The Generic Nanosatellite Bus (GNB) is a spacecraft platform designed to accommodate the integration of diverse payloads in a common housing of supporting components. The development of the GNB at the Space Flight Laboratory (SFL) under the Canadian Advanced Nanospace eXperiment (CanX) program provides accelerated access to space while reducing non-recurring engineering (NRE) costs. The work presented herein details the development of the attitude determination and control subsystem (ADCS) of the GNB. Specific work on magnetorquer coil assembly, integration, and testing (AIT) and reaction wheel testing is included. The embedded software development and unit-level testing of the GNB sun sensors are discussed. The characterization of the AeroAstro star tracker is also a major focus, with procedures and results presented here. Hardware models were developed and incorporated into SFL's in-house high-fidelity attitude dynamics and control simulation environment. This work focuses on specific contributions to the CanX-3, CanX-4&5, and AISSat-1 nanosatellite missions.

High Mass X-Ray Binary Stars (HMXBs) are stars that contain one early-type main sequence or giant star and one of a black hole, neutron star or white dwarf. HMXBs in the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) are instructive to study because both galaxies are metal poor in compari- son to the Milky Way and they are fairly transparent to both optical and X-ray radiation. This allows a more complete study of the whole population, without the biasing effects of gas and dust that occur in our own Galaxy. The objective of this study was to find the periods of HMXBs in the LMC and SMC with known optical counterparts in the dataset acquired by the Robotic Optical Transient Search Ex- periment telescope. Two possible orbital periods were found for the objects XTE J0055-724 and RX J0101.3-7211 of 1724 days and 478 days, respectively. Continued observations are recommended to conrm the two periods.

The Antennae (22 Mpc) is one of the most well-known mergers in the nearby Universe. Its distance allow us to observe and study the gas at the scales of stellar cluster formation. It is an ideal source to understand how the galaxy dynamics in mergers trigger the formation of stars. Most of the stars in the Antennae are formed in compact and massive stellar clusters, dubbed super-star clusters (SSCs). The most massive (>106 M⊙) and youngest (<6 Myr) SSCs are located in the overlap region, where the two galaxies collide, and are associated with massive (several 108 M⊙) and super-giant (few hundred of pc) molecular complexes (SGMCs). The formation of SSCs must involve a complex interplay of merger-driven gas dynamics, turbulence fed by the galaxy interaction, and dissipation of the kinetic energy of the gas. Within SGMCs, a hierarchy of structures must be produced, including dense and compact concentrations of molecular gas massive enough to form SSCs, pre-cluster clouds (PCCs). For star formation to occur, the mechanical energy of PCCs must be radiated away to allow their self-gravity to locally win over their turbulent gas pressure. Specific tracers of turbulent dissipation are therefore key inputs to test the validity of this theoretical scenario. In my thesis, I studied the Antennae overlap region. My work is based on observations with the SINFONI spectro-imager at the VLT, which includes H2 rovibrational and Brγ line emission, and with ALMA, which includes the CO(3-2) line and dust continuum emission. Both data-sets have the needed sub-arcsecond angular resolution to resolve the scales of SSC formation. The spectral resolutions are enough to resolve motions within SGMCs. Combining CO and H2 line emission is key in my PhD work. I use CO as a tracer of the distribution and kinematics of the molecular gas, and H2 as a tracer of the rate at which the gas mechanical energy is dissipated.My thesis focuses on diverse sources in the Antennae overlap region which trace different stages of star formation: the gathering of mass necessary to form SGMCs, the formation of PCCs within SGMCs and the disruption of a parent cloud by a newly formed SSC. I show that at each stage turbulence plays a key role. I found that the kinetic energy of the galaxies is not thermalized in large scale shocks, it drives the turbulence in the molecular ISM at a much higher level than what is observed in the Milky Way. Near-IR spectral diagnostics show that, outside of SSCs embedded in their parent clouds, the H2 line emission is powered by shocks and traces the dissipation of the gas turbulent kinetic energy. I relate the H2 emission to the loss of kinetic energy required to form gravitationally bound clouds. This interpretation is supported by the discovery of a compact, bright H2 source not associated with any known SSC. It has the largest H2/CO emission ratio and is located where the data show the largest velocity gradient in the interaction region. To our knowledge, this is the first time that an extragalactic source with such characteristics is identified. We would be witnessing the formation of a cloud massive enough to form a SSC. The data also allow us to study the disruption of a parent molecular cloud by an embedded SSC. Its matter is loosely bound and its gravity would be supported by turbulence, which makes it easier for feedback to disrupt the parent cloud. I end my manuscript presenting two projects. I propose to establish additional energy dissipation tracers observable with ALMA, which gives us the high spatial and spectral resolution needed to isolate scales at which clusters form. This is a Cycle 1 proposal accepted in first priority. I also plan to expand my work to other nearby extragalactic sources by investigating the turbulence-driven formation of stars in different extragalactic sources by combining near-IR and submillimeter observations.

