# Browsing by Subject "Perturbation theory"

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Item Cosmology with high (z>1) redshift galaxy surveys(2010-08) Jeong, Donghui; Komatsu, Eiichiro; Bromm, Volker; Hill, Gary; Seljak, Uros; Shapiro, PaulShow more Galaxy redshift surveys are powerful probes of cosmology. Yet, in order to fully exploit the information contained in galaxy surveys, we need to improve upon our understanding of the structure formation in the Universe. Galaxies are formed/observed at late times when the density field is no longer linear so that understanding non-linearities is essential. In this thesis, we show that, at high redshifts, we can accurately model the galaxy power spectrum in redshift space by using the standard cosmological perturbation theory. Going beyond the power spectrum, we can use the three-point function, or the bispectrum, to gain important information on the early universe as well as on the galaxy formation via measurements of primordial non-Gaussianity and galaxy bias. We show that the galaxy bispectrum is more sensitive to primordial non-Gaussianities than previously recognized, making high-redshift galaxy surveys a particularly potent probe of the physics of inflation. Weak lensing offers yet another way of probing cosmology. By cross correlating the angular position of galaxies with the shear measurement from galaxy lensing or CMB lensing, we also show that one can obtain the information on cosmological distance scale, the galaxy bias, and the primordial non Gaussianity from weak lensing method.Show more Item Expansion of perturbation theory applied to shim rotation automation of the Advanced Test Reactor(2011-08) Peterson, Joshua Loren; Schneider, Erich A.; Nigg, Dave; Beigalski, Steven; Deinert, Mark; Carey, GrahamShow more In 2007, the Department of Energy (DOE) declared the Advanced Test Reactor (ATR) a National Scientific User Facility (NSUF). This declaration expanded the focus of the ATR to include diversified classes of academic and industrial experiments. An essential part of the new suite of more accurate and flexible codes being deployed to support the NSUF is their ability to predict reactor behavior at startup, particularly the position of the outer shim control cylinders (OSCC). The current method used for calculating the OSCC positions during a cycle startup utilizes a heuristic trial and error approach that is impractical with the computationally intensive reactor physics tools, such as NEWT. It is therefore desirable that shim rotation prediction for startup be automated. Shim rotation prediction with perturbation theory was chosen to be investigated as one method for use with startup calculation automation. A modified form of first order perturbation theory, called phase space interpolated perturbation theory, was developed to more accurately model shim rotation prediction. Shim rotation prediction is just one application for this new modified form of perturbation theory. Phase space interpolated perturbation theory can be used on any application where the range of change to the system is known a priori, but the magnitude of change is not known. A cubic regression method was also developed to automate shim rotation prediction by using only forward solutions to the transport equation.Show more Item Low-thrust trajectory design techniques with a focus on maintaining constant energy(2014-08) Hernandez, Sonia, active 21st century; Akella, Maruthi Ram, 1972-Show more Analytical solutions to complex trajectory design problems are scarce, since only a few specific cases allow for closed-form solutions. The main purpose of this dissertation is to design simple algorithms for trajectory design using continuous thrust, with a focus on low-thrust applications. By “simple” here we seek to achieve algorithms that either admit an analytical solution, or require minimal input by the user and minimal computation time. The three main contributions of this dissertation are: designing Lyapunov-based closed-loop guidance laws for orbit transfers, finding semi-analytical solutions using a constant magnitude thrust, and perturbation theory for approximate solutions to low-thrust problems. The technical aspect that these problems share in common is that they all use, fully or partially, a thrusting model in which the energy of the system is kept constant. Many orbit transfer problems are shown to be solved with this thrusting protocol.Show more Item Perturbation methods for rapid modeling and inversion of single-phase pressure diffusion measurements(2017-08-11) Escobar Gomez, Juan Diego; Torres-Verdín, Carlos; Sepehrnoori, Kamy; Balhoff, Matthew; Heidari, Zoya; Alpak, Faruk OShow more Numerical simulation enables improved quantitative understanding of pressure diffusion phenomena in spatially complex reservoirs. Despite recent computational advances, traditional numerical simulation algorithms still pose significant challenges in flexibility and computer performance, especially concerning the solution of time-domain problems that require multiple implementations of a forward model. In this dissertation I develop a time-domain perturbation theory suitable for modeling anisotropic and heterogeneous single-phase flow systems. Although theoretically valid for any spatially-dependent rock/fluid property, the study emphasizes arbitrary spatial variations of tensorial permeability. The efficiency of integral-equation solutions is invoked by coupling perturbation theory and the superposition principle to accurately model arbitrary transient flow regimes, boundary conditions, and rockproperty distributions. Developed algorithms require a maximum of two numerical simulations to construct