<p> Despite numerous efforts to better understand binary star evolution, some aspects of it remain poorly constrained. In particular, the evolution of eccentric binaries has remained elusive mainly because the Roche lobe formalism derived for circular binaries does not apply, and other approximations must be used. Here, we report the results of our Smoothed Particle Hydrodynamics simulations of eccentric binaries using a novel way of modeling only the outermost layers of the stars with appropriate boundary conditions. We find that our boundary treatment conserves energy well and that it is well suited for the modeling of interacting binary stars. Using this new technique, along with properly relaxed model stars, we find clear trends in the mass transfer episodes. In particular, we show that these episodes can be described by Gaussians with a FWMH of ~ 0.12 P orb and that the peak rates occur after periastron, around an orbital phase of ~ 0.55, independent of the eccentricity and masses of the stars. The accreted material, on the other hand, is observed to form a rather sparse envelope around either or both stars. Although the fate of this envelope is not modeled in our simulations, we show that a constant fraction (~5%) of the material transferred is ejected from the systems. We discuss this result in terms of the poorly constrained non-conservative mass transfer scenario and argue that it can help calibrate it. Finally, we discuss the limitations of our technique and conditions under which it performs best. The results presented in this thesis represent an improvement upon previous hydrodynamical work and could be used in analytical and binary population synthesis studies to better constrain the evolution of eccentric binaries and the formation of exotic stellar populations. </p> / Thesis / Doctor of Philosophy (PhD)

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<p> This thesis defends the use of genetic algorithms (GA) to solve the maximum number of repetitions in a binary string. Repetitions in strings have significant uses in many different fields, whether it is data-mining, pattern-matching, data compression or computational biology 14]. Main extended the definition of repetition, he realized that in some cases output could be reduced because of overlapping repetitions, that are simply rotations of one another [10]. As a result, he designed the notion of a run to capture the maximal leftmost repetition that is extended to the right as much as possible. Franek and Smyth independently computed the same number of maximum repetition for strings of length five to 35 using an exhaustive search method. Values greater than 35 were not computed because of the exponential increase in time required. Using GAs we are able to generate string with very large, if not the maximum, number of runs for any string length. The ability to generate strings with large runs is an advantage for learning more about the characteristics of these strings. </p> / Thesis / Master of Science (MSc)