Strongly correlated materials are an important class of materials for research in condensed matter physics. Other than ordinary solid-state physical systems, which can be well described and analyzed by the energy band theory, the electron-electron correlation effects in strongly correlated materials are far more significant. So it is necessary to develop theories and methods that are beyond the energy band theory to describe their rich and varied behaviors. Not only are there electron-electron correlations, typically the multiple degrees of freedom in strongly correlated materials, such as charge distribution, orbital occupancies, spin orientations, and lattice structure exhibit cooperative or competitive behaviors, giving rise to rich phase diagrams and sensitive or non-perturbative responses to changes in external parameters such as temperature, strain, electromagnetic fields, etc. This thesis is divided into two parts. In the first part, we use the density functional theory (DFT) plus U correction, i.e., the DFT+U method, to calculate the equilibrium and nonequilibrium phase transitions of LuNiO3 and VO2. The effect of adding U is manifested in both materials as the change of band structure in response to the change of orbital occupancies of electrons, i.e., the soft band effect. This effect bring about competitions of electrons between different orbitals by lowering the occupied orbitals and raising the empty orbitals in energy, giving rise to multiple metastable states. In the second part, we study the dynamic mean field theory (DMFT) as a beyond band-theory method. This is a Green's function based theory for open quantum systems. By selecting one lattice site of an interacting lattice model as an open system, the other lattice sites as the environment are equivalently replaced by a set of non-interaction orbitals according to the hybridization function, so the whole system is transformed into an Anderson impurity model. We studied how to use the density matrix renormalization group (DMRG) method to perform real-time evolutions of the Anderson impurity model to study the non-equilibrium dynamics of a strongly correlated lattice system. We begin in Chapter 1 with an introduction to strongly correlated materials, density functional theory (DFT) and dynamical mean-field theory (DMFT). The Kohn-Sham density functional theory and its plus U correction are discussed in detail. We also demonstrate how the DMFT reduces the lattice sites other than the impurity site as a set of non-interacting bath orbitals. Then in Chapters 2 and 3, we show material-related studies of LuNiO3 as an example of rare-earth nickelates under substrate strain, and VO2 as an example of a narrow-gap Mott insulator in a pump-probe experiment. These are two types of strongly correlated materials with localized 3d orbitals (for Ni and V). We use the DFT+U method to calculate their band structures and study the structural phase transitions in LuNiO3 and metal-insulator transitions in both materials. The competition between the charge-ordered and Jahn-Teller distorted phases of LuNiO3 is studied at various substrate lattice constants within DFT+U. A Landau energy function is constructed based on group theory to understand the competition of various distortion modes of the NiO6 octahedra. VO2 is known for its metal-insulator transition at 68 degree C, above which temperature it's a metal and below which it's an insulator with a doubled unit cell. For VO2 in a pump-probe experiment, a metastable metal phase was found to exist in the crystal structure of the equilibrium insulating phase. Our work is to understand this novel metastable phase from a soft-band picture. We also use quantum Boltzmann equation to justify the prethermalization of electrons over the lifetime of the metastable metal, so that the photoinduced transition can be understood in a hot electron picture. Finally, in Chapters 4 and 5, we show a focused study of building a real-time solver for the Anderson impurity model out of equilibrium using the density matrix renormalization group (DMRG) method, towards the goal of building an impurity solver for nonequilibrium dynamical mean-field theory (DMFT). We study both the quenched and driven single-impurity Anderson models (SIAM) in real time, evolving the wave function written in a form with 4 matrix product states (MPS) in DMRG. For the quenched model, we find that the computational cost is polynomial time if the bath orbitals in the MPSs are ordered in energy. The same energy-ordering scheme works for the driven model in the short driving period regime in which the Floquet-Magnus expansion converges. In the long-period regime, we find that the computational time grows exponentially with the physical time, or the number of periods reached. The computational cost reduces in the long run when the bath orbitals are quasi-energy ordered, which is discussed in further detail in the thesis.

Magnetic source magnetic resonance imaging (msMRI) is an fMRI technique that has been under development for direct detection of neuronal magnetic fields to map brain activity and has been shown to be experimentally detectable using conventional means, but there is debate on the detection of the msMRI signal since it can be only a 0.2% change. Detection of its temporal characteristics has yet to be reported and may strengthen the case for msMRI detection. The temporal characteristics of the detected msMRI signal were examined in this work, but it was found that the sensitivity of conventional analysis techniques are low within the context of msMRI, preventing consistent msMRI signal detection and analysis of its temporal characteristics. Examination of blood oxygen level dependent (BOLD) contrast contamination and application of mean-shift clustering (MSC) to fMRI analysis were performed to look into the possibility of improving the low sensitivity. fMRI analysis is commonly performed with cross correlation analysis (CCA) and techniques based on the General Linear Model (GLM), but both CCA and GLM techniques typically perform calculations on a per-voxel basis and do not consider relationships neighboring voxels may have. MSC is a technique to consider for this purpose and shows improved activation detection for both simulated and real BOLD fMRI data. To consider the issue of BOLD contamination, the hemodynamic response over time was examined using repeated median nerve stimulation. On average, the results show the BOLD signal is not detectable after the second fMRI run. The results are consistent with previous hemodynamic habituation effect studies with other types of stimulation, but they do not completely agree with findings of evoked potential studies. Overall, this work shows that the low detection sensitivity may be able to be addressed with the purpose of furthering msMRI research.