flow-history-dependent Permeability Sensitivity Functions (PSF) for the entire spatial-temporal domain. Rapid Forward Modeling (RFM) of pressure transients is implemented via perturbed-type solutions by weighing the sensitivity functions with spatial permeability perturbations. Regardless of the gradient-based technique, Rapid Inverse Modeling (RIM) of hydraulic measurements is also approached by efficiently adapting the sensitivity functions to calculate the entries of the associated Jacobian matrix. Research findings confirm the flexibility and reliability of perturbation methods after successful validation with numerical reservoir simulators in both cylindrical and Cartesian coordinates. Multidimensional synthetic studies modeling hydraulic-testing tools and multi-well conditions were examined for diverse anisotropic, heterogeneitydominated fluid-flow regimes. With perturbations of more than one order of magnitude in background permeability, it was found that perturbed-type solutions can be obtained in approximately three orders of magnitude less CPU time compared to conventional finitedifference methods, with relative errors in pressure as low as < 7%. Additionally, the use of sensitivity functions for (1) selecting the subset of measurements input to the estimation of spatial distributions of permeability and (2) reducing the sequential calculation of Jacobian matrices invoked by nonlinear, gradient-based inversion, provide a stable and efficient alternative for the quantitative interpretation of single-phase transient pressure measurements.Show more Item Three transdimensional factors for the conversion of 2D acoustic rough surface scattering model results for comparison with 3D scattering(2013-12) Tran, Bryant Minh; Wilson, Preston S.; Isakson, Marcia J.Show more Rough surface scattering is a problem of interest in underwater acoustic remote sensing applications. To model this problem, a fully three-dimensional (3D) finite element model has been developed, but it requires an abundance of time and computational resources. Two-dimensional (2D) models that are much easier to compute are often employed though they don’t natively represent the physical environment. Three quantities have been developed that, when applied, allow 2D rough surface scattering models to be used to predict 3D scattering. The first factor, referred to as the spreading factor, adopted from the work of Sumedh Joshi [1], accounts for geometrical differences between equivalent 2D and 3D model environments. A second factor, referred to as the perturbative factor, is developed through the use of small perturbation theory. This factor is well-suited to account for differences in the scattered field between a 2D model and scattering from an isotropically rough 2D surface in 3D. Lastly, a third composite factor, referred to as the combined factor, of the previous two is developed by taking their minimum. This work deals only with scattering within the plane of the incident wave perpendicular to the scatterer. The applicability of these factors are tested by comparing a 2D scattering model with a fully three-dimensional Monte Carlo finite element method model for a variety of von Karman and Gaussian power spectra. The combined factor shows promise towards a robust method to adequately characterize isotropic 3D rough surfaces using 2D numerical simulations.Show more Item Toward an understanding of the large scale structure of the universe with galaxy surveys(2011-12) Shoji, Masatoshi; Komatsu, Eiichiro; Gebhardt, Karl; Hill, Gary; Hui, Lam; Shapiro, PaulShow more Large-scale structures we see in the universe, such as galaxies, galaxy clusters and structures beyond the scale of clusters, result from gravitational instability of almost isotropic and homogeneous density distribution in the early universe. The degree of the initial anisotropy of the universe and the subsequent growth of gravitational instability, coupled with the expansion rate of the universe, determine the scale and abundance of the structures formed in the universe at later times. A galaxy survey directly observes a distribution of structures in the sky using galaxies as a tracer of the underlying density distribution, and yields constraints on cosmological models when compared to a physical theory of structure formation based on a given cosmological model. Among many cosmological and astronomical phenomena to be understood from a galaxy survey, the nature of the observed accelerated expansion of the universe is the most profound problem in the modern physics. Motivated by various planned and on-going galaxy surveys, including our own Hobby-Ebery Telescope Dark Energy eXperiment (HETDEX), we show the way to fully exploit the data from a galaxy survey. We improve a model of structure formation to include the effect of baryonic pressure and the free-streaming of massive neutrinos at a mildly non-linear regime. Future galaxy surveys are to reach the level of accuracy, where the effect of massive neutrinos on the observed power spectrum is no longer negligible. Proper understanding of these effects gives a way to measure the absolute masses of neutrinos: one of the most fundamental particles, which, by itself, will be a major development in the field of particle physics. Yet, most of the space (~80%) observed by galaxy surveys is occupied by voids. An ellipticity probability distribution function of voids offers yet another way of probing cosmology. Especially, a distribution of ellipticities in the redshift space provides a unique way to measure a growth rate of the structure in the universe apart from other cosmological parameters when combined with the galaxy power spectrum.Show more