Дисертації з теми "QMC model"

In the vast realm of inorganic materials, the Cu2+-containing cuprates form one of the richest classes. Due to the combined effect of crystal-field, covalency and strong correlations, all undoped cuprates are magnetic insulators with well-localized spins S=1/2, whereas the charge and orbital degrees of freedom are frozen out. The combination of the spin-only nature of their magnetism with the unique structural diversity renders cuprates as excellent model systems. The experimental studies, boosted by the discovery of high-temperature superconductivity in doped La2CuO4, revealed a fascinating variety of magnetic behaviors observed in cuprates. A digest of prominent examples should include the spin-Peierls transition in CuGeO3, the Bose-Einstein condensation of magnons in BaCuSi2O6, and the quantum critical behavior of Li2ZrCuO4. The magnetism of cuprates originates from short-range (typically, well below 1 nm) exchange interactions between pairs of spins Si and Sj, localized on Cu atoms i and j. Especially in low-dimensional compounds, these interactions are strongly anisotropic: even for similar interatomic distances |Rij|, the respective magnetic couplings Jij can vary by several orders of magnitude. On the other hand, there is an empirical evidence for the isotropic nature of this interaction in the spin space: different components of Si are coupled equally strong. Thus, the magnetism of cuprates is mostly described by a Heisenberg model, comprised of Jij(Si*Sj) terms. Although the applicability of this approach to cuprates is settled, the model parameters Jij are specific to a certain material, or more precisely, to a particular arrangement of the constituent atoms, i.e. the crystal structure. Typically, among the infinite number of Jij terms, only several are physically relevant. These leading exchange couplings constitute the (minimal) microscopic magnetic model. Already at the early stages of real material studies, it became gradually evident that the assignment of model parameters is a highly nontrivial task. In general, the problem can be solved experimentally, using elaborate measurements, such as inelastic neutron scattering on large single crystals, yielding the magnetic excitation spectrum. The measured dispersion is fitted using theoretical models, and in this way, the model parameters are refined. Despite excellent accuracy of this method, the measurements require high-quality samples and can be carried out only at special large-scale facilities. Therefore, less demanding (especially, regarding the sample requirements), yet reliable and accurate procedures are desirable. An alternative way to conjecture a magnetic model is the empirical approach, which typically relies on the Goodenough-Kanamori rules. This approach links the magnetic exchange couplings to the relevant structural parameters, such as bond angles. Despite the unbeatable performance of this approach, it is not universally applicable. Moreover, in certain cases the resulting tentative models are erroneous. The recent developments of computational facilities and techniques, especially for strongly correlated systems, turned density-functional theory (DFT) band structure calculations into an appealing alternative, complementary to the experiment. At present, the state-of-the-art computational methods yield accurate numerical estimates for the leading microscopic exchange couplings Jij (error bars typically do not exceed 10-15%). Although this computational approach is often regarded as ab initio, the actual procedure is not parameter-free. Moreover, the numerical results are dependent on the parameterization of the exchange and correlation potential, the type of the double-counting correction, the Hubbard repulsion U etc., thus an accurate choice of these crucial parameters is a prerequisite. In this work, the optimal parameters for cuprates are carefully evaluated based on extensive band structure calculations and subsequent model simulations. Considering the diversity of crystal structures, and consequently, magnetic behaviors, the evaluation of a microscopic model should be carried out in a systematic way. To this end, a multi-step computational approach is developed. The starting point of this procedure is a consideration of the experimental structural data, used as an input for DFT calculations. Next, a minimal DFT-based microscopic magnetic model is evaluated. This part of the study comprises band structure calculations, the analysis of the relevant bands, supercell calculations, and finally, the evaluation of a microscopic magnetic model. The ground state and the magnetic excitation spectrum of the evaluated model are analyzed using various simulation techniques, such as quantum Monte Carlo, exact diagonalization and density-matrix renormalization groups, while the choice of a particular technique is governed by the dimensionality of the model, and the presence or absence of magnetic frustration. To illustrate the performance of the approach and tune the free parameters, the computational scheme is applied to cuprates featuring rather simple, yet diverse magnetic behaviors: spin chains in CuSe2O5, [NO]Cu(NO3)3, and CaCu2(SeO3)2Cl2; quasi-two-dimensional lattices with dimer-like couplings in alpha-Cu2P2O7 and CdCu2(BO3)2, as well as the 3D magnetic model with pronounced 1D correlations in Cu6Si6O18*6H2O. Finally, the approach is applied to spin liquid candidates --- intricate materials featuring kagome-lattice arrangement of the constituent spins. Based on the DFT calculations, microscopic magnetic models are evaluated for herbertsmithite Cu3(Zn0.85Cu0.15)(OH)6Cl2, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, as well as for volborthite Cu3[V2O7](OH)2*2H2O. The results of the DFT calculations and model simulations are compared to and challenged with the available experimental data. The advantages of the developed approach should be briefly discussed. First, it allows to distinguish between different microscopic models that yield similar macroscopic behavior. One of the most remarkable example is volborthite Cu3[V2O7](OH)2*2H2O, initially described as an anisotropic kagome lattice. The DFT calculations reveal that this compound features strongly coupled frustrated spin chains, thus a completely different type of magnetic frustration is realized. Second, the developed approach is capable of providing accurate estimates for the leading magnetic couplings, and consequently, reliably parameterize the microscopic Hamiltonian. Dioptase Cu6Si6O18*6H2O is an instructive example showing that the microscopic theoretical approach eliminates possible ambiguity and reliably yields the correct parameterization. Third, DFT calculations yield even better accuracy for the ratios of magnetic exchange couplings. This holds also for small interchain or interplane couplings that can be substantially smaller than the leading exchange. Hence, band structure calculations provide a unique possibility to address the interchain or interplane coupling regime, essential for the magnetic ground state, but hardly perceptible in the experiment due to the different energy scales. Finally, an important advantage specific to magnetically frustrated systems should be mentioned. Numerous theoretical and numerical studies evidence that low-dimensionality and frustration effects are typically entwined, and their disentanglement in the experiment is at best challenging. In contrast, the computational procedure allows to distinguish between these two effects, as demonstrated by studying the long-range magnetic ordering transition in quasi-1D spin chain systems. The computational approach presented in the thesis is a powerful tool that can be directly applied to numerous S=1/2 Heisenberg materials. Moreover, with minor modifications, it can be largely extended to other metallates with higher value of spin. Besides the excellent performance of the computational approach, its relevance should be underscored: for all the systems investigated in this work, the DFT-based studies not only reproduced the experimental data, but instead delivered new valuable information on the magnetic properties for each particular compound. Beyond any doubt, further computational studies will yield new surprising results for known as well as for new, yet unexplored compounds. Such "surprising" outcomes can involve the ferromagnetic nature of the couplings that were previously considered antiferromagnetic, unexpected long-range couplings, or the subtle balance of antiferromagnetic and ferromagnetic contributions that "switches off" the respective magnetic exchange. In this way, dozens of potentially interesting systems can acquire quantitative microscopic magnetic models. The results of this work evidence that elaborate experimental methods and the DFT-based modeling are of comparable reliability and complement each other. In this way, the advantageous combination of theory and experiment can largely advance the research in the field of low-dimensional quantum magnetism. For practical applications, the excellent predictive power of the computational approach can largely alleviate designing materials with specific properties.

Ce travail de thèse a été réalisé, dans le cadre de la convention CIFRE 1538/2010, au sein d'adixen Vacuum Products (aVP) à Annecy (France). Il a été en partie financé par le projet S.P.A.M. (Surface Physics for Advanced Manufacturing). Il s'agit d'un projet ITN financé par le programme Pierre et Marie Curie de la Communauté Européenne rassemblant des partenaires universitaires et industriels dont aVP. L'objectif de ce programme était de contribuer à l'étude et au développement de la lithographie et en particulier la lithographie à ultraviolet extrême (EUVL). Ce travail porte sur la problématique de la contamination moléculaire dans l'industrie des semi-conducteurs ainsi que les besoins de maitrise de contamination pour la photolithographie EUVL. Pour ce faire, des modèles mathématiques de sorption ont été recherchés, testés et validés à l'aide d'une microbalance à quartz (QCM). Cette technique, possédant une très haute sensibilité (au niveau du ng), permet d'étudier les phénomènes de sorption relatifs à tout matériau déposable sur un cristal de quartz mis au contact de différents gaz dont la pression partielle est maitrisée. Par conséquent, le protocole détaillé dans cette thèse peut être utilisé pour d'autres types d'expériences dans toute discipline nécessitant une telle précision. Le déroulement de notre plan d'expérience comprend deux types de matériaux naturellement différents : un polymère (PCBA) d'une part et deux substrats métalliques (SS AISI 304 et CuC1) d'autre part pour lesquels le transfert de masse n'intervient pas de la même manière. Les gaz d'étude ont été sélectionnés pour leur intérêt dans l'industrie des semi-conducteurs (vapeur d'eau, HF). Le résultat de l'interaction des gaz d'étude avec les substrats ciblés est suivi en direct par la QCM, ce qui permet non seulement de valider et/ou améliorer les modèles mathématiques déjà disponibles dans la bibliographie mais aussi de les ajuster aux données obtenues expérimentalement. Nous pouvons ainsi non seulement prévoir le comportement des contaminants à l'équilibre (isothermes) et à l'état transitoire mais aussi réaliser des estimations de sorption à des températures autres que celles retenues pour notre plan d'expérience
This thesis was carried out within the framework of the CIFRE 1538/2010 convention at adixen Vacuum Products (aVP) in Annecy (France). It is has been partly funded by the ITN project SPAM (Surface Physics for Advanced Manufacturing). SPAM is an ITN project funded by the Pierre and Marie Curie program of the European Community bringing together academic institutions and industrial partners including aVP. The objective of this program was to contribute to the study and development of lithography and extreme ultraviolet lithography (EUVL). This work deals with the issues caused by the airborne molecular contamination (AMC) in the semiconductor industry and their control needs in EUVL and the current photolithography. In order to tackle the problem, sorption mathematical models have been investigated and validated using a quartz crystal microbalance (QCM). This technique, which confers a high sensitivity (ng level), allows the study of the sorption phenomena related to any deposable material onto a quartz crystal in contact with different gases whose concentrations are accurately controlled. Consequently, the protocol detailed in this thesis may be used for other types of experiments in any discipline requiring such precision. The conduct of our experimental plan includes two types of naturally different materials: a polymer (PCBA) on the one hand and two metallic substrates (stainless steel AISI 304 and CuC1) on the other hand, for which the matter transfer does not occur in the same manner. Studied gases were selected for their interest in the semiconductor industry (water vapor, HF). The resulting interaction between the studied gases and the targeted substrates is continuously followed by the QCM, which allows not only to validate the mathematical models already proposed by the literature but also to fit the experimentally obtained data. This enables us not only to predict the behavior of the AMC at equilibrium (isotherms) and the transient state but also to provide sorption estimations at temperatures other than those specified in our experimental plan

