renormalization Group, Monte Carlo simulations, and direct integration of the equation of motion. Different interface relaxation mechanisms will be discussed with a focus on surface diffusion, which is believed to be the dominant effect in Molecular Beam Epitaxy. These interface growth models generate self-affine structures with various correlations satisfying a dynamic scaling law. We compute the scaling exponents and functions. Finally, we study the effect of quenched impurities on the dynamics of a driven interface with a conservation law. The impurity effect leads to anomalous scaling exponents and qualitatively changes the interface dynamics. Our results are summarized in two articles to be published: Refs. (Govind and Guo, 1992; Govind, Guo and Grant, 1992).

Conformal methods have proven to be very useful in the analysis global properties and stability of vacuum spacetimes in general relativity. These methods transform the physical spacetime into a different Lorentzian manifold known as the unphysical spacetime where the ideal points at infinity are located at a finite position. This thesis makes use of conformal methods and applies them to various problems involving trace-free matter models. In particular, it makes progress towards the understanding of the evolution of unphysical spacetimes perturbed by trace-free matter as well as the behaviour of the the matter itself. To this end, evolution equations (wave equations) are derived and analyzed for both the unphysical spacetime and the matter. To investigate the relation between solutions of these wave equations to the Einstein field equations, a suitable system of subsidiary evolution equations is also derived. Furthermore, this thesis looks in detail at the behaviour of an unphysical spacetime coupled to the simplest matter trace free model: the confomally invariant scalar field. Finally, the system of conformal wave equations is used to show that the deSitter spacetime is non-linearly stable under perturbations by trace-free matter.

This dissertation demonstrates the usefulness of exactly solvable quantum models in the investigation of light-matter interaction phenomena associated with the propagation of ultrashort laser pulses through gaseous media. This work fits into the larger research effort towards remedying the weaker portions of the standard set of medium modeling equations commonly used in simulations. The ultimate goal is to provide a self-consistent quantum mechanical description that can integrate Maxwell and Schrödinger systems and provide a means to realistically simulate nonlinear optical experiments on relevant scales. The study of exactly solvable models begins with one of the simplest quantum systems available, one with a 1D Dirac-delta function potential plus interaction with the light field. This model contains, in the simplest form, the most important "ingredients" that control optical filamentation, i.e. discrete and continuum electronic states. The importance of both states is emphasized in the optical intensity regime in which filaments form, where both kinds of electronic states simultaneously play a role and may not even be distinguishable. For this model atom, an analytical solution for the time-dependent light-induced atomic response from an arbitrary excitation waveform is obtained. Although this system is well-known and has been studied for decades, this result is probably the most practically useful and general one obtained thus far. Numerical implementation details of the result are also given as the task is far from trivial. Given an efficient implementation, the model is used in light-matter interaction simulations and from these it is apparent that even this toy model can qualitatively reproduce many of the nonlinear phenomena seen in experiments. Not only does this model capture the basic physics of optical filamentation, but it is also well-suited for high harmonic generation simulations. Next, a theoretical framework for using Stark resonant states (or metastable states) to represent the medium's polarization response is presented. Researchers have recognized long ago the utility of Gamow resonant states as a description of various decay processes. Even though a bound electron experiences a similar decay-like process as it transitions into the continuum upon ionization, it was unclear whether field-induced Stark resonant states carry physically relevant information. It is found that they do, and in particular it is possible to use them to capture a medium's polarization response. To this end, two quantum systems with potentials represented by a 1D Dirac-delta function and a 1D square well are solved, and all the necessary quantities for their use as medium models are presented. From these results it is possible to conjecture some general properties that hold for all resonance systems, including systems that reside in higher than one dimensional space. Finally, as a practical application of this theory, the Metastable Electronic State Approach (MESA) is presented as a quantum-based replacement for the standard medium modeling equations.

Scientific curiosity and thirst for knowledge have driven human progress and helped mankind develop an always deeper understanding of our world. New - and sometimes controversial - ideas have been proposed in order to explain its mysteries. Looking for alternative perspectives has proven essential, particularly when the current paradigms do not give complete satisfaction. Such is the case for three important questions in modern astrophysics and cosmology, which we intend to investigate: the Paradox of Youth, Dark Matter and Dark Energy. We will first explore a new possible explanation to the paradoxical observation of young, massive stars near the centre of our galaxy. Hosting a solar mass black hole might allow them to spare some of their burning material, giving them enough time to travel from further galactic distances. In the second part of our thesis, we will study Dark Matter accretion onto neutron stars. Considering different types of Dark Matter particles, we will determine the consequences of their capture by these very dense objects and look for observable signatures. Finally, our current views on Dark Energy will be examined through its role in void models. Among them, the Swiss-Cheese Universe and central void models will be analysed in order to evaluate the impact of inhomogeneities on the determination of cosmological parameters. All three parts are similarly structured: conceptual introduction, analytical and computational considerations, commented results and conclusive remarks. Bibliographies are given separatly after each part. Lists of figures, tables and abbreviations can be found at the end of the document.

