We use cosmological hydrodynamic simulations to study the impact of out-flows and radiative feedback on high-redshift galaxies. For outflows, we consider simulations that assume (i) no winds, (ii) a .constant-wind. model in which the mass-loading factor and outflow speed are constant, and (iii) "momentum driven" winds in which both parameters vary smoothly with mass. In order to treat radiative feedback, we develop a moment-based radiative transfer technique that operates in both post-processing and coupled radiative hydrodynamic modes. We first ask how outflows impact the broadband spectral energy distributions (SEDs) of six observed reionization-epoch galaxies. Simulations reproduce five regardless of the outflow prescription, while the sixth suggests an unusually bursty star formation history. We conclude that (i) simulations broadly account for available constraints on reionization-epoch galaxies, (ii) individual SEDs do not constrain outflows, and (iii) SED comparisons efficiently isolate objects that challenge simulations. We next study how outflows impact the galaxy mass metallicity relation (MZR). Momentum-driven outflows uniquely reproduce observations at z = 2. In this scenario, galaxies obey two equilibria: (i) The rate at which a galaxy processes gas into stars and outflows tracks its inflow rate; and (ii) The gas enrichment rate owing to star formation balances the dilution rate owing to inflows. Combining these conditions indicates that the MZR is dominated by the (instantaneous) variation of outflows with mass, with more-massive galaxies driving less gas into outflows per unit stellar mass formed. Turning to radiative feedback, we use post-processing simulations to study the topology of reionization. Reionization begins in overdensities and then .leaks. directly into voids, with filaments reionizing last owing to their high density and low emissivity. This result conflicts with previous findings that voids ionize last. We argue that it owes to the uniqely-biased emissivity field produced by our star formation prescriptions, which have previously been shown to reproduce numerous post-reionization constraints. Finally, preliminary results from coupled radiative hydrodynamic simulations indicate that reionization suppresses the star formation rate density by at most 10.20% by z = 5. This is much less than previous estimates, which we attribute to our unique reionization topology although confirmation will have to await more detailed modeling.

In this thesis, we examine the role of accretion disks in the formation of stellar systems, focusing on young massive disks which regulate the flow of material from the parent molecular core down to the star. We study the evolution of disks with high infall rates that develop strong gravitational instabilities. We begin in chapter 1 with a review of the observations and theory which underpin models for the earliest phases of star formation and provide a brief review of basic accretion disk physics, and the numerical methods which we employ. In chapter 2 we outline the current models of binary and multiple star formation, and review their successes and shortcomings from a theoretical and observational perspective. In chapter 3 we begin with a relatively simple analytic model for disks around young, very massive stars, showing that instability in these disks may be responsible for the higher multiplicity fraction of massive stars, and perhaps the upper mass to which they grow. We extend these models in chapter 4 to explore the properties of disks and the formation of binary companions across a broad range of stellar masses. In particular, we model the role of global and local mechanisms for angular momentum transport in regulating the relative masses of disks and stars. We follow the evolution of these disks throughout the main accretion phase of the system, and predict the trajectory of disks through parameter space. We follow up on the predictions made in our analytic models with a series of high resolution, global numerical experiments in chapter 5. Here we propose and test a new parameterization for describing rapidly accreting, gravitationally unstable disks. We find that disk properties and system multiplicity can be mapped out well in this parameter space. Finally, in chapter 6, we address whether our studies of unstable disks are relevant to recently detected massive planets on wide orbits around their central stars.

Recent studies regarding the habitability, observability, and possible orbital evolution of the indirectly detected exoplanet Proxima b have mostly assumed a planet with M similar to 1.3 M-circle plus, a rocky composition, and an Earth-like atmosphere or none at all. In order to assess these assumptions, we use previous studies of the radii, masses, and compositions of super-Earth exoplanets to probabilistically constrain the mass and radius of Proxima. b, assuming an isotropic inclination probability distribution. We find it is similar to 90% likely that the planet's density is consistent with a rocky composition; conversely, it is at least 10% likely that the planet has a significant amount of ice or an H/He envelope. If the planet does have a rocky composition, then we find expectation values and 95% confidence intervals of < M >(rocky) = 1.63(-0.72)(+1.66) M-circle plus for its mass and < R >(rocky) = 1.07(-0.31)(+0.38) R-circle plus for its radius.