High Mass X-Ray Binary Stars (HMXBs) are stars that contain one early-type main sequence or giant star and one of a black hole, neutron star or white dwarf. HMXBs in the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) are instructive to study because both galaxies are metal poor in compari- son to the Milky Way and they are fairly transparent to both optical and X-ray radiation. This allows a more complete study of the whole population, without the biasing effects of gas and dust that occur in our own Galaxy. The objective of this study was to find the periods of HMXBs in the LMC and SMC with known optical counterparts in the dataset acquired by the Robotic Optical Transient Search Ex- periment telescope. Two possible orbital periods were found for the objects XTE J0055-724 and RX J0101.3-7211 of 1724 days and 478 days, respectively. Continued observations are recommended to conrm the two periods.

The Quark Gluon Plasma (QGP) is a form of matter in which quarks and gluons are deconfined, and was suggested to be formed in high-energy heavy-ion collisions. Since the discovery of high-pT hadron suppression in central Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC), and the related discovery of the quenching of the away-side jet in these collisions, the role of jets as key probes of the QGP was re-affirmed. The Solenoidal Tracker At RHIC (STAR) detector system, which is suited for jet studies because of its large solid-angle coverage, has produced a number of interesting jet measurements in recent years, including gamma-jet measurements, attempts at full heavy-ion jet reconstruction, and two-dimensional correlations. A long-range correlation in pseudorapidity (the ?Ridge?) was studied (with statistical significance) out to pT^trig. <? 7 GeV /c and was assumed to have an integrated yield independent of pT^trig. Further studies out to higher pT were limited by the minimum biased statistics taken in Run 4 (2004) with STAR. This work presents results of a ridge analysis with (non-reconstructed) pi0s and direct-gamma-rich triggers out to ?13.5 GeV /c in pT^trig. Using triggered data from Run 7 (2007) and Run 10 (2010) Au+Au collisions detected with STAR. Preliminary results seem to indicate that the ridge yield decreases with pT^trig., and that the ridge yield for direct-?-rich triggers is consistent with zero.