Le phénomène de mouvement collectif est présent parmi beaucoup de systèmes biologiques comme dans les volées d'oiseaux ou des bancs de poissons. Dans ces systèmes, le mouvement collectif apparait sans aucun leader ni force extérieure et est exclusivement dû à l'interaction parmi les individus et à la nature hors-équilibre de tout le système. Nous voulons étudier des modèles simples de mouvement collectif afin d'établir des classes d'universalité parmi la matière active sèche, c'est-à-dire des individus interagissant sans l'aide d'un fluide. Beaucoup de ces systèmes ont déjà été étudiés microscopiquement. Nous voulons obtenir des équations hydrodynamiques de ces systèmes pour confirmer les résultats microscopiques et pour prédire des propriétés nouvelles. Nous effectuons une dérivation d'équations hydrodynamiques en utilisant l'approche Boltzmann-Ginzburg-Landau introduit dans cette thèse. Quatre modèles de type Vicsek sont considérés. Un modèle polaire simple identique au modèle de Vicsek, un modèle mixte avec des particules polaires avec interactions nématiques, un modèle avec des particules polaires et interactions nématiques et finalement un modèle avec des particules polaires avec des interactions non-métriques. Dans chaque cas les équations obtenues sont étudiées de façon analytique et numérique. Nous trouvons que les équations obtenues reproduisent de façon fidèles les propriétés qualitatives des modèles microscopiques considérées, comme les différentes phases observées et la nature de transition entre ces phases. Dans certains cas des phases nouvelles sont trouvées, qui n'ont pas été reportées auparavant dans les modèles microscopiques. Beaucoup d'entre elles ont été confirmées a posteriori dans les simulations numériques de ces modèles
The phenomenon of collective motion is present among many different biological systems like bird flocks or fish schools. In these systems, the collective motion arises without any leader or external force, and is only due to interaction among individuals and the out of equilibrium nature of the whole system. We want to study simple models of collective motion in order to establish universality classes among dry active matter, i. E. Individuals that interact without the help of a fluid medium. Many of such systems have already been studied microscopically. We want to obtain coarse-grained equations of such models to confirm the microscopical results and to predict new properties. We perform a derivation of hydrodynamic equations using the introduced Boltzmann-Ginzburg-Landau approach. The equations are derived for four different Vicsek type models. A simple polar model, a mixed case of polar particles with nematic interactions, a model of nematic particles with nematic interactions and finally a model for polar particles with metric free interactions. In each case, the obtained equations are studied analytically and numerically. We find out that the hydrodynamic equations reproduce faithfully the qualitative properties of underlying microscopical models, like the different observed phases and the nature of phase transition between them. Some new phases not previously observed in microscopical models are found. Most of them where a posteriori confirmed in simulations of microscopical models

We present results from a constrained path Monte Carlo (CPMC) study of a modified two-dimensional Hubbard model. We include more general forms of the band structure and electron interaction in order to examine their effects on ground-state properties, such as electron pairing correlations. Both next-nearest neighbor hopping, t', and third-nearest neighbor hopping, t″, are introduced in the Hamiltonian. A nearest neighbor interaction of strength V is also included. We carry out CPMC calculations on system sizes up to 16 x 16, at various electron fillings, to investigate the ground state of the model for different values of these parameters. For realistic systems, these calculations indicate that Hubbard-like models are not capable of showing enhanced pairing. The modified Hamiltonian also presents an opportunity to more closely examine the accuracy and robustness of the CPMC algorithm. Results of further benchmark calculations involving CPMC are presented. These benchmarks confirm that CPMC is able to show enhanced pairing in systems where such behavior is known to exist.

Diffusion MRI microstructure imaging provides a unique noninvasive probe into tissue microstructure. The technique relies on mathematical models, relating microscopic tissue features to the MR signal. The assumption of Gaussian diffusion oversimplifies the behaviour of water in complex media. Multi-compartment models fit the signal better and enable the estimation of more specific indices, such as axon diameter and density. A previous model comparison framework used data from fixed rat brains to show that three compartment models, designed for intra/extra-axonal diffusion, best explain multi-b-value datasets. The purpose of this PhD work is to translate this analysis to in vivo human brain white matter. It updates the framework methodology by enriching the acquisition protocol, extending the model base and improving the model fitting. In the first part of this thesis, the original fixed rat study is taken in-vivo by using a live human subject on a clinical scanner. A preliminary analysis cannot differentiate the models well. The acquisition protocol is then extended to include a richer angular resolution of diffusion- sampling gradient directions. Compared with ex-vivo data, simpler three-compartment models emerge. Changes in diffusion behaviour and acquisition protocol are likely to have influenced the results. The second part considers models that explicitly seek to explain fibre dispersion, another potentially specific biomarker of neurological diseases. This study finds that models that capture fibre dispersion are preferred, showing the importance of modelling dispersion even in apparently coherent fibres. In the third part, we improve the methodology. First, during the data pre-processing we narrow the region of interest. Second, the model fitting takes into account the varying echo time and compartmental tissue relaxation; we also test the benefit to model performance of different compartmental diffusivities. Next, we evaluate the inter- and intra-subject reproducibility of ranking. In the fourth part, high-gradient Connectom-Skyra data are used to assess the generalisability of earlier results derived from a standard Achieva scanner. Results showed a reproducibility of major trends in the model ranking. In particular, dispersion models explain low gradient strength data best, but cannot capture Connectom signal that remains at very high b-values. The fifth part uses cross-validation and bootstrapping as complementary means to model ranking. Both methods support the previous ranking; however, the leave-one-shell-out cross- validation supports less difference between the models than bootstrapping.

Title from PDF of title page (University of Missouri--Columbia, viewed on March 10, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Thesis advisor: Dr. Steve Osterlind. Includes bibliographical references.

