A (3+1)-evolutionary method in the framework of Regge Calculus, known as "Parallelisable Implicit Evolutionary Scheme", is analysed and revised so that it accounts for causality. Furthermore, the ambiguities associated with the notion of time in this evolutionary scheme are addressed and a solution to resolving such ambiguities is presented. The revised algorithm is then numerically tested and shown to produce the desirable results and indeed to resolve a problem previously faced upon implementing this scheme. An important issue that has been overlooked in "Parallelisable Implicit Evolutionary Scheme" was the restrictions on the choice of edge lengths used to build the space-time lattice as it evolves in time. It is essential to know what inequalities must hold between the edges of a 4-dimensional simplex, used to construct a space-time, so that the geometry inside the simplex is Minkowskian. The only known inequality on the Minkowski plane is the "Reverse Triangle Inequality" which holds between the edges of a triangle constructed only from space-like edges. However, a triangle, on the Minkowski plane, can be built from a combination of time-like, space-like or null edges. Part of this thesis is concerned with deriving a number of inequalities that must hold between the edges of mixed triangles. Finally, the Raychaudhuri equation is considered from the point of view of Regge Calculus. The Raychaudhuri equation plays an important role in many areas of relativistic Physics and Astrophysics, most importantly in the proof of singularity theorems. An analogue to the Raychaudhuri equation in the framework of Regge Calculus is derived. Both (2+1)-dimensional and (3+1)-dimensional cases are considered and analogues for average expansion and shear scalar are found.

Interacting galaxies are thought to be the essential building blocks of elliptical galaxies under the hierarchical galaxy formation scenario. The goal of my dissertation is to broaden our understanding of galaxy merger evolution through both observational studies and instrument developments. Observationally, I approach the goal photometrically and spectroscopically. The photometric studies better constrain the number density evolution of wet and dry mergers through five CFHTLS broad band photometry up to z~1. Meanwhile, by comparing the merger and elliptical galaxy mass density function, I discovered that the most massive mergers are not all formed via merging processes, unless the merging timescale is much longer than the expected value. Spectroscopically, the kinematic properties of close pair galaxies were studied to understand how star formation were quenched at z~0.5. I discovered that the number of red-red pairs are rare, which does not support the gravitational quenching mechanism suggested by the hot halo model. In instrumentation, one efficient way to study galaxy mergers is to use the integral field spectroscopic technique, capitalizing its intrinsic capability of obtaining 2-D spectra effectively. However, the currently available integral field spectrographs are inadequate to provide the required combination of integral field size and spectral resolution for merger studies. I, therefore, have developed two optical designs of a wide integral field infrared spectrograph (WIFIS), which I call WIFIS1 and WIFIS2, to satisfy the requirements of merger studies. Both the designs provide an integral field of 12" x 5" on 10-m telescopes (or equivalently 52" x 20" on 2.3-m telescopes). WIFIS1 delivers spectral resolving powers of 5,500 covering each of JHK bands in a single exposure; WIFIS2 does a lower power of 3,000 focusing on a shorter wavebands of zJ and H bands. All the WIFIS2 optical components have either been or being fabricated, and some of the components have been characterized in the laboratory, including its integral field unit, gratings, and mirrors. The expected completion of WIFIS based on WIFIS2 is 2013 summer, which will be followed by WIFIS1-based spectrograph in a few years.