The energy consumption of residential buildings in Canada accounts for 17% of national energy use (Trudeau, 2005). Production homes represent a considerable portion of new housing. In an effort to reduce the national energy demand, the energy consumption of these homes must be addressed. Techniques, methods and materials to achieve reductions in residential energy use are readily available. The goal of this thesis is to show that it is possible to build a low-energy home for less total carrying cost than a home built to the 2006 Ontario Building Code. To show how this is possible, a range of cost-effective and practical-to-implement upgrades are identified, and quantitative projections of cost-savings and benefits gained by the homeowner are generated. The interest in, and demand for, greener less energy consumptive homes is increasing. As oil prices rise, climate changes, landfills become overburdened and water restrictions become more frequent, the public pushes harder for change. The residential housing sector has seen increased demand for energy efficient homes that incorporate green features, high efficiency appliances and mechanical systems. Increased environmental concern has put ‘Green’ in demand. This thesis reviews a variety of North American green rating systems and contrasts their energy performance requirements with those of the Ontario Building Code. The Ontario Building Code was considered the baseline. Although the R2000 program was originally developed nearly 30 years ago it has managed to maintain a standard of performance that has always exceeded the OBC. It has a wider range of requirements than either the building code or ENERGY STAR, but falls short of the LEED for homes program in terms of breadth of environmental concerns. The literature review shows that homes that use 75% less heating energy than a standard house could be built in the 1980s for a mere 5% construction cost premium. When care is taken to produce quality designs and specifications, and to ensure that details are properly finished, these types of homes can be built almost anywhere. Some of the most successful technology and strategies of the 80’s have found their way into mainstream Canadian houses. As a result, the average new Canadian home consumes less energy than its predecessors. The Ontario building code has some of the most stringent thermal insulation and energy performance requirements of all provincial codes in Canada. However, significantly more can be done to economically reduce house energy consumption. A parametric analysis of a representative urban house was performed. This analysis suggests that there is significant room for improvement in the minimum Ontario Building Code requirements, especially with regard to the insulation and air tightness specifications. In 2006 the OBC requirements for above grade wall insulation were increased from R17 to R19 whereas this investigation found that R34 could be justified financially. The fenestration requirements in the 2006 OBC require windows to attain at least R2.8, while this investigation shows that a further 25% increase to R3.5 will soon be financially sensible.

Given positive integers c1,c2,...,ck with gcd(c1,c2,...,ck) = 1, the Frobenius problem (FP) is to compute the largest integer g(c1,c2,...,ck) that cannot be written as a non-negative integer linear combination of c1,c2,...,ck. The Frobenius problem in a free monoid (FPFM) is a non-commutative generalization of the Frobenius problem. Given words x1,x2,...,xk such that there are only finitely many words that cannot be written as concatenations of words in {x1,x2,...,xk}, the FPFM is to find the longest such words. Unlike the FP, where the upper bound g(c1,c2,...,ck)≤max 1≤i≤k ci2 is quadratic, the upper bound on the length of the longest words in the FPFM can be exponential in certain measures and some of the exponential upper bounds are tight. For the 2FPFM, where the given words over Σ are of only two distinct lengths m and n with 1<m<n, the length of the longest omitted words is ≤g(m, m|Σ|n-m + n - m). In Chapter 1, I give the definition of the FP in integers and summarize some of the interesting properties of the FP. In Chapter 2, I give the definition of the FPFM and discuss some general properties of the FPFM. Then I mainly focus on the 2FPFM. I discuss the 2FPFM from different points of view and present two equivalent problems, one of which is about combinatorics on words and the other is about the word graph. In Chapter 3, I discuss some variations on the FPFM and related problems, including input in other forms, bases with constant size, the case of infinite words, the case of concatenation with overlap, and the generalization of the local postage-stamp problem in a free monoid. In Chapter 4, I present the construction of some essential examples to complement the theory of the 2FPFM discussed in Chapter 2. The theory and examples of the 2FPFM are the main contribution of the thesis. In Chapter 5, I discuss the algorithms for and computational complexity of the FPFM and related problems. In the last chapter, I summarize the main results and list some open problems. Part of my work in the thesis has appeared in the papers.

