Dust grains are a crucial component of disks around young stellar systems where current observations and theory show that planets form. Dust grains must grow 10 orders of magnitude in size to become planets. However, one of the early steps in this growth phase faces stringent theoretical constraints. The metre barrier relates to two well-studied physical mechanisms which inhibit grain growth beyond centimetre sizes. We report on numerical studies which probe these early stages of planet formation including instabilities that promote dust concentration such as the streaming instability (SI). We explore several different SPH models for dusty gas evolution. We find the linear SI is difficult for SPH to capture because it begins with perturbations below the 1% level. We also employ the Athena 3rd order Eulerian code which has been used to study the SI in the linear phase and the non-linear or saturated phase. We present numerical confirmations of recent analytical predictions of enhancements to the SI growth rates caused by the dust settling to the disk midplane in the earliest stages of the protoplanetary disk evolution. Symmetric analytical predictions for SI growth are not directly relevant to the non-axisymetric, planar geometry of the saturated, non-linear phase. We lay the ground work to explore this in future work. / Thesis / Master of Science (MSc)

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Parametric instability processes are thought to produce Stimulated Electromagnetic Emissions (SEE) during ionospheric heating experiments. The phenomenon is primarily attributed to plasma turbulence excited by the high frequency HF heater in the altitude region where the pump frequency <i>ω</i>₀ is near the plasma upper hybrid frequency <i>ω_uh</i>. In this study, parametric instability processes thought to produce SEE are studied using theoretical and electrostatic Particle-In-Cell PIC simulation models. The simulation plasma is driven with a uniform oscillating electric field directed nearly perpendicular to the background geomagnetic field {B} to consider interactions when <i>ω_uh</i> is near electron cyclotron harmonics <i>nΩ_ce</i>. The pump frequency and amplitude are varied to consider the effects on the simulation electric field power spectrum. In this study, theoretical predictions and numerical simulations are used to study the three-wave decay instability process thought to be responsible for the generation of the down-shifted sidebands, the downshifted peak DP and the downshifted maximum DM. In particular, the lower hybrid decay instability LHDI and the ion cyclotron decay instability ICDI are studied in detail. The theory is used to provide the angular regime, with respect to the direction perpendicular to the magnetic field, at which the sidebands develop as well as the frequency and wavenumber regimes of both the LHDI and the ICDI. The effect of the temperature ratio <i>T_e/T_i</i> for both instabilities is discussed. A comparison between the theoretical predictions, the simulation electric field power spectrum and the experimental observations are presented in this study. Time evolution of both the LHDI and the ICDI is also investigated. The theoretical predictions are also used to investigate the cascading of the LHDI and the ICDI. The spectra show consistencies with the experimental observations. A four-wave parametric decay instability process thought to be responsible for SEE broad up-shifted sideband spectral features is discussed as well. Many theoretical results are presented, in which the effect of stepping the heater frequency closer to the upper hybrid frequency on the angle of maximum growth <i>θ_max</i>, the growth rate γ and on both the frequency and wavenumber regimes of the four-wave process is investigated. The simulation electric field power spectrum showed a large amplitude up-shifted sideband and a much smaller amplitude down-shifted sideband, consistent with the experimental observations. Comparisons between the theoretical predictions, the simulation electric field power spectrum and the experimental observations are discussed in detail. The time evolution of the four-wave process is one important aspect that is also presented in this study. The development of density irregularities, cavities and particle heating is also analyzed and investigated in this study. / Ph. D.

Underground mining has one of the highest fatal injury rates among any of the industries in the United States, which is more than five times the national average of the other industries (MSHA). Many of these incidents take place due to stress redistribution resulting from mine workings. Thus it is very important to develop some tools to predict this failure in advance and prevent any fatalities arising from the failure. The current study uses two tools — numerical modeling and laboratory tomography - to image the stress distribution in laboratory rock samples as they are uniaxially loaded. The discrete element code, PFC3D, is used. The laboratory properties of the rock sample need to be converted to the micro-properties of the particles in the model. Currently no theory exists for this conversion. In the current study an equation has been developed for this process. Based on the users' input, the equation determines the micro-properties for the model. Further, various techniques to study the stress redistribution from these models at the particle level are discussed. Tomography is a non-destructive technique through which the interior of a body can be imaged without penetrating the surface by any physical means. In the current study sensors were attached around the rock sample and tomograms were obtained at certain intervals of the load. Initially, an indentation load was applied on a rectangular block to study the comparison between the stress and the velocity in two dimensions. In the last part of the study three-dimensional tomograms were obtained from the rock samples as they were loaded to failure. / Ph. D.