Magnetohydrodynamics (MHD) studies the dynamics of an electrically conducting fluid under the influence of a magnetic field. Many astrophysical phenomena are related to MHD, and computer simulations are used to model these dynamics. In this thesis, we conduct MHD simulations of non-radiative black hole accretion as well as fast magnetic reconnection. By performing large scale three dimensional parallel MHD simulations on supercomputers and using a deformed-mesh algorithm, we were able to conduct very high dynamical range simulations of black hole accretion of Sgr A* at the Galactic Center. We find a generic set of solutions, and make specific predictions for currently feasible observations of rotation measure (RM). The magnetized accretion flow is subsonic and lacks outward convection flux, making the accretion rate very small and having a density slope of around $-1$. There is no tendency for the flows to become rotationally supported, and the slow time variability of the RM is a key quantitative signature of this accretion flow. We also provide a constructive numerical example of fast magnetic reconnection in a three-dimensional periodic box. Reconnection is initiated by a strong, localized perturbation to the field lines and the solution is intrinsically three-dimensional. Approximately $30\%$ of the magnetic energy is released in an event which lasts about one Alfv\'en time, but only after a delay during which the field lines evolve into a critical configuration. In the co-moving frame of the reconnection regions, reconnection occurs through an X-like point, analogous to the Petschek reconnection. The dynamics appear to be driven by global flows rather than local processes. In addition to issues pertaining to physics, we present results on the acceleration of MHD simulations using heterogeneous computing systems \cite. We have implemented the MHD code on a variety of heterogeneous and multi-core architectures (multi-core x86, Cell, Nvidia and ATI GPU) using different languages (FORTRAN, C, Cell, CUDA and OpenCL). Initial performance results for these systems are presented, and we conclude that substantial gains in performance over traditional systems are possible. In particular, it is possible to extract a greater percentage of peak theoretical performance from some heterogeneous systems when compared to x86 architectures.

This thesis aims to improve our understanding of the early stages of massive star formation and of the physical properties of interstellar clouds. To achieve this, I have used submillimeter continuum dust emission data obtained by the Balloon-borne Large Aperture submillimeter Telescope (BLAST) in the first science flight in 2005, with a 2-m telescope operating simultaneously at 250, 350, and 500 micron. Unfortunately, BLAST produced images of about 3'3 resolution due to an uncharacterized optical problem. In Chapter~2, I discuss implementation of the Lucy-Richardson (L-R) method of deconvolution to restore BLAST images to near diffraction limited resolution. Its performance and convergence have been extensively analyzed through simulations and comparison of deconvolved images with available high-resolution maps. In Chapter~3, I study diverse phenomena in the Cygnus~X region associated with high mass star-formation. To interpret the BLAST emission more fully and place the compact sources in context, archival data cubes of 13CO line emission from KOSMA, MIPS images from the Spitzer Legacy Survey of this region, and 21-cm radio continuum emission from the Canadian Galactic Plane Survey have been used. Utilizing available ancillary multi-wavelength observations, the influence of OB stars and stellar clusters on Cygnus~X has been studied,revisiting the well-known DR HII regions and their surroundings in the light of submillimeter continuum dust emission and CO line emission. An effort has been made to assess the evolutionary sequence of the compact sources (spatial extent of about 1~pc) on the basis of L-M diagram and subsequently to relate this sequence to independent empirical evidence and theory. Using multi-resolution observations, evidence for hierarchical substructures within molecular clouds has been examined. Finally, in Chapter~4, a multi-wavelength power spectrum analysis of the large scale brightness fluctuations in the Galactic plane is presented. This analysis has been used to assess the level of cirrus noise which limits the detection of faint sources. A characteristic power law exponent of about -2.7 has been obtained for sub-regions of Aquila and Cygnus~X. The observed relative amplitudes of power spectra at different wavelengths have been related through a spectral energy distribution, thereby determining a characteristic temperature for the Galactic diffuse emission.

In this thesis I present near-infrared detections of the thermal emission of a number of hot Jupiters and likely transit depth differences from different wavelength observations of a super-Earth. I have pioneered ``Staring Mode'' using the Wide-field Infrared Camera on the Canada-France-Hawaii Telescope to achieve the most accurate photometry to-date in the near-infrared from the ground. I also discuss avenues that should allow one to achieve even more accurate photometry in the future. Using WIRCam on CFHT my collaborators and I have detected the thermal emission of the following hot Jupiters: TrES-2b and TrES-3b in Ks-band, WASP-12b in the J, H \& Ks-bands, and WASP-3b in the Ks-band on two occasions. Near-infrared detections of the thermal emission of hot Jupiters are important, because the majority of these planets' blackbodies peak in this wavelength range; near-infrared detections allow us to obtain the most model-independent constraints on these planets' atmospheric characteristics, their temperature-pressure profiles with depth and an estimate of their bolometric luminosities. With these detections we are able to answer such questions as: how efficiently these planets redistribute heat to their nightsides, if they're being inflated by tidal heating, whether there's any evidence that one of these planets is precessing, and whether another experiences extreme weather and violent storms? My collaborators and I have also observed several transits of the super-Earth GJ 1214b. We find a deeper transit depth in one of our near-infrared bands than the other. This is likely indicative of a spectral absorption feature. For the differences in the transit depth to be as large as we observed, the atmosphere of GJ 1214b must have a large scale height, low mean molecular weight and thus have a hydrogen/helium dominated atmosphere. Given that other researchers have not found similar transit depth differences, we also discuss the most likely atmospheric makeup for this planet that results from a combination of all the observations to date. Lastly, by searching for long-term linear trends in radial velocity data, I constrain the theory that most hot Jupiters migrated to their present positions via the Kozai mechanism with tidal heating.