Earths and mini Neptunes likely have a wide range of atmospheric compositions, ranging from low molecular mass atmospheres of H-2 to higher molecular atmospheres of water, CO2, N-2, or other species. Here we systematically investigate the effects of atmospheric bulk compositions on temperature and wind distributions for tidally locked sub-Jupiter-sized planets, using an idealized 3D general circulation model (GCM). The bulk composition effects are characterized in the framework of two independent variables: molecular weight and molar heat capacity. The effect of molecular weight dominates. As the molecular weight increases, the atmosphere tends to have a larger day-night temperature contrast, a smaller eastward phase shift in the thermal phase curve, and a smaller zonal wind speed. The width of the equatorial super-rotating jet also becomes narrower, and the "jet core" region, where the zonal-mean jet speed maximizes, moves to a greater pressure level. The zonal-mean zonal wind is more prone to exhibit a latitudinally alternating pattern in a higher molecular weight atmosphere. We also present analytical theories that quantitatively explain the above trends and shed light on the underlying dynamical mechanisms. Those trends might be used to indirectly determine the atmospheric compositions on tidally locked sub-Jupiter-sized planets. The effects of the molar heat capacity are generally small. But if the vertical temperature profile is close to adiabatic, molar heat capacity will play a significant role in controlling the transition from a divergent flow in the upper atmosphere to a jet-dominated flow in the lower atmosphere.

We explore the effects of rotation on convective carbon, oxygen, and silicon shell burning during the late stages of evolution in a 20 M-circle dot star. Using the Modules for Experiments in Stellar Astrophysics we construct one-dimensional (1D) stellar models both with no rotation and with an initial rigid rotation of 50% of critical. At different points during the evolution, we map the 1D models into 2D and follow the multidimensional evolution using the FLASH compressible hydrodynamics code for many convective turnover times until a quasi-steady state is reached. We characterize the strength and scale of convective motions via decomposition of the momentum density into vector spherical harmonics. We find that rotation influences the total power in solenoidal modes, with a slightly larger impact for carbon and oxygen shell burning than for silicon shell burning. Including rotation in 1D stellar evolution models alters the structure of the star in a manner that has a significant impact on the character of multidimensional convection. Adding modest amounts of rotation to a stellar model that ignores rotation during the evolutionary stage, however, has little impact on the character of the resulting convection. Since the spatial scale and strength of convection present at the point of core collapse directly influence the supernova mechanism, our results suggest that rotation could play an important role in setting the stage for massive stellar explosions.

High levels of dust have been detected in the immediate vicinity of many stars, both young and old. A promising scenario to explain the presence of this short-lived dust is that these analogues to the zodiacal cloud (or exozodis) are refilled in situ through cometary activity and sublimation. As the reservoir of comets is not expected to be replenished, the presence of these exozodis in old systems has yet to be adequately explained. It was recently suggested that mean-motion resonances with exterior planets on moderately eccentric (e(p) greater than or similar to 0.1) orbits could scatter planetesimals on to cometary orbits with delays of the order of several 100 Myr. Theoretically, this mechanism is also expected to sustain continuous production of active comets once it has started, potentially over Gyr time-scales. We aim here to investigate the ability of this mechanism to generate scattering on to cometary orbits compatible with the production of an exozodi on long time-scales. We combine analytical predictions and complementary numerical N-body simulations to study its characteristics. We show, using order of magnitude estimates, that via this mechanism, low-mass discs comparable to the Kuiper belt could sustain comet scattering at rates compatible with the presence of the exozodis which are detected around Solar-type stars, and on Gyr time-scales. We also find that the levels of dust detected around Vega could be sustained via our proposed mechanism if an eccentric Jupiter-like planet were present exterior to the system's cold debris disc.

Chan Kai Yam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 80-82). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Parameter Identification in Heat Conduction Systems --- p.1 / Chapter 1.2 --- Inverse Problems --- p.3 / Chapter 1.3 --- Challenges in Inverse Problems --- p.6 / Chapter 2 --- Tools in Parameter Identification --- p.9 / Chapter 2.1 --- Output Least Squares Method --- p.10 / Chapter 2.2 --- Tikhonov Regularization --- p.11 / Chapter 2.3 --- Our Approach --- p.14 / Chapter 3 --- Numerical Implementations --- p.20 / Chapter 3.1 --- Finite Element Discretization and Its Convergence --- p.20 / Chapter 3.2 --- Steepest Descent Method --- p.22 / Chapter 3.3 --- Multigrid Techniques --- p.26 / Chapter 4 --- Numerical Experiments --- p.29 / Chapter 4.1 --- One Dimensional Examples --- p.30 / Chapter 4.1.1 --- Selection of mk --- p.31 / Chapter 4.1.2 --- Selection of nk --- p.34 / Chapter 4.1.3 --- Selection of Number of Levels in the Coarse Grid Correction Step --- p.37 / Chapter 4.1.4 --- Convergence with Different Regularization Pa- rameters γ --- p.39 / Chapter 4.1.5 --- Convergence with Different Initial Guesses --- p.42 / Chapter 4.1.6 --- Comparisons between MG and SG Methods --- p.44 / Chapter 4.1.7 --- Comparisons between MG and RMG Methods --- p.46 / Chapter 4.1.8 --- More Examples --- p.49 / Chapter 4.1.9 --- Coarse Grid Correction in Another Approach --- p.60 / Chapter 4.2 --- Two Dimensional Examples --- p.71 / Chapter 4.3 --- Conclusions --- p.78 / Bibliography --- p.80