The behavior of MR phase and frequency in demyelination and damage in central nervous tissue white matter arises not only from traditionally associated bulk susceptibility changes, but also from changes to its tissue microstructure. A recently proposed generalized Lorentzian model of microstructure-related magnetic susceptibility effects predicts an increase in MR frequency due to damage in myelin in MS lesions. The same model also predicts reduction in MR frequency due to axonal degeneration. Here, we investigate the effect of both myelin and axonal damage through transection of white matter fibers in the dorsal column of rat cervical spinal cord. This injury generates secondary damage consisting of neurodegeneration along nerve tracts bilateral to the transection site, producing cases of Wallerian and retrograde degeneration free of excessive hemorrhage and inflammation. High-resolution frequency maps of degenerating tracts were correlated with histopathology for axons, myelin, degenerated myelin, and macrophages. Damage to myelin sheaths is prominent in Wallerian degeneration, where we observe strong correlations with increasing frequency up to 8 weeks post-injury. Retrograde degeneration, which consists predominantly of axonal damage, produces decreased frequency shift over time. The MR frequency shifts are sensitive to the effects of macrophage in filtration and debris clearance, which vary with white matter fiber density and affect rates of degeneration. We demonstrate how MR frequency can successfully characterize injury in rat spinal cord white matter in a manner consistent with predictions outlined by the Generalized Lorentzian Approximation Model, and conclude that these results suggest potential applications of MR frequency to supplement or replace current clinical techniques, such as myelin water and diffusion weighted imaging, as a non-invasive and quantitative method of assessing white matter damage in CNS.
Science, Faculty of
Physics and Astronomy, Department of
Graduate

L’imagerie de résonance magnétique de diffusion (dMRI) est une technique très sensible pour la tractographie des fibres de substance blanche et la caractérisation de l’intégrité et de la connectivité axonale. A travers la mesure des mouvements des molécules d’eau dans les trois dimensions de l’espace, il est possible de reconstruire des cartes paramétriques reflétant l’organisation tissulaire. Parmi ces cartes, la fraction d’anisotropie (FA) et les diffusivités axiale (λa), radiale (λr) et moyenne (MD) ont été largement utilisés pour caractériser les pathologies du système nerveux central. L’emploi de ces cartes paramétriques a permis de mettre en évidence la survenue d’altérations micro structurelles de la substance blanche (SB) et de la substance grise (SG) chez les patients atteints d’une sclérose en plaques (SEP). Cependant, il reste à déterminer l’origine de ces altérations qui peuvent résulter de processus globaux comme la cascade inflammatoire et les mécanismes neurodégénératifs ou de processus plus localisés comme la démyélinisation et l’inflammation. De plus, ces processus pathologiques peuvent survenir le long de faisceaux de SB afférents ou efférents, conduisant à une dégénérescence antero- ou rétrograde. Ainsi, pour une meilleure compréhension des processus pathologiques et de leur progression dans l’espace et dans le temps, une caractérisation fine et précise des faisceaux de SB est nécessaire. En couplant l’information spatiale de la tractographie des fibres aux cartes paramétriques de diffusion, obtenues grâce à un protocole d’acquisitions longitudinal, les profils des faisceaux de SB peuvent être modélisés et analysés. Une telle analyse des faisceaux de SB peut être effectuée grâce à différentes méthodes, partiellement ou totalement non-supervisées. Dans la première partie de ce travail, nous dressons l’état de l’art des études déjà présentes dans la littérature. Cet état de l’art se focalisera sur les études montrant les effets de la SEP sur les faisceaux de SB grâce à l’emploi de l’imagerie de tenseur de diffusion. Dans la seconde partie de ce travail, nous introduisons deux nouvelles méthodes,“string-based”, l’une semi-supervisée et l’autre non-supervisée, pour extraire les faisceaux de SB. Nous montrons comment ces algorithmes permettent d’améliorer l’extraction de faisceaux spécifiques comparé aux approches déjà présentes dans la littérature. De plus, dans un second chapitre, nous montrons une extension de la méthode proposée par le couplage du formalisme “string-based” aux informations spatiales des faisceaux de SB. Dans la troisième et dernière partie de ce travail, nous décrivons trois algorithmes automatiques permettant l’analyse des changements longitudinaux le long des faisceaux de SB chez des patients atteints d’une SEP. Ces méthodes sont basées respectivement sur un modèle de mélange Gaussien, la factorisation de matrices non-négatives et la factorisation de tenseurs non-négatifs. De plus, pour valider nos méthodes, nous introduisons un nouveau modèle pour simuler des changements longitudinaux réels, base sur une fonction de probabilité Gaussienne généralisée. Des hautes performances ont été obtenues avec ces algorithmes dans la détection de changements longitudinaux d’amplitude faible le long des faisceaux de SB chez des patients atteints de SEP. En conclusion, nous avons proposé dans ce travail des nouveaux algorithmes non supervisés pour une analyse précise des faisceaux de SB, permettant une meilleure caractérisation des altérations pathologiques survenant chez les patients atteints de SEP
Diffusion Magnetic Resonance Imaging (dMRI) is a meaningful technique for white matter (WM) fiber-tracking and microstructural characterization of axonal/neuronal integrity and connectivity. By measuring water molecules motion in the three directions of space, numerous parametric maps can be reconstructed. Among these, fractional anisotropy (FA), mean diffusivity (MD), and axial (λa) and radial (λr) diffusivities have extensively been used to investigate brain diseases. Overall, these findings demonstrated that WM and grey matter (GM) tissues are subjected to numerous microstructural alterations in multiple sclerosis (MS). However, it remains unclear whether these tissue alterations result from global processes, such as inflammatory cascades and/or neurodegenerative mechanisms, or local inflammatory and/or demyelinating lesions. Furthermore, these pathological events may occur along afferent or efferent WM fiber pathways, leading to antero- or retrograde degeneration. Thus, for a better understanding of MS pathological processes like its spatial and temporal progression, an accurate and sensitive characterization of WM fibers along their pathways is needed. By merging the spatial information of fiber tracking with the diffusion metrics derived obtained from longitudinal acquisitions, WM fiber-bundles could be modeled and analyzed along their profile. Such signal analysis of WM fibers can be performed by several methods providing either semi- or fully unsupervised solutions. In the first part of this work, we will give an overview of the studies already present in literature and we will focus our analysis on studies showing the interest of dMRI for WM characterization in MS. In the second part, we will introduce two new string-based methods, one semi-supervised and one unsupervised, to extract specific WM fiber-bundles. We will show how these algorithms allow to improve extraction of specific fiber-bundles compared to the approaches already present in literature. Moreover, in the second chapter, we will show an extension of the proposed method by coupling the string-based formalism with the spatial information of the fiber-tracks. In the third, and last part, we will describe, in order of complexity, three different fully automated algorithms to perform analysis of longitudinal changes visible along WM fiber-bundles in MS patients. These methods are based on Gaussian mixture model, nonnegative matrix and tensor factorisation respectively. Moreover, in order to validate our methods, we introduce a new model to simulate real longitudinal changes based on a generalised Gaussian probability density function. For those algorithms high levels of performances were obtained for the detection of small longitudinal changes along the WM fiber-bundles in MS patients. In conclusion, we propose, in this work, a new set of unsupervised algorithms to perform a sensitivity analysis of WM fiber bundle that would be useful for the characterisation of pathological alterations occurring in MS patients