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Mobile Social Networks (MSNs) are social structures in which members relate in groups and interaction is accomplished through information and communication technologies using portable devices and wireless network technologies. Healthcare is one among the many possible areas of RSMs application. The MobileHealthNet project, developed in partnership by UFMA and PUC-Rio, aims to develop a middleware that allows access to social networks and facilitate the development of collaborative services targeting the health domain, the exchange of experiences and communication between patients and health professionals, as well as a better management of health resources by government agencies. An important aspect in the development of the MobileHealthNet middleware is the infrastructure necessary for the gathering, distribution and processing of context data. In this master thesis we propose a software infrastructure incorporated to the MobileHealthNet middleware that allows the specification, acquisition, validation and distribution of context data, considering quality requirements, making them available to context-aware applications. The distribution of context data is based on a data-centric the publish/subscribe model, using the OMG-DDS specification.
Redes Sociais Móveis (RSMs) são estruturas sociais em que seus membros relacionam-se em grupos e a interação é realizada através de tecnologias de informação e comunicação utilizando dispositivos portáteis com acesso a tecnologias de rede sem fio. Entre os muitos domínios de aplicação das RSMs, temos a área da saúde. O projeto MobileHealthNet, desenvolvido em parceria pela UFMA e PUC-Rio, tem por objetivo desenvolver um middleware que permita o acesso às redes sociais e facilite o desenvolvimento de serviços colaborativos para o setor da saúde, a troca de experiências e a comunicação entre pacientes e profissionais da saúde, além de uma melhor gestão dos recursos da saúde por órgãos governamentais. Um aspecto importante no desenvolvimento do middleware proposto pelo projeto MobileHealthNet é a infraestrutura necessária para a coleta, distribuição e processamento de dados de contexto. Neste trabalho de mestrado é proposta uma infraestrutura de software incorporada ao middleware MobileHealthNet que permite a especificação, obtenção, validação e distribuição de dados de contexto, considerando requisitos de qualidade, tornando-os disponíveis a aplicações sensíveis ao contexto. A distribuição dos dados de contexto é baseado no modelo publish/subscribe centrado em dados, utilizando-se a especificação OMG-DDS.

Characterization of edge tokamak plasma instabilities by measuring emergent phenomena within a range of frequencies above the ion cyclotron frequency have been explored in two ways: using the inter-event waiting times of Edge Localized Modes (ELMs) occurrences in measured time series of JET plasmas and by performing 2D/3D simulations of filamentary structures dynamics using a hybrid model plasma description, i.e. kinetic ion particles and massless charge neutralizing electron fluid. The analysis of ELMs time series using characteristic emission lines Da of JET tokamak in otherwise similar plasmas was performed with only a minimal number of drivers such as the gas puffing rate. They have shown a key role in changing the underlying system mode cycle where a threshold value revealed its transition from single harmonic behaviour to a transitioning phase into a total lost of the state and born of a higher frequency resonant mode. Hybrid simulations of blobs/filaments are performed in 2D/3D to observe the kinetic evolution of these plasma structures over several ion gyroperiods. Novel 3D simulations represent the first kinetic simulations of these structures along the parallel direction using a kinetic description. We have investigated the evolution and the internal density currents which provide insight of the effects of finite Larmor radius in the blobs dynamics and evolution.

The subject of this thesis is the study of mass transport using experimental and theoretical techniques, specifically the investigation of transport through phospholipid barriers which serve as a model for biological systems. To this end, experimental monolayer and bilayer membranes are produced, and the permeation of gas and weak acid molecules is quantitatively measured. Potentiostatic measurement of oxygen permeation in monolayers formed using two varieties of phospholipid at the air/water interface, under varying levels of compression (and hence surface pressure), was performed using ultramicroelectrodes, followed by finite element simulations to parameterise the approach curves produced and hence determine the first-order rate constant for the permeation process. As expected, the rate of permeation decreases significantly as the monolayers are compressed, with a simple surface pressure model proving insufficient to describe these trends. Molecular dynamics simulations are employed to investigate the excess free energy barriers for permeating oxygen molecules using umbrella sampling and the weighted histogram analysis method. The results are shown to be unreliable in their description of the permeation process. Experimental bilayers are formed from lecithin, pure POPC, and a mixture of POPC and cholesterol in a supporting electrolyte solution. The permeation of a homologous series of protonated weak acids is studied using laser scanning confocal microscopy to selectively excite and detect the state of fluorescein, a dye with pH-sensitive fluorescence intensity. These experimental results are again parameterised with finite element models, and the trend of decreasing permeation coefficient as the weak acid molecules increase in size is reported. This is in direct contradiction to the established Overton’s Rule. Molecular dynamics simulations of the permeation of three of the weak acids in a POPC bilayer is performed to determine excess free energy profiles using umbrella sampling, combined with the weighted histogram analysis method. Serious flaws are found in the method and execution of this aspect of the work.

This thesis is devoted to the phenomenological analysis at the large hadron collider (LHC), as well at a future electron positron collider, of the 4 dimensional (4D) composite Higgs model (4DCHM), a compelling beyond the standard model scenario where the Higgs state arises as a pseudo Nambu Goldstone boson. The motivations and the main characteristics of the model are summarised and then an analysis of the gauge and Higgs sectors of the 4DCHM is performed. Finally we propose a general framework for the analysis of models with an extended quark sector that we have applied to a simplified composite Higgs scenario.

The recent discovery of the Higgs boson by the ATLAS and CMS exper- iments and the subsequent measurements of it properties are the latest vindications of the Standard Model of particle physics. The SM has a number of well known flaws, and the continuing dearth of Beyond the Standard Model signatures from experiment has led to investigations into whether the SM is valid up to very high scales. The motivation for much of this work comes from the quartic Higgs coupling λ and its β function, which run to an extremely small values at high scales. These may be hints of new UV dynamics, in particular the Multiple Point Principle which posits the existence of a second degenerate minimum in the effective potential at the Planck scale, and Asymptotic Safety, where the dimensionless couplings of the potential run towards an interacting UV fixed point. In this work we will investi- gate the possibility for similar high scale boundary conditions in extensions of the Standard Model. Specifically, we look at the Real Singlet model, the Complex Sin- glet model, the Type-II Two Higgs Doublet Model, and the Inert Doublet Model. We will apply the relevant theoretical constraints to the parameter space of theses models, as well as experimental constraints such as those from ATLAS, CMS, LEP, the Tevatron, WMAP, Planck and LUX. Points that pass these constraints will also be investigated for their validity under a number of high scale boundary conditions on its scalar sector, and the valid parameter space will be checked for signatures in the mass spectrum that can be probed by current and future collider experiments.