The effectiveness of the Additive Correction Multigrid (ACM) algorithm, a line-byline Tri-diagonal Matrix Algorithm (TDMA), and simple Gauss-Seidel (GS) iteration in numerical heat transfer analysis is investigated on a conventional single processor computer and on a distributed memory parallel computer. The performance of these methods is studied by solving a two-dimensional, steady heat conduction problem. The execution time of ACM on a single processor is proportional to the number of unknowns to the 1.5 power. This is in contrast to the execution time of the TDMA for which the execution time is proportional to the number of unknowns to the 2.0 power. The GS , TDMA and ACM algorithms are adapted to a model IPSC2 Intel hypercube which has a 32 processing nodes each with 8 MBytes oflocal memory. Because GS is a local method, it has almost perfect speed up, but it also converges more slowly than TDMA, The TDMA, on the other hand, is affected by domain decomposition to a greater extent than GS. As the number of processors used to solve the problem is increased, the execution times for GS and TDMA are essentially equal. Solving the model problem with 32 processors on a 192x192 grid resulted in parallel efficiencies of 95%, 80% and 78% for the GS, TDMA, and ACM algorithms, respectively. Though the parallel efficiency of ACM was the lowest of the three, the parallel ACM algorithm required an order of magnitude less time to solve the model than either parallel GS or parallel TDMA without multigrid.

The objective of this thesis is to develop a more efficient solver for a large system of linear equations arising from finite element discretization on unstructured tetrahedral meshes for a scalar elliptic partial differential equation of second order for pressure in a commercial computational fluid dynamics (CFD) simulation. Segregated solution methods (or pressure correction type methods) are a widely used approach to obtain solutions of Navier-Stokes equations during numerical simulation by many commercial CFD codes. At each time step, these simulations usually require the approximate solution of a series of scalar equations for velocity, pressure and temperature. Even if the simulation does not require high-accuracy approximations, the large systems of linear equations for pressure may not be efficiently solved. The matrices of these systems of linear equations of real-life industry problems often strongly violate weak diagonal dominance and the numerical simulation often requires solutions of very large systems with over a few hundred thousands degrees of freedom. These conditions produce very ill-conditioned systems of linear equations. Therefore, it is very difficult to solve such systems of linear equations efficiently using most currently available common iterative solvers. A survey of solvers for systems of linear equations was undertaken to determine the preferred solution methodology. An algebraic multigrid preconditioned conjugate gradient (AMGPCG) method solver was chosen for these problems. This solver uses the algebraic multigrid (AMG) cycle as a preconditioner for the conjugate gradient (CG) method. The disadvantages of the conventional AMG method are an expensive setup time and large memory requirements, particularly for three dimensional problems. The disadvantage of an expensive setup time needs to be overcome because the simulation usually requires only low-accuracy approximations for pressure. Also it is important to overcome the disadvantage of the large memory requirements for use in commercial software. In this work, an efficient AMGPCG solver is developed by overcoming the disadvantages of the conventional AMG method. The robustness of AMGPCG is shown theoretically so that the solver is always convergent. Optimum or close to optimum rates of convergence behavior for the solver are shown numerically so that the number of necessary iterations to obtain the estimated solution is approximately independent of mesh resolution. Furthermore, numerical experiments of solving pressure for some industry problems were carried out and compared with other efficient solvers including a fast commercial AMGPCG solver (SAMG, release 20b1). It was found that the developed AMGPCG solver was the fastest among these solvers for solving these problems and its algorithm has been numerically proven to be efficient. In addition, the memory requirement is at an acceptable level for commercial CFD codes.

Integral equations arise in many scienti c and engineering problems. A large class of initial and boundary value problems can be converted to Volterra or Fredholm integral equations. The potential theory contributed more than any eld to give rise to integral equations. Integral equations also has signi cant application in mathematical physics models, such as di rac- tion problems, scattering in quantum mechanics, conformal mapping and water waves. The Volterra's population growth model, biological species living together, propagation of stocked sh in a new lake, the heat transfer and the heat radiation are among many areas that are described by integral equations. For limited applicability of analytical techniques, the numer- ical solvers often are the only viable alternative. General computational techniques of solving integral equation involve discretization and generates equivalent system of linear equations. In most of the cases the discretization produces dense matrix. Multigrid methods are widely used to solve partial di erential equation. We discuss the multigrid algorithms to solve integral equations and propose usages of distributive relaxation and the Kaczmarz method. / Department of Mathematical Sciences