Includes abstract.
Includes bibliographical references.
In order to understand nuclear matter at high temperatures and densities formed in heavy ion collisions, it is useful to use statistical-thermal models to analyse the final state. We apply different types of statistical distributions and discuss their effects. We discuss the hadron resonance gas model and its extension to include the Hagedorn spectrum [1, 2, 3]. The Hagedorn temperature, TH is determined from the number of hadronic resonances including all mesons and baryons. This leads to the result TH = 174±1l MeV consistent with the critical and the chemical freeze-out temperatures at zero chemical potential. We apply this result to calculate the speed of sound and other thermodynamic quantities in the resonance hadron gas model for a wide range of baryon chemical potentials using the chemical freeze-out curve [4, 5]. We compare some of our results to those obtained previously [6, 7]. We have also made additions to THERMUS [8] by including charm and bottom hadrons from the particle data table . Then, we analyze and discussthe hadronic abundances measured in proton-proton (p-p), gold-gold (Au-Au) and lead-lead (Pb-Pb) collisions at Relativistic Heavy-Ion Collider (RHIC) [10] and Large Hadron Collider (LHC) [11, 12, 13] experiments using THERMUS. The THERMUS results obtained with the 2002 particle data table and new particle data table (2008 particle data table) and their differences are discussed. In particular, the data from the RHIC experiment for Au-Au collisions at 130 GeV and 200 GeV [10] are discussed and analyzed. Similarly, using the preliminary particle yield results of p-p collisions at 0.9 TeV and 7 TeV as well as Pb-Pb collision at 2.76 TeV [11, 12, 13l are presented and the thermodynamic parameters are obtained from the fit are discussed.

In this dissertation, we investigate various aspects of dark matter detection and model building. Motivated by the cosmic ray positron excess observed by PAMELA, we construct models of decaying dark matter to explain the excess. Specifically we present an explicit, TeV-scale model of decaying dark matter in which the approximate stability of the dark matter candidate is a consequence of a global symmetry that is broken only by instanton-induced operators generated by a non-Abelian dark gauge group. Alternatively, the decaying operator can arise as a Planck suppressed correction in a model with an Abelian discrete symmetry and vector-like states at an intermediate scale that are responsible for generating lepton Yukawa couplings. A flavor-nonconserving dark matter decay is also considered in the case of fermionic dark matter. Assuming a general Dirac structure for the four-fermion contact interactions of interest, the cosmic-ray electron and positron spectra were studied. We show that good fits to the current data can be obtained for both charged-lepton-flavor-conserving and flavor-violating decay channels. Motivated by a possible excess of gamma rays in the galactic center, we constructed a supersymmetric leptophilic higgs model to explain the excess. Finally, we consider an improvement on dark matter collider searches using the Razor analysis, which was originally utilized for supersymmetry searches by the CMS collaboration.

Un des problèmes les plus intrigants de la physique moderne est l'identification de la nature d'une composante de matière non-relativiste présente dans l'univers, contribuant à plus de 25% de sa densité d'énergie totale, appelée matière noire. Les particules "WIMPs" (Weakly Interacting Massive Particles) sont parmi les catégories de candidats à la matière noire les plus considérées. Cependant, en l'absence de résultats concluants d'expériences de détection directe, indirecte et auprès de collisionneurs de particules, la première partie de cette thèse est dévouée à l'étude du paradigme "WIMP" dans le contexte de modèles simplifiés. Des modèles considérant des extensions de jauge sont étudiés par la suite tels que des théories présentant des couplages de Chern-Simons ainsi qu'un modèle motivé par l'observation récente d'anomalies dans le domaine de la physique la saveur lié à l'observable RK(*). La deuxième partie de cette thèse est dévouée à l'étude de mécanismes alternatifs de production thermique de matière noire en particulier en considérant une réalisation spécifique du mécanisme "SIMP" (Strongly Interacting Massives Particles) dans le contexte d'une symétrie de jauge non-abélienne cachée. Dans une dernière partie, la possibilité de produire une composante de matière noire de manière non-thermique à travers le mécanisme "freeze-in" est étudiée. En particulier, le fort impact de l'époque post-inflationnaire de l'univers sur la production de densité de matière noire est illustré par l'étude d'un modèle de matière noiremédiée par un champ de spin 2 massif en plus du graviton standard
One of the most puzzling problems of modern physics is the identification of the nature a non-relativistic matter component present in the universe, contributing to more than 25% of the total energy budget, known as Dark Matter. Weakly Interacting Massive Particles (WIMPs) are among the best motivated dark matter candidates. However, in light of non conclusive detection signals and strong constraints from collider, direct and indirect detection experiments, this thesis presents constraints on several realizations of the WIMP paradigm in the context of simplified dark matter models. More elaborated models considering extended gauge structures are discussed further on, such as constructions involving generalized Chern-Simons couplings and a specific WIMP scenario motivated by some recently observed flavor anomalies related to the RK(*) observable. The second part of this thesis is devoted to the discussion of an alternative dark matter thermal production mechanism where an explicit realization of the Strongly Interacting Massive Particles (SIMPs) paradigm is discussed in the context of a non-Abelian hidden gauge structure. In a last part, the possibility of producing non-thermally a dark matter component via the "freeze-in" mechanism was investigated and the strong impact of the postinationary reaheating stage of the universe on such constructions illustrated by the specific case where dark matter density production is mediated by a heavy spin-2 field in addition to the standard graviton