Due to the escalating challenge of antibiotic resistance in bacteria over the past several decades, interest in the identification and development of antibiotic alternatives has intensified. Antimicrobial peptides (AMPs), which serve as part of the innate immune systems of most eukaryotic organisms, are being researched extensively as potential alternatives. However, the mechanism behind their bactericidal capabilities is not well understood. Previous studies have suggested that AMPs may first attach to the cell membranes, leading to pore formation caused by peptide insertion, lipid removal in the form of peptide-lipid aggregates, or a combination of both mechanisms. In addition to the lack of mechanistic knowledge, a significant hurdle in AMP-based drug development is their potential cytotoxicity to mammalian cells. Understanding AMP interactions with eukaryotic model membranes would allow therapeutics to be tailored for preferential action toward specific classes of bacterial membranes. In this study, we developed novel methods of quartz crystal microbalance with dissipation monitoring (QCM-D) data analysis to determine the fundamental mechanism of action between eukaryotic and bacterial membrane mimics and select membrane-active AMPs. A new technique for creating supported membranes composed entirely of anionic lipids was developed to model Gram-positive bacterial membranes. Atomic force microscopy (AFM) imaging was also used to capture the progression of AMP-induced changes in supported lipid membranes over time and to validate our method of QCM-D analysis. QCM-D and AFM were used to investigate the molecular-scale interactions of four peptides, alamethicin, chrysophsin-3, sheep myeloid antimicrobial peptide (SMAP-29) and indolicidin, with a supported zwitterionic membrane, which served as a model for eukaryotic cell membranes. Since established methods of QCM-D analysis were not sufficient to provide information about these interaction mechanisms, we developed a novel method of using QCM-D overtones to probe molecular events occurring within supported lipid membranes. Also, most previous studies that have used AFM imaging to investigate AMP-membrane interactions have been inconclusive due to AFM limitations and poor image quality. We were able to capture high-resolution AFM images that clearly show the progression of AMP-induced defects in the membrane. Each AMP produced a unique QCM-D signature that clearly distinguished their mechanism of action and provided information on peptide addition to and lipid removal from the membrane. Alamethicin, an alpha-helical peptide, predominantly demonstrated a pore formation mechanism. Chrysophsin-3 and SMAP-29, which are also alpha-helical peptides of varied lengths, inserted into the membrane and adsorbed to the membrane surface. Indolicidin, a shorter peptide that forms a folded, boat-shaped structure, was shown to adsorb and partially insert into the membrane. An investigation of rates at which the peptide actions were initiated revealed that the highest initial interaction rate was demonstrated by SMAP-29, the most cationic peptide in this study. The mechanistic variations in peptide action were related to their fundamental structural properties including length, net charge, hydrophobicity, hydrophobic moment, accessible surface area and the probability of alpha-helical secondary structures. Due to the charges associated with anionic lipids, previous studies have not been successful in forming consistent anionic supported lipid membranes, which were required to mimic Gram-positive bacterial membranes. We developed a new protocol for forming anionic supported lipid membranes and supported vesicle films using a vesicle fusion process. Chrysophsin-3 was shown to favor insertion into the anionic lipid bilayer and did not adsorb to the surface as it did with zwitterionic membranes. When introduced to supported anionic vesicle films, chrysophsin-3 caused some vesicles to rupture, likely through lipid membrane disruption. This study demonstrated that molecular-level interactions between antimicrobial peptides and model cell membranes are largely determined by peptide structure, peptide concentration, and membrane lipid composition. Novel techniques for analyzing QCM-D overtone data were also developed, which could enable the extraction of more molecular orientation and interaction dynamics information from other QCM-D studies. A new method of forming supported anionic membranes was also designed, which may be used to further investigate the behavior of bacterial membranes in future studies. Insight into AMP-membrane interactions and development of AMP structure-activity relationships will facilitate the selection and design of more efficient AMPs for use in therapeutics that could impact the lives of millions of people per year who are threatened by antibiotic-resistant organisms.

The Standard Model of particle physics successfully describes the fundamental particles and their interactions, but suffers from a few critical limitations which raise the intriguing possibility of new physics beyond it. My dissertation focuses on the study of the phenomenologically important quantities in the Standard Model, particularly, involving the high precision first principle calculations in the low-energy ($\sim1$GeV) regime of Quantum Chromodynamics (QCD), the $SU(3)$ component of the Standard Model. In this regime, since the QCD coupling becomes strong and the quarks and the gluons are confined to bound states called hadrons, a perturbative expansion in the coupling constant is not possible. However, the introduction of a four-dimensional Euclidean space-time lattice allows for an ab-initio treatment of QCD and provides a powerful tool - lattice QCD to study the low energy dynamics of the hadrons using numerical simulations. I have used existing methods of lattice QCD and developed new methods to study the pseudoscalar and the vector mesons (quark-antiquark hadrons) made of valence light (up and down), strange and charm quarks which are important final states in a number of decay processes that are studied in experiments and are sensitive to new physics. From the large time exponential behaviour of the meson correlators generated on lattice, I have extracted the masses and the decay constants (annihilation amplitude) of the mesons. My results include the most accurate lattice QCD calculation to date of the properties of the vector mesons $\phi$ and $\rho$. In lattice QCD calculations, the systematic uncertainty coming from the renormalisation constants relating the lattice results to the continuum results can be crucial and therefore has been determined precisely. Subsequently, we realised that our methods can also be extended to the calculation of the hadronic vacuum polarisation (HVP) contribution to the anomalous magnetic moment of the muon, $a_\mu$. The anomalous magnetic moment of the muon, shows a large discrepancy ($\sim3\sigma$) between theoretical and experimental results, putting the Standard Model to one of its most stringent tests. To complement the plans for a four-fold improvement in its experimental uncertainty, this project aims to improve the dominant contributions in the theoretical uncertainty coming from the hadronic vacuum polarisation to $\sim1\%$. I with my collaborators have developed a new lattice QCD method to calculate the HVP, making a significant progress over previous calculations by achieving an unprecedented precision ($\sim2\%$) in the HVP. The quark flavour sector of the Standard Model is also a fertile ground to test any new physics effect through the Unitarity test of the Cabbibo-Kobayashi-Maskawa (CKM) matrix. Therefore, my aim was to perform a lattice QCD calculation of the scalar and the vector form factors (over a large $q^2$ region including $q^2=0$) associated with the $D\rightarrow Kl\nu$ semi-leptonic decay. The central CKM matrix element, $V_{cs}$ in the Standard Model, is then calculated by comparing the lattice QCD results for the form factors and the experimental decay rate. For my research I have used publicly avalilable MILC HISQ configurations with dynamical up, down, strange and charm quarks. For most of my calculations I have used HISQ valence quarks except for the renormalisation of currents where for the comparison between different lattice formalisms I have also used the clover valence quarks.

In recent years, Grand Unified Theories (GUTs) constructed from F-theory have been extensively studied due to the substantial scope for model building and phenomenology which they provide. This thesis will motivate and introduce the basic tools required for model building in the setting of local F-theory. Starting with GUT groups of E6, SO(10) and SU(5), a group theoretic dictionary between the three types of theory is formulated, which provides considerable insight into how to build a realistic model. The spectral cover formalism is then applied to each case, enabling the possible low energy spectra after flux breaking of the GUT group to be found. Using these results an E6 based model is constructed that demonstrates, for the first time, that it is possible to construct a phenomenologically viable model which leads to the MSSM at low energies. In addition to the MSSM model, the E6 starting point is also used to build F-theory models in which the low energy supersymmetric theory contains the particle content of three 27 dimensional representations of the underlying E6 gauge group, with the possibility of a gauged U(1) group surviving down to the TeV scale. The models with TeV scale exotics initially appear to be inconsistent due to a splitting of the gauge couplings at the unification scale which is too large, and incompatible with the formalism. However, in E6 models with flux breaking, there are bulk exotics coming from the 78 dimensional adjoint representation which are always present in the spectrum, and it turns out that a set of these exotics provide a natural way to achieve gauge coupling unification at the one-loop level, even for models with TeV exotics. This motivates a detailed study of bulk exotics, where specific topological formulae determining the multiplicities of bulk states are investigated, and the constraints imposed by these relations applied to the spectra of the models previously studied. In particular, bulk exotics are relevant to the almost miraculous restoration of gauge coupling unification in the case of the models with TeV scale exotics. The consistent local F-theory models with low energy exotics have distinctive characteristics when compared with other, similar models, and so provide potential opportunities to be tested at the LHC.

This work investigates extensions to the Standard Model that are inspired by supersymmetric models with an E6 gauge group. The models are non-minimal supersymmetric theories which keep the Higgs mass stable against the quantum corrections from higher energy physics, but do not contain the mu-problem or little hierarchy problem of the Minimal Supersymmetric Standard Model (MSSM). Also, unlike conventional Grand Unified Theories, the E6 inspired models do not contain any doublet-triplet splitting and the Minimal E6 Supersymmetric Model (ME6SSM) only contains complete E6 multiplets at low energies. A particularly exciting feature of the ME6SSM is the prediction of gauge coupling unification at the Planck scale rather than the conventional GUT scale, hinting at a potential unification of the Standard Model forces with quantum gravity. If extended with a discrete non-Abelian family symmetry, the E6 inspired models can explain the masses and mixings of the quarks and leptons that are observed in particle experiments. These are not understood in the Standard Model since they are free parameters, creating a flavour problem for the theory. Extending the Standard Model or MSSM with a family symmetry oers an attractive resolution to the flavour problem, and the recent discovery of neutrino oscillations, which indicate a high-level of symmetry in the lepton mixings, has led to a renewed interest in these models. However, explaining why the Higgs mass is small is essential in these models since it sets the scale for the quark and lepton masses. This motivates the synthesis of a family symmetry with the E6 inspired supersymmetric models, which resolves a number of problems facing the Standard Model including the hierarchy problem and the avour problem. A particular success of the resulting models is their ability to suppress proton decay and favour changing neutral currents, from supersymmetry and extended Higgs sectors, using the same family symmetry that is responsible for a tri-bi-maximal mixing of leptons.

