A high-order, conservative integrator with local time-stepping

We present a family of multistep integrators based on the Adams-Bashforth methods. These schemes can be constructed for arbitrary convergence order with arbitrary step size variation. The step size can differ between different subdomains of the system. It can also change with time within a given subdomain. The methods are linearly conservative, preserving a wide class of analytically constant quantities to numerical roundoff, even when numerical truncation error is significantly higher. These methods are intended for use in solving conservative PDEs in discontinuous Galerkin formulations or in finite-difference methods with compact stencils. A numerical test demonstrates these properties and shows that significant speed improvements over the standard Adams-Bashforth schemes can be obtained.Comment: 29 page

Not Out of the Blue: Sun Yat-sen and the ROC-PRC Paradox

Thesis advisor: Rebecca NedostupSeeing as how the leadership of both the Republic of China and the People's Republic of China have claimed a sense of inheritance and legitimacy from the political philosophy of Sun Yat-sen, it seems a paradox how different the political situations are in their respective domains. It is the intent of this thesis to discern how prioritizing different elements of Sun Yat-sen's political theory resulted in divergent decisions made by the leaders of the Kuomintang and the Chinese Communist Party, which in turn help explain conditions found in the Republic of China on Taiwan and the People's Republic of China.Thesis (BA) — Boston College, 2011.Submitted to: Boston College. College of Arts and Sciences.Discipline: College Honors Program.Discipline: History Honors Program.Discipline: History

What does a binary black hole merger look like?

We present a method of calculating the strong-field gravitational lensing caused by many analytic and numerical spacetimes. We use this procedure to calculate the distortion caused by isolated black holes and by numerically evolved black hole binaries. We produce both demonstrative images illustrating details of the spatial distortion and realistic images of collections of stars taking both lensing amplification and redshift into account. On large scales the lensing from inspiraling binaries resembles that of single black holes, but on small scales the resulting images show complex and in some cases self-similar structure across different angular scales.Comment: 10 pages, 12 figures. Supplementary images and movies can be found at http://www.black-holes.org/the-science-numerical-relativity/numerical-relativity/gravitational-lensin

High precision calculation of generic extreme mass ratio inspirals

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 63-64).Orbits around black holes evolve due to gravitational-wave emission, losing energy and angular momentum, and driving the orbiting body to slowly spiral into the black hole. Recent theoretical advances now make it possible to model the impact of this wave emission on generic (eccentric and inclined) black hole orbits, allowing us to push beyond the handful of constrained (circular or equatorial) cases that previous work considered. This thesis presents the first systematic study of how generic black hole orbits evolve due to gravitational-wave emission. In addition to extending the class of orbits which can be analyzed, we also introduce a new formalism for solving for the wave equation which describes radiative backreaction. This approach is based on a spectral decomposition of the radiation field originally introduced by Mano, Suzuki, and Takasugi (MST), and was then adapted for numerical analysis by Fujita and Tagoshi (FT). We find that the MST-FT formalism allows us to compute various quantities significantly more accurately than previous work, even in strong field regimes. We use this code to explore the location in orbital parameter space of the surface at which the evolution of orbital eccentricity changes sign from negative (orbits circularize) to positive (orbits become more eccentric).by William Throwe.S.B

A High-Order, Conservative Integrator with Local Time-Stepping

We present a family of multistep integrators based on the Adams--Bashforth methods. These schemes can be constructed for arbitrary convergence order with arbitrary step size variation. The step size can differ between different subdomains of the system. It can also change with time within a given subdomain. The methods are linearly conservative, preserving a wide class of analytically constant quantities to numerical roundoff, even when numerical truncation error is significantly higher. These methods are intended for use in solving conservative PDEs in discontinuous Galerkin formulations or in finite-difference methods with compact stencils. A numerical test demonstrates these properties and shows that significant speed improvements over the standard Adams--Bashforth schemes can be obtained