Air pollution is a problem that is becoming increasingly important in modern society as they are observed correlations between the level of pollution and damage to the environment and human health. Pollutants may be of various kinds: solid, liquid or gaseous fuels, a portion is very important and relevant to health is represented by particulate air pollution. The process of corrosion of a material is influenced by PM through different activities which include the presence of substances able to: change the speed of corrosion and to participate in the reactions of galvanic corrosion. Furthermore, the PM is the main responsible for the absorption of water on the metal surface. So it is important to define the strategies for the evaluation of the effects of the particulates on the environment, particularly related to the activity of corrosion, in this context are relevant the works Aerosol Corrosion Prevention and Energy- Saving Strategies in the Design of Green Data Centers. A study on the impact of the corrosivity influenced by relative humidity in indoor environments. A better knowledge of the behavior of atmospheric aerosols, with particular reference to their deliquescence crystallization, and their interactions with the circuit elements of Printed Circuit Boards could allow the identification of conditions of security for data centers that optimize air conditioning systems and reduce energy consumption operated by the Data Center. It is important to implement computational models for the study of molecular interactions that occur among the components of atmospheric particles and that give rise to receptors and signal transduction leading to effects on human health, Given the specificity and temporal and spatial variability of particulate matter is important to assess the specificity and selectivity of individual proteins. Being able to perform these tests requires high experimental economic resources, to overcome this problem it is important to implement a computational strategy for the evaluation and analysis of the molecular mechanisms. Computationally this type of simulations require long timescales of traditional infrastructure so it is desirable to develop new infrastructure to reduce the time of calculation. The article Homology Modeling, Docking Studies and Molecular Dynamic Simulations Using Graphical Processing Unit Architecture to Probe the Type-11 Phosphodiesterase Catalytic Site: A Computational Approach for the Rational Design of Selective Inhibitors describe a computational approach based on homology models, docking and molecular dynamics simulations to derive a 3D model predictive of PDE11. This work underlines the importance of strategies for the screen- ing of ligands and in the assessment of the interactions to evaluate the effects due to the specificity and selectivity of the ligand-protein interaction. In particular the implementation of a GPU infrastructure permits to simulate long molecular dynamic that enable to highlight the key residues of interaction between the Phosphodiesterase and the ligand, so using this protocol is possible to studies different receptor and let know the principal residues involved in the interaction and develop specific ligands that better interact with the protein. As noted by literature studies, some effects of PM are due to its passage into the blood stream, in particular it is associated with alterations in circulating levels of coagulation-related parameters such as serum levels of fibrinogen, von Willebrand factor, factor VIII and protein C. So it is important to assess the molecular interactions that are generated in the blood fow to assess the possible effects of particulate air pollution, and this highlights the need for experimental problems in the evaluation of interactions and formation of protein complexes. This is the context of the work: Molecular dynamics and docking simulation of a natural variant of Activated Protein C with impaired protease activity: Implications for integrin-mediated antiseptic function. In this paper has highlighted the importance of an infrastructure performance and has illustrated a protocol for a computational study on the functional activity of the protein C, which involved the creation of various docking simulation to better understand the protein interaction and the need of the definition of a new scoring function that included biological information of the interaction of the protein in addition to the energies of docking to better ranking the results of docking. In addition to the effects on the circulatory and respiratory system are important the effects on the endocrine system. The effects on the endocrine system are due to endocrine disrupting chemicals (EDCs), with this term refers to a broad category of substances mainly, but not only, of artificial origin, which are able to bind as agonists or antagonists to the receptors of various hormones. Endocrine disruptors are substances that then interfere with the synthesis, secretion, transport, binding, action or elimination of natural hormones in the body, responsible for the development, behavior, fertility, and maintenance of cellular homeostasis. These compounds can cause serious damage to exposed organisms, but often aren’t immediately apparent because at low doses there aren’t acute toxicity, and may, in the case of large environmental exposures produce effects at the population level. Many of the pollutants that are objects of deep environmental and toxicological studies are EDCs. Epidemiological and experimental studies suggest that EDCs may increase the risk of cancer, metabolic disorders, reproductive and developmental disorders. It is extremely importance their interaction with nuclear hormone receptors (NHRs), in facts these receptor regulate cognate gene networks involved in key physiological functions such as cell growth and differentiation, development, homeostasis or metabolism. Human NHRs are a family of 48 transcription factors, very preserved in term of structural and functional features; many of NHR have been shown to be activated by ligands. These evidences motivate the need to provide a system for the assessment of the interaction of various xenobiotics with nuclear receptors, an preliminary tool has highlighted in the work Nuclear Receptor Database Evaluates the effects of the EDC on the Endocrine System, which shows an in silico protocol for the preliminary assessment of the interactions between pollutants, particularly EDCs, and nuclear receptors.