We explore some applications of the Standard Model (SM) Effective Field Theory (EFT) as a tool with which to describe generic nonresonant new physics (NP) at hadron colliders. A global fit of the dimension-six Wilson Coefficients relevant to top quark production is presented, utilizing diverse experimental datasets from both the Large Hadron Collider (LHC) Runs I and II and the TeVatron, with current results in good agreement with the SM. Machinery is developed to systematically treat redundancies between higher-dimensional operators in the automated model-building and phenomenology toolkit FeynRules, and a general SMEFT model implementation for event generators detailed. We then investigate the importance of high momentum transfer final states in top pair production to the EFT fit, taking advantage of boosted reconstruction techniques. We find sensitivity is typically driven by fully resolved analyses in several benchmark scenarios for total integrated luminosity and experimental systematic uncertainties.

In this thesis I study the collider phenomenology of BSM physics at the LHC, concentrating on the Higgs boson and supersymmetery. The implications and effects on cross sections of the loss of unitarity in scattering processes involving multiple vector bosons and/or the Higgs, when the Higgs couplings to the W and the Z are non-SM, is studied using an effective Lagrangian. Subsequently methods to remove unwanted background from transversely polarised vector bosons are explored, which enable an estimation of the potential to measure the Higgs couplings to weak bosons in a model-independent way via vector boson fusion. MSSM effects on Higgs production and decay are also considered, concentrating on the effects due to light stops, sbottoms and staus. Amongst other things, we find that light 3rd generation squarks generally produce asymmetrical alteration in signal strengths of different production channels, generally causing μV BF μggF > 1. Finally we extend some ATLAS analyses in the low ∆m = m˜t − m˜x01 region, extending the excluded masses of light stops. This enables us to limit the maximum effects of light stops on the Higgs, and further limits the parameter space where the light stop scenario of electroweak baryogenesis is viable.

We look at models of neutrino mass and mixing which represent an important aspect of physics beyond the Standard Model (SM). We derive approximate analytic formulae for the neutrino mixing angles in general SD involving NLO and NNLO corrections. These expressions, which are given in terms of input see-saw parameters, provide a useful guide for unified model building. We then evaluate these formulae in the cases of CSD and PCSD for two numerical GUT inspired models in order to measure the effect of NLO and NNLO corrections. In addition to this, we analyse the effects of charged lepton corrections and Renormalisation Group (RG) running on neutrino mixing angles and various sum rules, in models where tri-bimaximal mixing is exactly achieved at high energy scale. We find the RG corrections to neutrino sum rules to be typically small for the case of hierarchical neutrinos. Another aspect of physics beyond the Standard Model concerns the search for viable four dimensional string models. We look at moduli stabilisation in the framework of four dimensional models arising from heterotic and type IIA string theories. The superpotentials in these models involve ux and non-perturbative terms. We consider a set of conditions which lead to moduli solutions for Minkowski minima of the scalar potential. Following this procedure, we correct models presented in the literature and uplift the at directions. We also study inflation in the framework of these models. We find that it is successfully achieved along the axionic directions of the moduli fields for values of the initial conditions within substantial regions of parameter space. A very interesting structure of the potential is obtained when considering the evolution of two axionic directions in one of the models in the presence of a gaugino condensate term. This structure, which involves the existence of multiple local minima surrounding the global one, represents a perfect background for realising in ation.

This thesis explores three classes of beyond-the-Standard Model (BSM) theories: Minimal Universal Extra Dimensions (MUED), the 4D Composite Higgs Model (4DCHM) and Technicolor. In particular, Higgs boson data from the Large Hadron Collider (LHC) is used to test the viability of these models and constrain their parameter spaces. It turns out that this provides a valuable constraint for MUED, requiring that the compactification scale R-1 of the theory be greater than 500 GeV. More direct searches for MUED are also considered, and the creation of a software implementation of MUED in CalcHEP is discussed. This implementation is used to determine that the tri-lepton final state is the most promising discovery signature due to the high lepton multiplicity in MUED and that the exclusion reach of MUED using this signature is up to R-1 = 1200 GeV with 20 fb-1 of data from the 8 TeV LHC. The 4DCHM is also analysed in light of the Higgs data. It is found that, once direct detection constraints are applied, the model is actually a slightly better fit to Higgs data than the Standard Model for most points in the 4DCHM parameter space considered. Finally, various Technicolor models are tested against Higgs data using a more sophisticated statistical analysis and it is found that most provide viable Higgs boson candidates with broadly Standard-Model like couplings.

This thesis concerns inferring core collapse supernova physics using gravitational waves. The mechanism through which the supernova is re-energised is not well understood and there are many theories of the physical processes behind the so called supernova mechanism. Gravitational waves provide an opportunity to see through to the core of a collapsing star. This thesis provides an algorithm that will analyse a detected gravitational waveform from a core collapse supernova and identify the supernova mechanism. This is achieved through the use of Bayesian model selection and a nested sampling algorithm. This Bayesian data analysis algorithm is called the Supernova Model Evidence Extractor (SMEE). SMEE is designed to classify detected gravitational waveforms from core-collapse supernovae and 3 different versions which employ different types of data have been developed. These 3 versions utilise time domain (which has been fast Fourier transformed into the frequency domain), power spectrum domain and spectrogram data and the success of each version is investigated. Firstly, results for a simplified idealised version of SMEE are discussed. In this scenario only a single gravitational wave detector is considered and the effect of the sky position of the source are ignored. Next, techniques which can be employed to improve SMEE are investigated. Finally, SMEE is tested using 3 gravitational wave detectors and the full effect of the time delay between detectors and the antenna response on each detector is included. As well as this, recoloured detector noise from the Science runs from both LIGO and Virgo are utilised here. This thesis demonstrates that each version of SMEE is successful and are able to infer the supernova mechanism for a galactic supernova. The spectrogram version of SMEE is deemed the most accurate and it is recommended that this technique should be further explored in the future.

We discuss existing free energy methods for use with investigation of solid-solid polymorphism. An alternative implementation for phase switch Monte Carlo is introduced which samples from two synchronised Markov chains exploring both polymorphs, using a set of generalised coordinates to transform between Markov chains. This is validated against the existing results for face-centred cubic (fcc) and hexagonal close-packed (hcp) hard sphere crystals. The extension to more complex crystals including flexibility and constraints is explored. This extension is applied to a hard sphere model of linear alkanes. A phase transition in density is accurately located between two polymorphs of n-butane with increasing density; this is suggested as a rigorous benchmark for free energy methods. We also demonstrate the importance of including anisotropic volume moves when simulating crystalline solids. Generalised coordinates for any fully flexible molecular system of soft particles are presented. These are used to investigate a coarse-grain model of cholesterol in regards to the polymorphic transition between two anhydrous cholesterol crystals. A phase transition in temperature is found and the limitations in the model are discussed.

Nous presentons l'etude de nouvelles donnees experimentales au + au a 150 et 400 a. Mev obtenues avec le detecteur fopi. Nous etudions principalement le flot, determine a partir de la methode de danielewicz sans reconstruction du plan de reaction et le pouvoir d'arret de la matiere en fonction de la charge des fragments et en fonction de la centralite des collisions. Nous comparons ensuite les donnees experimentales avec differentes versions du modele qmd afin d'etudier les effets de milieu nucleaire sur les sections efficaces et sur le potentiel n-n. La premiere version (gqmd) utilise le formalisme de matrice g pour calculer de maniere microscopique les sections efficaces et les potentiels. Cette version inclue donc naturellement les effets de milieu nucleaire. La seconde version (iqmd) utilise un potentiel de skyrme et un terme dependant de l'impulsion pour reproduire les effets de milieu. Le pouvoir d'arret est surrestime par les deux versions du modele. En ce qui concerne le flot, la dependance en impulsion est plus grande dans gqmd et permet de reproduire les evenements plus peripheriques. Par contre, le modele gqmd qui possede une equation d'etat soft manque de dependance en densite pour reproduire les evenements centraux. Cette comparaison montre donc qu'une equation d'etat hard est necessaire pour reproduire le flot dans les collisions centrales et qu'une grande dependance en impulsion permet de reproduire les collisions semi-centrales et peripheriques

Fine tuning in the Standard Model (SM) is the basis for a widespread expectation that the minimal model for electroweak symmetry breaking, with a single Higgs boson, is not realised in nature and that new physics, in addition to (or instead of) the Higgs, will be discovered at the Large Hadron Collider (LHC). However constraints on new physics indicate that many models which go beyond the SM (BSM) may also be fine tuned (although to a much lesser extent). To test this a reliable, quantitative measure of tuning is required. We review the measures of tuning used in the literature and propose an alternative measure. We apply this measure to several toy models and a constrained version of the Minimal Supersymmetric Standard Model. The Exceptional Supersymmetric Standard Model (E6SSM) is another BSM motivated by naturalness. As a supersymmetric theory it solves the SM hierarchy problem and by breaking a new gauged U(1) symmetry it also solves the μ-problem of the MSSM. We investigate the Renormalisation Group Evolution of the model and test for radiative electroweak symmetry breaking in two versions of the model with different high scale constraints. First we briefly look at scenarios with non-universal Higgs masses at the GUT scale and present a particle spectrum that could be observed at the LHC. Secondly we study the constrained E6SSM (CE6SSM), with universal scalar (m0), trilinear (A0) and gaugino (M) masses. We reveal a large volume of CE6SSM parameter space where the correct breakdown of the gauge symmetry can be achieved and all experimental constraints can be satisfied. We present benchmark points corresponding to different patterns of the particle spectrum. A general feature of the benchmark spectra is a light sector of SUSY particles consisting of a light gluino, two light neutralinos and a light chargino. Although the squarks, sleptons and Z′ boson are typically much heavier, the exotic color triplet charge 1/3 fermions as well as the lightest stop can be also relatively light leading to spectacular new physics signals at the LHC.