In this study we provide a new proof of C¹,α boundary regularity for finite perimeter sets with flat boundary which are local minimizers of a variational mean curvature formula. Our proof is provided for curvature term H∈LΩ. The proof is a generalization of Cafarelli and C#243;rdoba's method, and combines techniques from geometric measure theory and the theory of viscosity solutions which have been developed in the last 50 years. We rely on the delicate interplay between the global nature of sets which are variational minimizers of a given functional, and the pointwise local nature of comparison surfaces which satisfy certain PDE. As a heuristic, in our proof we can consider the curvature as an error term which is estimated and controlled at each point of the calculation.

Existing opportunities in advanced interceptor, satellite guidance and aircraft navigation technologies, requiring higher signal processing speeds and lower noise environments, are demanding Ring Laser Gyro (RLG) based Inertial Systems to reduce initialization and operational data latency as well as correlated noise magnitudes. Existing signal processing algorithms are often less than optimal when considering these requirements. Advancements in micro-electronic processes have made Application Specific Integrated Circuits (ASIC) a fundamental building block for system implementation when considering higher-level signal processing algorithms. Research of real time adaptive signal processing algorithms embedded in ASICs for use in RLG based inertial systems will help to understand the trade-off in finite register length effects to correlated noise magnitude, organizational complexity, computational efficiency, rate of convergence, and numerical stability. Adaptive filter structures selected will directly affect meeting inertial system performance requirements for data latency, residual noise budgets and real time processing throughput. Research in this area will help to target specific adaptive noise cancellation algorithms for RLG based inertial systems in a variety of military and commercial space applications. Of particular significance is an attempt to identify an algorithm embedded in an ASIC that will reduce the correlated noise components to the theoretical limit of the RLG sensor itself. This would support a variety of applications for the low noise space environments that the RLG based inertial systems are beginning to find promise for such as advanced military interceptor technology and commercial space satellite navigation, guidance and control systems.

A soil climate monitoring network, consisting of seven automated weather stations, was established between 1999 and 2003 in the McMurdo Sound region of Antarctica. Soil temperature, soil water content, air temperature, relative humidity, solar radiation, and wind speed and direction are recorded hourly and downloaded annually. Two 30 m deep permafrost temperature monitoring boreholes were established adjacent to the soil climate stations in the Wright Valley and at Marble Point in January 2007. Sixteen thermistors (accurate to ±0.1°C) were installed in each borehole measuring temperature once every hour and recording the mean every six hours. One year of permafrost temperatures were available (January 2007 to January 2008). The overall aim of this thesis was to make use of the soil climate monitoring database from 1999 to 2007 to investigate Antarctic soil climate. Active layer depth (depth of thawing) varied inter-annually, with no significant trend between 1999 and 2007. The active layer increased with decreasing latitude (R2 = 0.94), and decreased with increasing altitude (R2 = 0.95). A multiple regression model was produced whereby active layer depth was predicted as a function of mean summer air temperature, mean winter air temperature, total summer solar radiation and mean summer wind speed (R2 = 0.73). Annual temperature cycles were observed at all depths in the boreholes. At Marble Point, an annual temperature range of lt;1°C occurred at 15.2 m, lt;0.5°C at 18.4 m and lt;0.1°C at 26.4 m and at Wright Valley, an annual temperature range of lt;1°C occurred at 14.0 m, lt;0.5°C at 17.2 m and lt;0.1°C at 25.2 m. Given that the depth of Zero Annual Amplitude determined depends on the sensitivity of the measurement method, it is suggested that instead of referring to a depth of Zero Annual Amplitude , the depth at which the annual temperature range is less than a given value is a more useful concept. Mean annual and mean seasonal air and soil temperatures varied inter-annually and there was no significant trend of warming or cooling over the 1999 - 2007 period. Mean annual air temperatures were primarily influenced by winter air temperatures. Mean annual and mean summer soil temperatures were warmer than air temperatures due to heating by solar radiation. Mean summer air temperatures correlated well with the Southern Annular Mode Index (SAMI) at all sites (0.61 lt; R2 lt; 0.73) except Victoria Valley; however there was no correlation between mean annual or mean winter temperatures and the SAMI. Air temperature was linearly correlated with near-surface soil temperature (1.3 - 7.5 cm) (R2 gt; 0.79). Near-surface soil temperature was strongly correlated with incoming solar radiation at Victoria Valley (0.14 lt; R2 lt; 0.76) and Granite Harbour (0.49 lt; R2 lt; 0.82), but was not significantly correlated at other sites (0 lt; R2 lt; 0.57). There was no significant correlation between air temperature and wind speed, air temperature and solar radiation and near-surface soil temperature and wind speed, despite occasions of strong correlation on the diurnal time scale. Diurnal summer cycles in air and soil temperatures were driven by solar radiation. Multiple regressions combining the effects of air temperature, solar radiation and wind speed approximated near-surface soil temperatures well at every site during both summer and winter (0.88 lt; R2 lt; 0.98).