The energy consumption of residential buildings in Canada accounts for 17% of national energy use (Trudeau, 2005). Production homes represent a considerable portion of new housing. In an effort to reduce the national energy demand, the energy consumption of these homes must be addressed. Techniques, methods and materials to achieve reductions in residential energy use are readily available. The goal of this thesis is to show that it is possible to build a low-energy home for less total carrying cost than a home built to the 2006 Ontario Building Code. To show how this is possible, a range of cost-effective and practical-to-implement upgrades are identified, and quantitative projections of cost-savings and benefits gained by the homeowner are generated. The interest in, and demand for, greener less energy consumptive homes is increasing. As oil prices rise, climate changes, landfills become overburdened and water restrictions become more frequent, the public pushes harder for change. The residential housing sector has seen increased demand for energy efficient homes that incorporate green features, high efficiency appliances and mechanical systems. Increased environmental concern has put ‘Green’ in demand. This thesis reviews a variety of North American green rating systems and contrasts their energy performance requirements with those of the Ontario Building Code. The Ontario Building Code was considered the baseline. Although the R2000 program was originally developed nearly 30 years ago it has managed to maintain a standard of performance that has always exceeded the OBC. It has a wider range of requirements than either the building code or ENERGY STAR, but falls short of the LEED for homes program in terms of breadth of environmental concerns. The literature review shows that homes that use 75% less heating energy than a standard house could be built in the 1980s for a mere 5% construction cost premium. When care is taken to produce quality designs and specifications, and to ensure that details are properly finished, these types of homes can be built almost anywhere. Some of the most successful technology and strategies of the 80’s have found their way into mainstream Canadian houses. As a result, the average new Canadian home consumes less energy than its predecessors. The Ontario building code has some of the most stringent thermal insulation and energy performance requirements of all provincial codes in Canada. However, significantly more can be done to economically reduce house energy consumption. A parametric analysis of a representative urban house was performed. This analysis suggests that there is significant room for improvement in the minimum Ontario Building Code requirements, especially with regard to the insulation and air tightness specifications. In 2006 the OBC requirements for above grade wall insulation were increased from R17 to R19 whereas this investigation found that R34 could be justified financially. The fenestration requirements in the 2006 OBC require windows to attain at least R2.8, while this investigation shows that a further 25% increase to R3.5 will soon be financially sensible.

Given positive integers c1,c2,...,ck with gcd(c1,c2,...,ck) = 1, the Frobenius problem (FP) is to compute the largest integer g(c1,c2,...,ck) that cannot be written as a non-negative integer linear combination of c1,c2,...,ck. The Frobenius problem in a free monoid (FPFM) is a non-commutative generalization of the Frobenius problem. Given words x1,x2,...,xk such that there are only finitely many words that cannot be written as concatenations of words in {x1,x2,...,xk}, the FPFM is to find the longest such words. Unlike the FP, where the upper bound g(c1,c2,...,ck)≤max 1≤i≤k ci2 is quadratic, the upper bound on the length of the longest words in the FPFM can be exponential in certain measures and some of the exponential upper bounds are tight. For the 2FPFM, where the given words over Σ are of only two distinct lengths m and n with 1<m<n, the length of the longest omitted words is ≤g(m, m|Σ|n-m + n - m). In Chapter 1, I give the definition of the FP in integers and summarize some of the interesting properties of the FP. In Chapter 2, I give the definition of the FPFM and discuss some general properties of the FPFM. Then I mainly focus on the 2FPFM. I discuss the 2FPFM from different points of view and present two equivalent problems, one of which is about combinatorics on words and the other is about the word graph. In Chapter 3, I discuss some variations on the FPFM and related problems, including input in other forms, bases with constant size, the case of infinite words, the case of concatenation with overlap, and the generalization of the local postage-stamp problem in a free monoid. In Chapter 4, I present the construction of some essential examples to complement the theory of the 2FPFM discussed in Chapter 2. The theory and examples of the 2FPFM are the main contribution of the thesis. In Chapter 5, I discuss the algorithms for and computational complexity of the FPFM and related problems. In the last chapter, I summarize the main results and list some open problems. Part of my work in the thesis has appeared in the papers.

I present numerical simulations of intensity and degree of polarization of light reflected by Earth-like exoplanets. The results are presented as a function of wavelength, and for a few different phase angles and a few different points on the planet. At this stage the aim is to show the working code and test a few different set ups of the star-planet system in order to find preferable configurations for observations. Not surprisingly, phase angle 90◦ shows the largest degree of polarization. For beneficial wavelength regions, visual light shows a larger overall degree of polarization, while NIR shows very clear absorption patterns in the degree of polarization, making detection of the atmospheric composition possible.