We have developed a precise beam dynamics model of the PSI Injector II, a high intensity separate-sector isochronous cyclotron operating at 2.2 mA current. A particle distribution with an intensity of 9.5 mA (DC) is injected into the central region and shaped by a sophisticated collimator system. This defines the initial condition for the subsequent formation of a round stationary bunch. The intensity limits are estimated based on the developed models, additionally supported by fitted scaling laws and measurements. In this research we consider two configurations: production and upgraded (adding two new cavities). The model is based on the OPAL (Object Oriented Parallel Accelerator Library) simulation code, a tool for charged-particle optics calculations in large accelerator structures and beam lines, including 3D space charge. Even though Injector II has been successfully operating for years, we do not know if the current production configuration is the best possible. Since we would like to extract as much current as possible with minimal losses, detailed simulations are needed to estimate those limits. This gives us possibility to look into the operation after the upgrade. This is the first attempt to model Injector II using powerful computing, allowing multi-particle space charge simulations. We have been able to perform more detailed analysis of the bunch parameters and halo development than any previous study. Also optimisation techniques enable better matching of the simulation set-up with Injector II parameters and measurements. We have found that the production configuration current scales to the power of four with the beam size, setting the limit to approximately 3 mA. Further analysis of the upgraded configuration suggests that intensities up to 5 mA could be produced with an adjusted collimation scheme.

Neutrino oscillation experiments discover that (left-handed) neutrinos have masses much less than charged leptons and quarks in the Standard Model. One solution to the light neutrino mass puzzle is the seesaw model where right-handed neutrinos are introduced with large Majorana masses. The heavy Majorana right-handed (RH) neutrinos lead to lepton number violation in the early universe. They decay into either leptons or anti-leptons via Yukawa couplings. The CP asymmetries of these decays result in lepton number asymmetry in the universe. The lepton number asymmetry can be converted into baryon number asymmetry via the electroweak sphaleron process. This mechanism explains the baryon asymmetry of universe problem and is called leptogenesis. However, one finds that in order to generated enough baryon number in the universe, the reheating temperature, which is required to be of order of the lightest right-handed neutrino mass, has to be higher than ∼ 10^9 GeV. The high reheating temperature would lead to the over-produced gravitinos in the universe, contrasting with the present observation. We investigate leptogenesis in the Exceptional Supersymmetric Standard Model. We find that the extra Yukawa couplings would enhance the CP asymmetries of the RH neutrino decay drastically. And the evolution of lepton/baryon asymmetries is described by Boltzmann Equations. Numerical calculation of the Boltzmann Equations shows that a correct amount of baryon number in the universe can be achieved when the lightest right-handed neutrino mass is ∼ 10^7 GeV, and then the gravitino-over-production problem is avoided.

In this work we consider nucleation in existing and novel lattice models of particles in solution, reviewing, testing and applying the modern methodology for free energy calculation and calculation of nucleation rates based on elements of classical nucleation, reaction rate and transition path theories. We introduce a multi-component lattice model where, at low temperatures, the solute phase can form three distinct solid structures, for which we accurately map the phase diagram, discussing the relevance of the model to the study of nucleation of polymorphic minerals. By analysing multi-dimensional free energy profiles, computed via a path sampling based Monte Carlo protocol, we demonstrate that solute precipitation in the developed model can proceed via nonclassical pathways, where the formation of nuclei of unstable solute phases is followed by their transformation into the thermodynamically preferred structure. Despite the existence of nonclassical nucleation pathways, we show that the conceptual framework of classical nucleation theory provides an adequate quantitative treatment of the nucleation process in our model over a broad range of parameter space.

The work in this thesis shows that it is possible to design a diffusion cell which will allow access to the flux and lag time of a permeant without the need for invasive sampling and that this novel cell is both sensitive and reproducible. It was also shown that the cell could be used in conjunction with both simple model membranes and more complex biological membranes, namely the epidermis. From the data achieved from the cell it was possible to derive a series of equations which allowed access to thermodynamic parameters such as ?H, ?G and ?S. An extension of this calculational approach revealed that manipulation of the van’t Hoff isochore, under the condition where enthalpy is constant over the temperature range, it should be possible to calculate the partition coefficient. Ultimately these parameters can be used in the description of structure activity relationships. The systems described in this thesis are of a complex biological nature consequently the returned data reflect this complexity. In order to utilise the data to their full potential some method for dealing with this complexity was sought. One approach widely discussed in the literature is that of chemometric analysis or soft modelling. Initial studies into the use of chemometric analysis proved positive for the data presented in this thesis, and suggested that formulation contributions from components with close absorbance maxima could be separated.

This research applies the capillary wave method (CWM) to quasi-2D systems in order to calculate the solid-liquid coexistence interfacial free energy (γ) of ice-Ic, ice-Ih and ice-0, with water, at 1 atm, within molecular dynamics simulations employing the coarse-grained monatomic water (mW) model. Investigations are performed to determine how the measured interfacial stiffness (~γ) is affected using various: i) order parameters, to distinguish between the solid and the liquid; ii) analysis discretisation, for interface profiling; iii) system thicknesses. The rationality that ice-I nucleation can be catalysed at strong supercooling within a shell of ice-0 is explored. It is found that at 215.2 K such nucleation could occur, forming an ice-0 shell of 3:3 Å thick around a core of ice-Ih. Free energy perturbation is also applied to the mW model using Monte Carlo simulations, in an attempt to increase the Gibbs free energy gap between ice-Ic and ice-Ih to more closely match values previously reported from experiments and ab initio calculations. However, the Gibbs free energy gap is only increased to 5.6 J mol⁻¹, at 240 K, before the ice-Ic and ice-Ih melting temperatures fall to below 240 K; failing to reach the expected value. This suggests that the mW model, despite its successes, does not capture the true mechanism behind the formation ice-Ic and ice-Ih stacking faults at all degrees of supercooling; the formation of which is rather an artefact of the model itself.

This thesis is based on work that investigates the fine tuning in low scale non-minimal supersymmetric models. We present a comparative and systematic study of the fine tuning in Higgs sectors in three scale-invariant NMSSM models: the first being the standard Z3 invariant NMSSM; the second is the NMSSM plus additional matter filling 3(5 + 5) representations of SU(5) and is called the NMSSM+; while the third model comprises 4(5 + 5) and is called the NMSSM++. Naively, one would expect the fine tuning in the plus-type models to be smaller than that in the NMSSM since the presence of extra matter relaxes the perturbativity bound on λ at the low scale. This, in turn, allows larger tree-level Higgs mass and smaller loop contribution from the stops. However we find that LHC limits on the masses of sparticles, especially the gluino mass, can play an indirect, but vital, role in controlling the fine tuning. In particular, working in a semi-constrained framework at the GUT scale, we find that the masses of third generation stops are always larger in the plus-type models than in the NMSSM without extra matter. This is an RGE effect which cannot be avoided, and as a consequence the fine tuning in the NMSSM+ (Δ ~ 200) is significantly larger than in the NMSSM (Δ ~ 100), with fine tuning in the NMSSM++ (Δ ~ 600) being significantly larger than in the NMSSM+. Moreover, supersymmetric unified models in which the Z’ couples to the Higgs doublets, as in the E6 class of models, have large fine tuning dominated by the experimental mass limit on the Z’. To illustrate this we investigate the degree of fine tuning throughout the parameter space of the Constrained Exceptional Supersymmetric Standard Model (cE6SSM) that is consistent with a Higgs mass mh ~ 125 GeV. Fixing tan β = 10, and taking specific values of the mass of the Z’ boson, with MZ’ ~ 2-4 TeV. We find that the minimum fine tuning set predominantly from the mass of Z’ and varies from ~200-400 as we vary MZ’ from~ 2-4 TeV. However, this is lower than the fine tuning in the constrained Minimal Supersymmetic Standard Model (cMSSM) of 0(1000), arising from the large stop masses required to achieve the Higgs mass. Finally, it was found that varying tan β below and above 10 does not correspond to lower fine tuning in the cE6SSM, nor does lowering the mass of the Z’ by lowering its associated coupling g’.

This work presents a large scale multifractal analysis of the electronic state in the vicinity of the localisation-delocalisation transition in the three-dimensional Anderson model of localisation using high-precision data and very large system sizes of up to L3 = 2403. The multifractal analysis is implemented using box- and system- size scaling of the generalized inverse participation ratios employing typical and ensemble averaging techniques. The statistical analysis in this study has shown that in the thermodynamic limit a proposed symmetry relation in the multifractal exponents is true for the 3D Anderson model in the orthogonal universality class. Better agreement with the symmetry is found when using system-size scaling with ensemble averaging in which a more complete picture of the multifractal spectrum f(α) is also obtained. A complete profile of f(α) has negative fractal dimensions and shows the contributions coming from the tails of the distribution. Various boxpartitioning approaches have been carefully studied such as the use of cubic and non-cubic boxes, periodic boundary conditions to enlarge the system, and single and multiple origins in the partitioning grid. The most reliable method is equal partitioning of a system into cubic boxes which has also been shown to be the least numerically expensive. Furthermore, this work gives an expression relating f(α) and the probability density function (PDF) of wavefunction intensities. The relation which contains a finite-size correction provides an alternative and simpler method to obtain f(α) directly from the PDF in which f(α) is interpreted as the scaleinvariant distribution at criticality. Finally, a generalization of standard multifractal analysis which is applicable to the critical regime and not just at the critical point is presented here. Using this generalization together with finite-size scaling analysis, estimates of critical disorder and critical exponent based on exact diagonalization have been obtained that are in excellent agreement, supporting for the first time previous results of transfer matrix calculations.

Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven toward a drastic end known as the `Big Rip' singularity where all the matter in the universe will be destroyed. Motivated by this possibility, other evolutionary scenarios have been explored by e.g. Barrow, including the phenomena which he called Sudden Future Singularities (SFS). In a model consisting of such events it is possible to have a blow up of the pressure occurring at sometime in the future evolution of the universe while the energy density would remain unaffected. The particular evolution of the scale factor of the universe in this model that results in a singular behaviour of the pressure also admits acceleration in the current era. In this thesis we will present the results of our confrontation of one example class of SFS models with the available cosmological data from high redshift supernovae, baryon acoustic oscillations (BAO) and the cosmic microwave background (CMB). We then discuss the viability of the model under consideration in light of the data.\\ More importantly however in this pursuit, we will make the case that the cosmological constraints employed in this analysis were not blindly applied to the non-standard model in question, which is not unfortunately the practice that is always followed in the cosmology community. This applicability issue is a very important one which if neglected could potentially result in biased and unreliable outcomes. Hence, although we have worked on one example non-standard cosmological model in this thesis, this work could be viewed as a demonstration of a thought through process of testing one's model against observations which can be applied to every other preferred model.

A well-motivated framework to naturally introduce neutrino masses is the B − L model, a U(1) extension of the standard odel related to the baryon minus lepton gauged number. Besides three right-handed neutrinos, that are included to cancel the anomalies (thereby naturally providing neutrino masses), this model also encompasses a complex scalar for the spontaneous symmetry breaking of the extended gauge sector and to give mass to the Z′ boson. We present the phenomenology, the discovery potential at the LHC, and the most up-to-date experimental and theoretical limits of the new particles in this model. In the gauge sector, a Z′ boson is present. We study its properties (i.e., production cross sections, branching ratios, total width), showing that it is dominantly coupled to leptons. We also present a detailed discovery power study at the LHC and at Tevatron for the Z′ boson. In the fermion sector, after implementing the see-saw mechanism, we end up with three heavy neutrinos. We show that they can be long-lived particles (therefore providing displaced vertices in the detector), and that they can induce spectacular multi-lepton decays of the Z′ boson. We also study the full signature pp → Z′ → νhνh, and present a parton level and a detector level analysis for the tri-lepton decay mode of the Z′ boson via heavy neutrinos. In the gauge sector, the two Higgs fields mix. We derive the unitarity bound and the constraints from the renormalisation group equations study. In the allowed region of the parameter space, we delineate the phenomenology of the Higgs bosons and we show characteristic signatures of the latter, at the LHC, involving the Z′ boson and the heavy neutrinos

This thesis is a dissemination of the experimental work I have carried out in the last three and a half years, under supervision of Prof. Miles Padgett and Dr. Sonja Franke-Arnold. Presented within are seven unique experiments investigating the orbital angular momentum (OAM) states of light, and the associated spatial modes. Six of these experiments relate to measurements on quantum-entangled photon pairs produced in down-conversion. The first chapter of my thesis is a brief review of the some of the contributions made to the field of research of OAM, both involving classical and quantum states of light. This chapter introduces some of the hallmark experiments within the subject, from which my experimental work reported in this thesis is inspired. The second chapter details the set up of the down conversion experiment, and the experimental techniques used to design a fully functioning quantum measurement system. Most importantly, this includes the holographic techniques used to measure the spatial states of the photon pairs. In addition to holographic measurements, a system to holographically auto-align the down-conversion experiment was developed. Due to the sensitive nature of the experiments presented, this automated system has been crucial to the success of all of the single photon experiments presented within this document. The experimental results are split into three separate categories. The first (Chapter 3) describes measurements investigating the Fourier relationship between OAM and angular position states, both at the classical and quantum levels. The following chapter (Chapter 4) consists of four experiments designed to quantify the degree of entanglement of states of OAM and angular position. This includes the first demonstration of the historic EPR (Einstein-Podolsky-Rosen) paradox for OAM and angle states, violation of a Bell-type inequality for arbitrary OAM states, and characterisation of the density matrices for a range of OAM state-spaces. The final chapter (Chapter 5) reports a new type of ghost imaging using down-converted photon pairs. In this experiment, we violate a Bell inequality within a ghost image, demonstrating the entangled nature of our system and contributing a new element to the long standing contention over quantum vs. classical features within ghost imaging. These experiments have seen a wide range of collaboration. The experimental work on the Fourier relation on single photons was carried out in collaboration with Dr. Anand Kumar Jha (University of Rochester). The work on ghost imaging was performed with collaboration with Prof. Monika Ritsch-Marte (Innsbruck Medical University), and the angular EPR paradox work was carried out in collaboration with Prof. Robert Boyd (Univ. of Rochester) and Prof. David Ireland (Univ. of Glasgow). The work I present here is experimental, however any theoretical developments are in a large part due to the support of Dr. Sonja Franke-Arnold and Prof. Steve Barnett (Univ. of Strathclyde).

As we enter the era of burning plasmas in next step devices such as ITER, the confinement of fusion born a-particles for sufficient duration that they impart their energy to the bulk fuel ions in order to maintain the thermonuclear burn is an important challenge in magnetically confined fusion. Fast ion driven plasma instabilities can cause significant redistribution and loss of the suprathermal energetic particle (EP) population, degrading performance. With dimensionless parameters such as the ratio of fast ion to thermal ion beta (Bfi/Bth ~50%) and the relative fast ion velocity to the Alfvén velocity (vfi/vA ~2) similar to those anticipated in ITER, the Mega Ampere Spherical Tokamak (MAST) provides the ideal place to study such instabilities. During periods of Neutral Beam Injection (NBI) heating, 'fishbone' instabilities are observed that coincide with a reduction to the fusion rate measured by drops in the neutron emission. Via experimental observations, fishbones are identified to be low frequency internal kink modes that burst in amplitude and chirp downwards in frequency and are synonymous with high power tokamak discharges on a wide range of devices around the world. This thesis provides a detailed analysis of what occurs during a single fishbone event. Experiments have been performed on MAST that have been interpreted using fast ion plasma physics codes. Modelling of the instability shows a resulting flux of fast ions away from the core, providing evidence at a fundamental level that they drive sufficient levels of anomalous fast ion transport to explain experimental observations. The diffusivity is shown to scale with mode amplitude, and the effect of altering other fishbone parameters within the scope of the experimental observations have been explained by identifying the extent of the fast ion population that is resonant with the mode. Resonant surfaces that sweep through phase space during the chirp are presented that coincide with populous domains of the EP distribution function; it is the gradients in this distribution function that define the drive and or damping of the instability. Via the use of synthetic diagnostics, changes to the radial profiles of neutron emissivity caused by a fishbone are shown to match those measured experimentally.

The work presented in this thesis explores ways of distinguishing models of physics beyond the Standard Model at the Large Hadron Collider (LHC). The focus is put on supersymmetric models, in particular the Minimal Supersymmetric Standard Model (MSSM) and the E6-inspired Supersymmetric Standard Model (E6SSM), which are well known and well motivated models. The muon decay channel of the pseudoscalar and heavy Higgs bosons in the MSSM is studied. It is shown that these decays to muons, in some scenarios, make it possible to measure the widths of these Higgs bosons at the LHC. This is the only known way of measuring this width at the LHC. The decays to muons also allow for the mass to be measured accurately which together with the width measurement offers a unique opportunity to pin down the value of the model parameter tan Beta, which could be used to distinguish different scenarios within the MSSM and potentially in its extensions. Gluino cascade decays are investigated as a tool to distinguish the MSSM from more complex models, with the E6SSM as an example. It is shown that the longer cascade decays of the E6SSM gluinos provide less missing transverse momentum and higher lepton multiplicity, implying the higher importance of multi-lepton searches at the LHC in models with a richer low-energy particle content. The three-lepton channel is shown to be a good discriminator between the models. In the case of a gluino discovery one would typically expect a signal in this channel if it is an E6SSM gluino but not if it is an MSSM gluino. Furthermore, the implications of limits from dark matter and Z' searches on the Higgs sector and other collider phenomenology are discussed. These implications are important to constrain and differentiate models. In addition, the contribution to fine-tuning from the Z' mass is discussed as an important measure of how attractive a model is, which should be considered by model builders

We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schrödinger (QNLS) model, introduced by Komori and Hikami using representations of the degenerate affine Hecke algebra. In particular, they can be generated using a vertex operator formalism analogous to the recursion that defines the symmetric QNLS wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation are generalized to the non-symmetric case.