To date, research has not focused on the behavior of concrete block stoppings subjected to excessive vertical loading due to roof to floor convergence. For this reason, the failure mechanism of stoppings under vertical loading has not been fully understood. Numerical models were used in combination with physical testing to study the failure mechanisms of concrete block stoppings. Initially, the behavior of a single standard CMU block was observed and simulated using FLAC. Full-scale stoppings were then tested in the Mine Roof Simulator and modeled using UDEC. Through a combination of physical testing and numerical modeling a failure mechanism for concrete block stoppings was established. This failure mechanism consists of development of stress concentrations where a height difference as small as 1/32â exists between adjacent blocks. These stress concentrations lead to tensile cracking and, ultimately, premature failure of the wall. / Master of Science

Thesis (M.A.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / This paper is divided into five sections. It is concerned with the derivation and application of a formula known as Quadrature by Differentiation. Section One derives the basic formula by applying integration by parts to a suitably chosen 2n^th. degree polynomial. By applying this method to a polynomial of degree m + n, Hummel and Seebeck's Generalized Taylor Expansion is obtained and shown identical with the Quadrature Formula when m is set equal to n. Finally the quadrature approximation is proved convergent if f(x) is analytic in a certain domain of the complex plane. Section Two deals with the representation of certain elementary functions using quadrature methods. These expansions, because they have integer coefficients and appear in a rational form, are far easier to compute than the corresponding Maclaurin Series with the same degree of accuracy. Section Three uses quadrature methods to solve ordinary differential equations whose boundary data are given at a single point. The method that is devoloped is a variation of the predictor corrector type. It is very accurate and is easily extended to solve almost every type of initial value problem. Section Four treats the linear "Two Point" and eigenvalue problem. This is accomplished by transforming the given differential equation into a system of linear algebraic relationships between the known and unknown boundary conditions. This section also deals briefly with the non linear "Two Point Problem" suggesting a iterative method, based on the results of Section Three, to obtain the missing boundary data. Section Five improves on something that Quadrature by Differentiation already is; an accurate integration formula. This is achieved by replacing derivatives with central differences. The final result is three integration formulas based only on the tabular values of the function being integrated. Since these formulas are derived using the basic interval, xg< x < xg + h, integration can be extended into s successive intervals using the same or different values of h. / 2999-01-01

Carbon-capture and sequestration (CCS) in geologic reservoirs is one strategy for reducing anthropogenic CO2 emissions from large-scale point source emitters. Recent developments have shown that basalt reservoirs are highly effective for permanent mineral trapping on the basis of CO2-water-rock interactions, which result in the formation of carbonate minerals. However, the injection of super-critical CO2 into the subsurface causes a disturbance in the pressure, temperature, and chemical systems within the target reservoir. How the ambient conditions change in response to a CO2 injection ultimately affects the transport and fate of the injected CO2. Understanding the behavior and transport of CO2 within a geologic reservoir is a difficult problem that is only exacerbated by heterogeneities within the reservoir; for example, permeability can be highly heterogeneous and exhibits significant control on the movement of CO2. This work is focused on constraining the permeability uncertainty within a flood basalt reservoir, specifically the Columbia River Basalt Group (CRBG). In order to do so, this dissertation is a culmination of four projects: (1) a geostatistical analysis resulting in a spatial correlation model of regional scale permeability within the CRBG, (2) a Monte Carlo-type modeling studying investigating the effects that permeability uncertainty has on the injectivity and storativity of the CRBG as a storage reservoir, (3) a modeling study utilizing 1-, 2-, and 3-D numerical models to investigate how the thermal signature of the CO2-water system evolves during a CO2 injection, and (4) a Monte Carlo-type modeling study focused on the integrity of the CRBG as a CO2 storage reservoir through a probabilistic assessment of static threshold criteria. / Doctor of Philosophy / The process of capturing CO2 from point-source emitters, such as power plants and injecting that CO2 into a geologic formation is one way to reduce anthropogenic CO2 emissions. Recent field studies have shown that basalt reservoirs may be very effective at permanently storing the injected CO2 making them a secure geologic formation to store the CO2. However, basalt reservoirs can be highly fractured, which causes the properties of the reservoir (e.g. permeability, porosity, etc.) to be nonuniform. Having nonuniform reservoir properties creates uncertainty when planning a large-scale CO2 injection. This research is focused on understanding and constraining the uncertainty of nonuniform reservoir properties associated with a large-scale CO2 injection. The work presented utilizes a geostatistical analysis of permeability to inform a variety of numerical models to study how nonuniform reservoir properties affect CO2 injection rate, how much CO2 can be stored, how the pressure and temperature of the reservoir changes, and how secure the storage reservoir is during a CO2 injection.