Although a number of methods with appropriate approximations, such as mean-field theory, local density approximation, and tight-binding method have been well developed and widely used in solid state physics, they possess strong limitations, and thus physicists never stop trying to find methods that could rigorously solve the models of condensed matter systems. This thesis presents several new exact solutions for electron pairing models with spin-orbit interactions and Zeeman coupling, which have not been studied before. First, a type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson’s previous work for 2D cases. Based on the exact solutions for the electron pairing model with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p+ip wave and the ground state possesses time-reversal symmetry, which are expected by the meanfield theory. And the difference is that such peroration from our framework is valid for any strength of the pairing interactions. Intriguingly, how Majorana fermions can emerge is also elaborated in a ribbon system as well. Condensation energy and critical magnetic field are calculated in two systems with the exact solutions, and compared with the relevant results achieved by the mean-field theory, the differences between our results and the mean-field theory show the significance of the work for exact solutions. Secondly, we generalize our scenario to 3D cases. Several remarks of the 3D case are given following the significant results from the 2D cases. And an unconventional type of Fulde-Ferrel-Larkin-Ovchinnikov ground state is revealed exactly, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. As a by-product, a similar Fulde-Ferrel-Larkin-Ovchinnikov state is also disclosed when the magnetic field is in the same plane of k for 2D case. In addition, applying the transformative Richardson ansatz in bosonic system, we elaborate on the drifting effect of the Zeeman field on the spin-orbit-coupled Bose-Einstein condensed matter as well. Finally, we discuss the application of the exact solutions in quantum entanglement quantification. The entanglement monotone concurrence is calculated with exact solutions for two models. It is found to be a smooth function of pairing interactions, as expected.
published_or_final_version
Physics
Doctoral
Doctor of Philosophy

In this study, the outgassing rate from an electropolished stainless steel surface following exposures to H{dollar}\sb2{dollar}O vapor under various conditions was measured. The results of the experiments showed that the outgassing rate is proportional to {dollar}p\sb0\sp{lcub}n{rcub}{dollar}, where {dollar}p\sb0{dollar} is the H{dollar}\sb2{dollar}O exposure pressure and n is about 0.25. The outgassing rate is not as strongly dependent on the system temperature as one would expect if the temperature is kept the same during exposure and pump-down. The outgassing rate is also a function of the exposure time for the first several hours of exposure, indicating that the adsorption saturation time is on the order of hours. The pump-down time of a vacuum system can be reduced significantly by reducing the moisture content of venting gases. The time taken to achieve an outgassing rate of 10{dollar}\sp{lcub}-10{rcub}{dollar} Torr {dollar}\ell{dollar}/cm{dollar}\sp2{dollar} s following dry N{dollar}\sb2{dollar} venting is about one hour in comparison to one day if the system was vented to ambient air. In the second part of this study, the effect on the water outgassing of dc glow discharge cleaning fueled by common gases was studied. It is shown that the water outgassing rate following a typical air vent can be reduced by a factor of 13 when the surface is exposed to a He glow discharge at a dose of 0.8 coulomb/cm{dollar}\sp2{dollar} for two hours.;To explain the 1/t power law obeyed by the outgassing rate and other experimental results, diffusion-type outgassing models were proposed. Initially, non-uniform H{dollar}\sb2{dollar}O concentrations throughout the oxide layer were assumed and the outgassing rate expressions were derived without taking into account the oxide layer microstructure. A more comprehensive model starts with a simplified microstructure of a porous oxide layer, which consists of cylindrical pores with a pore length distribution inversely proportional to the square of pore length. This model predicts the 1/t time dependence for the outgassing rate under saturation conditions where the coverage on the inner surfaces of the pores is uniform. It also explains the observation that the quantity of adsorbed H{dollar}\sb2{dollar}O is a linear function of the logarithm of the exposure time.

Big Bang Nucleosynthesis (BBN), together with the analyses of the Cosmic Microwave Background (CMB) anisotropies, confirm what our day to day experience of life attests :antimatter is far less present than matter in the Universe. In addition, these observables also permit to evaluate that there exists about one proton for every 10^{10} photons present in the Universe. This is in contradiction with expectations coming from the standard hot big bang, where no distinction between matter and antimatter is made, and where subsequent annihilations would lead to equal matter and antimatter contents, at a level 10^{−10} smaller than the observed one. The Standard Model of fundamental interactions fails to explain this result, leading us to search for ‘Beyond the Standard Model’ physics.

Among the possible mechanism which could be responsible for the creation of such a matter asymmetry, leptogenesis is particularly attractive because it only relies on the same ingredients previously introduced to generate neutrino masses. Unfortunatelly, this elegant proposal suffers from a major difficulty :it resists to any tentative of being probed by our low energy observables. In this thesis, we tackle the problem the other way around and propose a way to falsify this mechanism. Considering the type-I leptogenesis mechanism, i.e. a mechanism based on the asymmetric decay of right-handed neutrinos, in a left-right symmetric framework, we show that the observation of a right-handed gauge boson W_R at future colliders would rule out any possibility for such mechanism to be responsible of the matter asymmetry present in our Universe.

Another intriguing question that analyses of the anisotropies of the CMB confirmed is the presence of a non-baryonic component of matter in our Universe, i.e. the dark matter. As hinted by observations of galactic rotation curves, it should copiously be present in our galactic halo, but is notoriously difficult to detect directly. We can take advantage on the fact that antimatter almost disappeared from our surroundings to detect the contamination of cosmic rays from standard sources the annihilation products of dark matter would produce.