This study explores the principles of echolocation in bats which can be potentially adopted for bio-inspired sonar systems. Using a biological signal processing technique which was developed based on bat’s hearing system, the effect of auditory processing on the object discrimination is investigated for both CF (constant frequency) and FM (frequency modulated) signals respectively. These signals are considered as two representative types of echolocating calls. This study has simulated returning echoes from target discs using different types of calls by applying measured impulse responses of the objects. The simulated echoes were then processed through auditory models. The results have shown that the auditory processing contributes not only to increase the gain but also to enhance the ability to discriminate the sizes of discs. The peak and notch characteristics appearing in the auditory spectrum also confirms the flexibility of designing auditory models to manipulate spectral and temporal characteristics of the echo signals. Secondly, the effect of the bat’s head on the received signals at the two ears for varying distances was investigated by measuring the head-related transfer function (HRTF) of a bat-head cast. It has been reported that a bat changes bandwidth and duration of its echolocating call as it approaches a target. Adaptive change in the echolocating calls has been well explained in previous studies in terms of characteristics of signal structure. However, the range-dependent adaptive change in emitted signals also implies that the reflected signals reaching the two ears (i.e. binaural hearing) change in gain and frequency as the distance between the bat and the target varies. The result of measured HRTF has provided insights to range-dependent binaural information regarding the adaptive change of the echolocating calls. The results of measured data show that relatively higher gain at low frequencies (below 10 kHz1) is observed than that at high frequencies (above 10 kHz) as the bat-head cast approaches the sound source. It is also noted that interaural level differences (ILDs) at a fixed distance have less sensitive changes at low frequencies than at high frequencies as the angle of the source direction changes in the frontal axis. However, the sensitivity of the ILDs at low frequencies increase more than at high frequencies as the range reduces. It is concluded that the low frequency implies a more significant role during the target approaching stage in echolocation including distance perception. Also, the systematic change in sensitivity of the ILDs in various ranges suggests that the bat might be able to calibrate the angular resolution by broadening the bandwidth at low frequencies. Furthermore, the HRTF results calculated from a computational sphere model confirms the potential function of low frequency to calibrate the ILDs sensitivity for varying distances. Overall, this study has shown that customised auditory processing of the echolocating signal improves the quality of sonar representation and the results of investigations using the HRTFs of the bat-head cast guide the future design of effective adaptive signals based on the range-dependent HRTFs, to potentially enhance the performance of sonar systems. 1This study has defined the range of the low and the high frequencies based on the acoustical diffraction and reflection of the sound around the bat-head. The diffraction effect appeared to be prominent below 10 kHz.

We consider the evolution of sharp fronts and almost-sharp fronts for the ↵-equation, where for an active scalar q the corresponding velocity is defined by u = r?(−#)−(2 − ↵)/2q for 0 < ↵ < 1. This system is introduced as a model interpolating between the two-dimensional Euler equation (↵ = 0) and the surface quasi-geostrophic (SQG) equation (↵ = 1). The study of such fronts for the SQG equation was introduced as a natural extension when searching for potential singularities for the three-dimensional Euler equation due to similarities between these two systems, with sharp-fronts corresponding to vortex-lines in the Euler case (Constantin et al., 1994b). Almost-sharp fronts were introduced in C´ordoba et al. (2004) as a regularisation of a sharp front with thickness $, with interest in the study of such solutions as $ ! 0, in particular those that maintain their structure up to a time independent of $. The construction of almost-sharp front solutions to the SQG equation is the subject of current work (Fe↵erman and Rodrigo, 2012). The existence of exact solutions remains an open problem. For the ↵-equation we prove analogues of several known theorems for the SQG equations and extend these to investigate the construction of almost-sharp front solutions. Using a version of the Abstract Cauchy Kovalevskaya theorem (Safonov, 1995) we show for fixed 0 < ↵ < 1, under analytic assumptions, the existence and uniqueness of approximate solutions and exact solutions for short-time independent of $; such solutions take a form asymptotic to almost-sharp fronts. Finally, we obtain the existence and uniqueness of analytic almost-sharp front solutions.

Bursts in pneumatic conveyor pipelines in industrial processes are a well-known hindrance to the smooth operation of any plant. Unanticipated stoppages can have serious financial implications for any company using pneumatic conveying technology, and health and safety factors are also paramount. This thesis describes an attempt to enable improved prediction of bend-wear and bend lifetime, so that more cost-effective survey work can be undertaken in anticipation of bursts. This work delivers a tool that allows bend lifetime prediction to be made according to: the bend geometry and material; the material conveyed and its rate of transportation; and bend wall thickness. Firstly, a computational model based on the coupling of CFD and particle tracking techniques is created in order to encompass the mechanics of the erosion process. This erosion process is assumed to be dominated by impact damage, and predictions of bend lifetime are made using empirical erosion algorithms gleaned from laboratory experiments, commercial CFD code (PHOENICS, and GENTRA its particle tracking sister code), and custom erosion modelling code that employs a three-dimensional toroidal geometry. Secondly, matrices of predictions are built up using the mathematical modelling technology mentioned above. These predictions are collated behind a friendly interface to produce a far more accessible piece of PC software that an engineer can employ quickly and easily. More general bend-life predictions are interpolated from this fundamental dataset using behaviours established in the course of this work, according to the particular conveying conditions input by the user. Predictions in the desktop tool are calibrated to actual bend lives as established by experimentation on a full-scale pneumatic conveyor. This experimental work was an integral part of this EPSRC-funded project, and allows some estimation of error magnitude in the predictive tool.

Little Higgs models offer an innovative solution of the naturalness problem of the Standard Model. These models contain new particles which cancel the quadratic divergences in the Higgs mass caused by the top, gauge and Higgs loops. These new particles contribute to loop induced interactions of the Higgs boson. The loop induced decays of the Higgs to gluon and photon pairs are examined in two Little Higgs models - the Littlest Higgs Model and the Schmaltz Model. The production of Higgs pairs from gluon fusion, which proceeds via heavy quark loops, is also examined in these models. Another idea considered is the multiple point principle (MPP) applied to the two Higgs doublet extension of the Standard Model. The MPP stipulates that the coupling constants will be tuned to allow the existence of a maximal number of degenerate vacua. This principle is shown to lead to a Peccei-Quinn type symmetry which naturally suppresses phenomenologically dangerous flavour changing neutral currents. Quasi-fixed points of the renormalization group are then used to derive predictions for the Higgs masses and couplings.

A mean field spin model coupled to a thermal model of a solid is used as a description of the electrocaloric effect in relaxor ferroelectrics at both first and second order transitions. This theoretical model is also used in efforts to find the tricritical point of transitions to maximise the adiabatic temperature change due to the electrocaloric effect while minimising the hysteresis losses in a cooling cycle. The electrocaloric effect is the adiabatic temperature change exhibited by a material under the sequential application then removal of electric fields. Relaxor ferroelectrics are materials with two interaction scales, local interactions in polarised nano regions (PNRs) and longer range interactions between PNRs. Electric dipoles are modelled as spins and their alignment due to an external field is used to examine polarisationelectric field loops. The results are compared to experimental data to determine values of parameters that may be used in simulations to model the electrocaloric effect. I reproduced simulations of the electrocaloric effect in the ferroelectric material lead zinc niobate-lead titanate [Pb(Zn1=3Nb2=3)O3-PbTiO3] by coupling the dipolar entropy of the spins to the entropy of a thermal lattice one can examine the temperature increase that must occur as the dipolar entropy decreases in an external field. The results of this simulation agree with experiment. Novel work is carried out in a prediction of the strength of the electrocaloric effect in polyvinylidene fluoride trifloroethylene, P(VDF-TrFE), using a simulation where the material parameters are determined from the comparison of simulated polarisation-electric field hysteresis loops with experimental results. The simulations suggest that P(VDF-TrFE) is a material worth investigating experimentally because even though it has a weak electrocaloric strength, under large fields the potential adiabatic temperature change at room temperature has promise for replacing conventional refrigerants. Due to the simplicity of this coupled model and the physical similarities between the electrocaloric effect and the magnetocaloric effect (an analogous effect observed in certain magnetic materials where an adiabatic temperature change is seen under the application and removal of a magnetic field) an investigation is also carried out on the magnetocaloric material iron rhodium (FeRh). In simulations I varied global and local stoichiometry to affect the ordering of spins and thus the entropy and strength of the magnetocaloric effect. I compared the results of our simulations with experiment and examine the variation in peak isothermal entropy change and adiabatic temperature change under variation in stoichiometry as well as the effects on the full width at half maximum. The results show that a simple model can give a qualitative representation of the effect. Work of a different nature is presented at the end of the thesis due to it being a short and complete topic which interested me during my PhD. Details are given on how Catalan numbers may be used to determine the depth of leaves in binary tree graphs and path length between them using both diagrammatic notation and the methodology of generating functions. An analytic solution is drawn from a combinatoric problem that initially appeared to only be soluble by brute force numerics.