The Madden-Julian Oscillation is a tropical atmospheric phenomenon detected as anomalies in zonal winds, convection and cloudiness. This perturbation has a definitive timescale of about thirty to sixty days, allowing its signal to be extracted from background data. The Madden-Julian Oscillation originates over the western Indian Ocean and generates a convective region which moves east along the equatorial region. This perturbation is thought to contribute to the timing and intensity of the eastern hemisphere monsoons, the El Niño/ Southern Oscillation and tropical storms and cyclones. The current understanding of the Madden-Julian Oscillation is that it restricts the bulk of its' influence to the tropics, however some evidence suggested that the impact is more extensive. Analysis of about 30 years of data showed significant modulation of rainfall by the equatorial passage of the MJO. The real-time multivariate Madden-Julian Oscillation Index was used to estimate the location and amplitude of the Madden-Julian Oscillation, and forms the basis of the basic rainfall prediction tool developed. The method developed here clearly linked the low latitude passage of the Madden-Julian Oscillation with suppressed and enhanced rainfall events in the Australasian region and beyond. A rudimentary forecasting capability at the intraseasonal time scale has been developed suitable for assisting Australian agricultural sector. A subsequent and independent analysis of global mean sea level pressure anomalies provided evidence of teleconnections between the Madden-Julian Oscillation and higher latitude atmospheric entities. These anomalies confirm the existence of teleconnections capable of producing the rainfall pattern outputs. The MJO is strongly influenced by the season. However the seasonally dependant analysis of rainfall with respect to the Madden Julian Oscillation conducted was inconclusive, suggesting aspects of the MJO influence still require clarification. Considering the importance of rainfall variability to the Australian agricultural sector the forecasting tool developed, although basic, is significant.

<p>There is a big interest for alternative investment strategies than investing in traditional asset classes. Commodities are having a boom dynamic with increasing prices. This thesis is therefore based on applying Modern Portfolio Theory concept to this alternative asset class.</p><p>In this paper we manage to create optimal portfolios of commodities for investors with known and unknown risk preferences. When comparing expected returns to actual returns we found that for the investor with the known risk preference almost replicated the return of the markets. The other investor with unknown risk preference also profited but not as efficient as the market portfolio.</p>

<p>The emission legislations and the new On Board Diagnostics (OBD) legislations are becoming more strict and making the demands on control and fault detection higher. One way to</p><p>control and diagnose the engine is to use a control/diagnose strategy based on physical models and therefore better models are necessary. Also, to be competitive and meet the markets demand of higher power, longer durability and better fuel economy, the models needs to be improved continuously. In this thesis a mean value model of the intake system that predicts the charge air temperature has been developed. Three models of different complexity for the intercooler heat-exchanger have been investigated and validated with various results. The suggested intercooler heat-exchanger model is implemented in the mean value model of the intake system and the whole model is validated on three different data sets. The model predicts the intake manifold temperature with a maximum absolute error of 10.12 K.</p>

Abstract Detailed in this manuscript is a methodology to model ground state properties of 4He droplets at zero pressure and zero Kelvin using a density functional theory of liquid helium. The density functional approach examined here consists of two noted functionals from the literature and corresponding mean field definitions. A mean field and trial density are defined for each system and optimized to self-consistency using a matrix diagonalization technique. Initial calculations of planar slabs are performed and demonstrate reasonable agreement with experiment and with prior studies using density functional theory. Quantum properties of droplets and droplets containing atomic dopants are calculated. Three different He-dopant potentials are examined to test the limits of the functional methods. For each impurity interaction, an average of 12 atoms were found to reside in the first solvation shell with an atomic dopant placed at the droplet center. Maximum densities in the first solvation shell reached those of solid helium as predicted by DF methods.

No description available.