The second subject tackled in this work is the study of the imprints the Inert Doublet Modem (IDM) could leave in (charged) cosmic rays, namely positrons, antprotons and antideuterons. This model, first proposed to allow the Bout-Englert-Higgs particle to evade the Electroweak Precision Test (EWPT) measurements, introduces an additional scalar doublet which is inert in the sense that it does not couple directly to fermions. This latter property brings an additional virtue to this additional doublet :since it interacts weakly with particles, it can play the role of dark matter. This study will be done in the light of the data recently released by the PAMELA, ATIC and Fermi-GLAST collaborations, which reported e^± excesses in two different energy ranges.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

This thesis is divided in two parts. The first one is devoted to the dynamics of polariton condensates, with particular attention to their pattern-forming capabilities. In many configurations of physical interest, the dynamics of polariton condensates can be modelled by means of a non-linear PDE which is strictly related to the Gross-Pitaevskii and the complex Ginzburg-Landau equations. Numerical simulations of this equation are used to investigate the robustness of the rotating vortex lattice which is predicted to spontaneously form in a non-equilibrium trapped condensate. An idea for a polariton-based gyroscope is then presented. The device relies on peculiar properties of non-equilibrium condensates - the possibility of controlling the vortex emission mechanism and the use of pumping strength as a control parameter - and improves on existing proposals for superfluid-based gyroscopes. Finally, the important rôle played by quantum pressure in the recently observed transition from a phase-locked but freely flowing condensate to a spatially trapped one is discussed. The second part of this thesis presents work done in the context of the geometrical models of matter framework, which aims to describe particles in terms of 4-dimensional manifolds. Conserved quantum numbers of particles are encoded in the topology of the manifold, while dynamical quantities are to be described in terms of its geometry. Two infinite families of manifolds, namely ALF gravitational instantons of types A_k and D_k, are investigated as possible models for multi-particle systems. On the basis of their topological and geometrical properties it is concluded that A_k can model a system of k+1 electrons, and D_k a system of a proton and k-1 electrons. Energy functionals which successfully reproduce the Coulomb interaction energy, and in one case also the rest masses, of these particle systems are then constructed in terms of the area and Gaussian curvature of preferred representatives of middle dimension homology. Finally, an idea for constructing multi-particle models by gluing single-particle ones is discussed.

The research presented in this thesis models the diffusion-weighted MRI signal within brain white matter tissue. We are interested in deriving descriptive microstructure indices such as white matter axon diameter and density from the observed diffusion MRI signal. The motivation is to obtain non-invasive reliable biomarkers for early diagnosis and prognosis of brain development and disease. We use both analytic and numerical models to investigate which properties of the tissue and aspects of the diffusion process affect the diffusion signal we measure. First we develop a numerical method to approximate the tissue structure as closely as possible. We construct three-dimensional meshes, from a stack of confocal microscopy images using the marching cubes algorithm. The experiment demonstrates the technique using a biological phantom (asparagus). We devise an MRI protocol to acquire data from the sample. We use the mesh models as substrates in Monte-Carlo simulations to generate synthetic MRI measurements. To test the feasibility of the method we compare simulated measurements from the three-dimensional mesh with scanner measurements from the same sample and simulated measurements from an extruded mesh and much simpler parametric models. The results show that the three-dimensional mesh model matches the data better than the extruded mesh and the parametric models revealing the sensitivity of the diffusion signal to the microstructure. The second study constructs a taxonomy of analytic multi-compartment models of white matter by combining intra- and extra-axonal compartments from simple models. We devise an imaging protocol that allows diffusion sensitisation parallel and perpendicular to tissue fibres. We use the protocol to acquire data from two fixed rat brains, which allows us to fit, study and evaluate the models. We conclude that models which incorporate non-zero axon radius describe the measurements most accurately. The key observation is a departure of signals in the parallel direction from the two-compartment models, suggesting restriction, most likely from glial cells or binding of water molecules to the membranes. The addition of the third compartment can capture this departure and explain the data. The final study investigates the estimates using in vivo brain diffusion measurements. We adjust the imaging protocol to allow an in vivo MRI acquisition of a rat brain and compare and assess the taxonomy of models. We then select the models that best explain the in vivo data and compare the estimates with those from the ex vivo measurements to identify any discrepancies. The results support the addition of the third compartment model as per the ex vivo findings, however the ranking of the models favours the zero radius intra-axonal compartments.

Diffusion weighted magnetic resonance imaging (DW-MRI) is a powerful imaging technique that can probe the complex structure of the body, revealing structural trends which exist at scales far below the voxel resolution. Tractography utilises the information derived from DW-MRI to examine the structure of white matter. Using information derived from DW-MRI, tractography can estimate connectivity between distinct, functional cortical and sub-cortical regions of grey matter. Understanding how seperate functional regions of the brain are connected as part of a network is key to understanding how the brain works. Tractography has been used to deliniate many known white matter structures and has also revealed structures not fully understood from anatomy due to limitations of histological examination. However, there still remain many shortcomings of tractography, many anatomical features for which tractography algorithms are known to fail, which leads to discrepancies between known anatomy and tractography results. With the aim of approaching a complete picture of the human connectome via tractography, we seek to address the shortcomings in current tractography techniques by exploiting new advances in modelling techniques used in DW-MRI, which provide more accurate representation of underlying white matter anatomy. This thesis introduces a methodology for fully utilising new tissue models in DWMRI to improve tractography. It is known from histology that there are regions of white matter where fibres disperse or curve rapidly at length scales below the DW-MRI voxel resolution. One area where dispersion is particularly prominent is the corona radiata. New DW-MRI models capture dispersion utilising specialised parametric probability distributions. We present novel tractography algorithms utilising these parametric models of dispersion in tractography to improve connectivity estimation in areas of dispersing fibres. We first present an algorithm utilising the the new parametric models of dispersion for tractography in a simple Bayesian framework. We then present an extension to this algorithm which introduces a framework to pool neighbourhood information from multiple voxels in the neighbournhood surrounding the tract in order to better estimate connectivity, introducing the new concept of the neighbourhood-informed orientation distribution function (NI-ODF). Specifically, using neighbourhood exploration we address the ambiguity arising in ’fanning polarity’. In regions of dispersing fibres, the antipodal symmetry inherent in DW-MRI makes it impossible to resolve the polarity of a dispersing fibre configuration from a local voxel-wise model in isolation, by pooling information from neighbouring voxels, we show that this issue can be addressed. We evaluate the newly proposed tractography methods using synthetic phantoms simulating canonical fibre configurations and validate the ability to effectively navigate regions of dispersing fibres and resolve fanning polarity. We then validate that the algorithms perform effectively in real in vivo data, using DW-MRI data from 5 healthy subjects. We show that by utilising models of dispersion, we recover a wider range of connectivity compared to other standard algorithms when tracking through an area of the brain known to have significant white fibre dispersion - the corona radiata. We then examine the impact of the new algorithm on global connectivity estimates in the brain. We find that whole brain connectivity networks derived using the new tractography method feature strong connectivity between frontal lobe regions. This is in contrast to networks derived using competing tractography methods which do not account for sub-voxel fibre dispersion. We also compare thalamo-cortical connectivity estimated using the newly proposed tractography method and compare with a compteing tractography method, finding that the recovered connectivity profiles are largely similar, with some differences in thalamo-cortical connections to regions of the frontal lobe. The results suggest that fibre dispersion is an important structural feature to model in the basis of a tractography algorithm, as it has a strong effect on connectivity estimation.