Ears are a new biometric with major advantage in that they appear to maintain their structure with increasing age. Current approaches have exploited 2D and 3D images of the ear in human identification. Contending that the ear is mainly a planar shape we use 2D images, which are consistent with deployment in surveillance and other planar-image scenarios. So far ear biometric approaches have mostly used general properties and overall appearance of ear images in recognition, while the structure of the ear has not been discussed. In this thesis, we propose a new model-based approach to ear biometrics. Our model is a part-wise description of the ear structure. By embryological evidence of ear development, we shall show that the ear is indeed a composite structure of individual components. Our model parts are derived by a stochastic clustering method on a set of scale invariant features on a training set. We shall review different accounts of ear formation and consider some research into congenital ear anomalies which discuss apportioning various components to the ear's complex structure. We demonstrate that our model description is in accordance with these accounts. We extend our model description, by proposing a new wavelet-based analysis with a specific aim of capturing information in the ear's outer structures. We shall show that this section of the ear is not sufficiently explored by the model, while given that it exhibits large variations in shape, intuitively, it is significant to the recognition process. In this new analysis, log-Gabor filters exploit the frequency content of the ear's outer structures. In recognition, ears are automatically enrolled via our new enrolment algorithm, which is based on the elliptical shape of ears in head profile images. These samples are then recognized via the parts selected by the model. The incorporation of the wavelet-based analysis of the outer ear structures forms an extended or hybrid method. The performance is evaluated on test sets selected from the XM2VTS database. By results, bothin modelling and recognition, our new model-based approach does indeed appear to be a promising new approach to ear biometrics. In this, the recognition performance has improved notably by the incorporation of our new wavelet-based analysis. The main obstacle hindering the deployment of ear biometrics is the potential occlusion by hair. A model-based approach has a further attraction, since it has an advantage in handling noise and occlusion. Also, by localization, a wavelet can offer performance advantages when handling occluded data. A robust matching technique is also added to restrict the influence of corrupted wavelet projections. Furthermore, our automatic enrolment is tolerant of occlusion in ear samples. We shall present a thorough evaluation of performance in occlusion, using PCA and a robust PCA for comparison purposes. Our hybrid method obtains promising results recognizing occluded ears. Our results have confirmed the validity of this approach both in modelling and recognition. Our new hybrid method does indeed appear to be a promising new approach to ear biometrics, by guiding a model-based analysis via anatomical knowledge.

Byl studován kontakt mezi koulí a deskou pod tangenciálním zatížením ve vodě. Jako zdroj střižných kmitů byl použit akustický rezonátor (křemíkové mikrováhy – QCM). Kontakt koule s povrchem resonátoru indukuje změnu resonanční frekvence a šířky pásma. Byla měřena změna frekvence f a změna šířky pásma v závislosti na amplitudě oscilací. S rostoucí amplitudou docházelo k poklesu f a růstem , což je chování typické pro parciální skluz. Díky aplikaci Cattaneo-Mindlinova modelu byl vypočítán kontaktní poloměr a třecí koeficient. Kontaktní poloměr při nízké amplitudě stoupal při zvětšujícím se normálovým zatížením. Tato závislost se dobře shodovala s JKR modelem. Třecí koeficient se nacházel v odpovídajícím rozsahu. Při zvyšování externí normálové síly, docházelo k nepatrnému snižování hodnoty třecího koeficientu. Toto chování je vysvětleno příspěvkem adhezivních sil k totální normálové síle. Výpočtem byly získány dva typy třecích koeficientů, první ze změny frekvence f a druhý ze změny šířky pásma . Tyto dvě hodnoty se spolu shodovaly z ± 20 % pro měření prováděná ve vodě, zatímco pro dvě měření prováděných na hydrofilním povrchu ve vzduchu se lišila. Tento nesoulad poukazuje na nedostatek Cattaneo Mindlinovy teorie a mohl by být vysvětlen přítomností kapilárních sil.

The native corneal structure is highly organised and unified in architecture with structural and functional integration which mediates its transparency and mechanical strength. Two of the most demanding challenges in corneal tissue engineering are the replication of the native corneal stromal architecture and the preservation of stromal cell phenotype which prevents scar-like tissue formation. A concerted effort in this thesis has been devoted to the generation of a functional human corneal stromal model by the manipulation of chemical, topographical and cellular cues. To achieve this, previously built non-destructive, online, real-time monitoring techniques, micro-indentation and optical coherence tomography (OCT), which allow for the mechanical and contraction properties of corneal equivalents to be monitored, have been improved. These macroscopic parameters have been cross-validated by histological, imunohistochemical, morphological and genetic expression analysis.

Since its discovery a large effort has been made to improve analyses and make precision measurments of the properties of the Higgs Boson. At a mass of 125 GeV Higgs to bb is the dominant decay mode. However, large QCD backgrounds mean that the gluon-gluon fusion production mode is not directly accessible at the LHC. Instead an analysis of Higgs to bb can considered where the Higgs is produced in association with a Vector Boson (W/Z). This document outlines such an analysis perfomed on the ATLAS Run I 8 TeV data with focus on one particular channel where the Higgs is produces in association with a Z Boson which subsequently decays to a pair of neutrinos.

Finite element analysis is widely used to predict the behaviour of complex structures such as spacecraft and/or multi-physics systems. The ‘quality’ of the Finite Element Model (FEM), defined as the capability of the model to simulate the behaviour of the real physical hardware, is assessed by comparing the analytical results with experimental data. In this thesis, Modal Assurance Criterion (MAC) and Normalised Cross Orthogonality (NCO) check are examined for their usefulness in the correlation of real spacecraft structures and then applied to multi physics systems using the results of the ‘true’ FEM as the experimental or nominal data and those obtained from the erroneous FEM as analytical data. The NCO check requires a compatible mass matrix, which can be obtained from the global or complete FEM using the System Equivalent Reduction Expansion Process (SEREP). Here, a probabilistic approach is used to assess the robustness of a SEREP based test analysis model to inaccuracies by inputting a range of known errors into the modes of three spacecraft models. The effect of parameters used in the SEREP and the degree of inaccuracy tolerated in the modes before failing the NCO check were examined. The relationship between the capability of the FEM to predict some relevant responses and the quality of the model correlation determined using MAC and NCO check was also investigated. A method to optimise the choice of accelerometer locations to increase the robustness of the NCO check is proposed. In addition, the effectiveness of MAC and NCO criteria in the prediction of structural response under the base excitation was performed using three spacecraft models. It is observed that these criteria are not entirely satisfactory, particularly when the FEM is used to predict the forced response characteristics. A qualitative indicator termed the Base Force Assurance Criterion (BFAC) is then defined by comparing the nominal dynamic force at the base and the FEM predicted base force to predict the possible error in the peak acceleration and the dynamic displacement. The results show that the BFAC can better correlate the response than the conventional MAC or NCO check. The correlation of the FEM of two types of multi-physics systems, namely viscoelastic damped systems and a piezoelectric system were also carried out. The usefulness of MAC and NCO check in the prediction of loss factor of the viscoelastic systems is assessed and it is noted that these correlation methods fail to represent the dynamic characteristics under base excitation and once again, the BFAC is found to be a better tool to correlate the viscoelastic systems. The effect of temperature as an uncertainty on the MAC and NCO check is also studied using the viscoelastic systems. The usefulness of the MAC for the correlation of the FEM of a shunted piezoelectric system is also analysed under the harmonic excitation. It is observed that the MAC has limited use in the correlation of such systems. Finally, a new correlation method based on electric current is defined and it is shown that this criterion correlates the dynamic characteristics of the piezoelectric system better than the MAC.

We have investigated the thermodynamics of the square lattice planar rotator model. By calculating a variety of thermodynamic quantities for the planar rotator model on a sequence of one-dimensional geometries using transfer functions, we find evidence that the square lattice model exhibits an ordinary thermodynamic phase transition, with power-law singularities in the thermodynamics described by the usual set of critical exponents. This is in contrast to the widely-held view that the phase transition in the model should be of the Kosterlitz-Thouless type. We have constructed a Hubbard-type model of bilayer strontium ruthenate Sr₃Ru₂O₇. We find that the HartreeFock mean field solution of our model can be made to exhibit a metamagnetic jump that matches that seen in Sr₃Ru₂O₇, and this is clearly associated with a certain quasi one-dimensional feature in the electronic structure. We therefore suggest that this is the origin of the metamagnetism in Sr₃Ru₂O₇. The metamagnetism in our modelling is associated with a phase-separated mixture of low- and high-magnetisation solutions, which we suggest corresponds to the nematic phase in Sr₃Ru₂O₇.

This work is divided in two parts. The first part presents a careful computation of Electroweak Precision Tests constraints on the 4-Site model, and the resulting limits on fermion couplings. The new heavy W and Z bosons present in this model can couple significantly to Standard Model fermions. Previous computations of these quantities were performed using an approximation that is here shown to have a more restricted validity domain as what was originally thought. The second part of the discussion is about searches of extra W and Z bosons as predicted in some extensions of the Standard Model (such as the 4-Site model) in the Drell-Yan channels. The interference between the new physics and the Standard Model is commonly neglected in the interpretation of experimental searches. The importance of this effect is investigated in detail. The quantitative error in exclusion bounds due to neglecting the interference may be small, but important qualitative features are missed when using this approximation. It is important to be aware of the effect of interference in order to make sure wrong statements and bad conclusions are avoided, and to guarantee that analyses do stay within the domain of validity of the approximations they rely on

EU's 2007 enlargement by Bulgaria and Romania is evaluated by applying a simple macroeconomic integration model able to encompass as many of the theoretically predicted integration effects possible. The direct integration effects of Bulgaria and Romania spill-over to EU15, including Austria and the 10 new member states of the 2004 EU enlargement. The pattern of the integration effects is qualitatively similar to those of EU's 2004 enlargement by 10 new member states. Bulgaria and Romania gain much more from EU accession than the incumbents in the proportion of 20:1. In the medium-run up to 2020, Bulgaria and Romania can expect a sizable overall integration gain, amounting to additional ½ percentage point real GDP growth per annum. Within the incumbent EU member states Austria will gain somewhat more (+0.05%) than the average of EU15 (+0.02%) and the 10 new EU member states (+0.01%), which joined the EU in 2004. (author's abstract)
Series: EI Working Papers / Europainstitut