In the past three decades, spintronic devices have played an important technological role. Half-metallic alloys have drawn much attention due to their special properties and promised spintronic applications. This dissertation describes some theoretical techniques used in first-principal calculations of alloys that may be useful for spintronic device applications with an emphasis on half-metallic ferromagnets. I consider three types of simple spintronic materials using a wide range of theoretical techniques. They are (a) transition metal based half-Heusler alloys, like CrMnSb, where the ordering of the two transition metal elements within the unit cell can cause the material to be ferromagnetic semiconductors or semiconductors with zero net magnetic moment, (b) half-Heusler alloys involving Li, like LiMnSi, where the Li stabilizes the structure and increases the magnetic moment of zinc blende half-metals by one Bohr magneton per formula unit, and (c) zinc blende alloys, like CrAs, where many-body techniques improve the fundamental gap by considering the physical effects of the local field. Also, I provide a survey of the theoretical models and numerical methods used to treat the above systems.

Despite its indisputable successes, the Standard Model of particle physics (SM) is widely considered to be an effective low-energy approximation to an underlying theory that describes physics at higher energy scales. While there are many candidates for such a theory, nearly all of them predict the existence of additional particles beyond those of the Standard Model. In this work, we present three analyses aimed at discovering new particles at current and future particle colliders. The first two analyses are designed to probe extended scalar sectors, which often arise in theories beyond the Standard Model (BSM). The structure of these extended scalar sectors can be described by a physically well-motivated class of models, known collectively as Two- Higgs Doublet Models (2HDMs). The scalar mass spectrum of 2HDMs is comprised of two CP-even states h and H, a CP-odd state A, and a pair of charged states H± . Traditional searches for these states at particle colliders focus on finding them via their decays to SM particles. However, there are compelling scenarios in which these heavy scalars decay through exotic modes to non-SM final states. In certain regions of parameter space, these exotic modes can even dominate the conven- tional decay modes to SM final states, and thus provide a complementary avenue for discovering new Higgs bosons. The first analysis presented aims to discover charged Higgs bosons H± via top decay at the LHC. We find that the exotic decay modes outperform the conventional decay modes for regions of parameter space with low values of the 2HDM parameter tan β. The second analysis aims to systematically cover all the exotic decay scenarios that are consistent with theoretical and experimental con- straints, at both the 14 TeV LHC and a future 100 TeV hadron collider. We find that the preliminary results are promising - we are able to ex- clude a large swathe of 2HDM parameter space, up to scalar masses of 3.5 TeV, for a wide range of values of tan β, at a 100 TeV collider. In addition to these two analyses, we also present a third, aimed at discovering pair produced higgsinos that decay to binos at a 100 TeV collider. Higgsinos and binos are new fermion states that arise in the Minimal Supersymmetric Standard Model (MSSM). This heavily- studied model is the minimal phenomenologically viable incorporation of supersymmetry - a symmetry that connects fermions and bosons - into the Standard Model. In the scenario we consider, the bino is the lightest supersymmetric partner, which makes it a good candidate for dark matter. Using razor variables and boosted decision trees, we are able to exclude Higgsinos up to 1.8 TeV for binos up to 1.3 TeV.

After giving a description of the basic physical phenomena to be modelled, we begin by formulating a sharp-interface free-boundary model for the destruction of superconductivity by an applied magnetic field, under isothermal and anisothermal conditions, which takes the form of a vectorial Stefan model similar to the classical scalar Stefan model of solid/liquid phase transitions and identical in certain two-dimensional situations. This model is found sometimes to have instabilities similar to those of the classical Stefan model. We then describe the Ginzburg-Landau theory of superconductivity, in which the sharp interface is `smoothed out' by the introduction of an order parameter, representing the number density of superconducting electrons. By performing a formal asymptotic analysis of this model as various parameters in it tend to zero we find that the leading order solution does indeed satisfy the vectorial Stefan model. However, at the next order we find the emergence of terms analogous to those of `surface tension' and `kinetic undercooling' in the scalar Stefan model. Moreover, the `surface energy' of a normal/superconducting interface is found to take both positive and negative values, defining Type I and Type II superconductors respectively. We discuss the response of superconductors to external influences by considering the nucleation of superconductivity with decreasing magnetic field and with decreasing temperature respectively, and find there to be a pitchfork bifurcation to a superconducting state which is subcritical for Type I superconductors and supercritical for Type II superconductors. We also examine the effects of boundaries on the nucleation field, and describe in more detail the nature of the superconducting solution in Type II superconductors - the so-called `mixed state'. Finally, we present some open questions concerning both the modelling and analysis of superconductors.