The lifetime of a Giant Molecular Cloud (GMC) and the total mass of stars that form within it are crucial to the understanding of star formation rates across a whole galaxy. In particular, the stars within a GMC may dictate its disruption and the quenching of further star formation. Indeed, observations show that the Milky Way contains GMCs with extensive expanding bubbles while the most massive stars are still alive. Simulating entire GMCs is challenging, due to the large variety of physics that needs to be included, and the computational power required to accurately simulate a GMC over tens of millions of years. Using the radiative-magneto-hydrodynamic code Enzo, I have run many simulations of GMCs. I obtain robust results for the fraction of gas converted into stars and the lifetimes of the GMCs: (A) In simulations with no stellar outputs (or ``feedback''), clusters form at a rate of 30% of GMC mass per free fall time; the GMCs were not disrupted but contained forming stars. (B) Including ionization gas pressure or radiation pressure into the simulations, both separately and together, the star formation was quenched at between 5% and 21% of the original GMC mass. The clouds were fully disrupted within two dynamical times after the first cluster formed. The radiation pressure contributed the most to the disruption of the GMC and fully quenched star formation even without ionization. (C) Simulations that included supernovae showed that they are not dynamically important to GMC disruption and have only minor effects on subsequent star formation. (D) The inclusion of a few micro Gauss magnetic field across the cloud slightly reduced the star formation rate but accelerated GMC disruption by reducing bubble shell disruption and leaking. These simulations show that new born stars quench further star formation and completely disrupt the parent GMC. The low star formation rate and the short lifetimes of GMCs shown here can explain the low star formation rate across the whole galaxy.

Magnetohydrodynamics (MHD) studies the dynamics of an electrically conducting fluid under the influence of a magnetic field. Many astrophysical phenomena are related to MHD, and computer simulations are used to model these dynamics. In this thesis, we conduct MHD simulations of non-radiative black hole accretion as well as fast magnetic reconnection. By performing large scale three dimensional parallel MHD simulations on supercomputers and using a deformed-mesh algorithm, we were able to conduct very high dynamical range simulations of black hole accretion of Sgr A* at the Galactic Center. We find a generic set of solutions, and make specific predictions for currently feasible observations of rotation measure (RM). The magnetized accretion flow is subsonic and lacks outward convection flux, making the accretion rate very small and having a density slope of around $-1$. There is no tendency for the flows to become rotationally supported, and the slow time variability of the RM is a key quantitative signature of this accretion flow. We also provide a constructive numerical example of fast magnetic reconnection in a three-dimensional periodic box. Reconnection is initiated by a strong, localized perturbation to the field lines and the solution is intrinsically three-dimensional. Approximately $30\%$ of the magnetic energy is released in an event which lasts about one Alfv\'en time, but only after a delay during which the field lines evolve into a critical configuration. In the co-moving frame of the reconnection regions, reconnection occurs through an X-like point, analogous to the Petschek reconnection. The dynamics appear to be driven by global flows rather than local processes. In addition to issues pertaining to physics, we present results on the acceleration of MHD simulations using heterogeneous computing systems \cite. We have implemented the MHD code on a variety of heterogeneous and multi-core architectures (multi-core x86, Cell, Nvidia and ATI GPU) using different languages (FORTRAN, C, Cell, CUDA and OpenCL). Initial performance results for these systems are presented, and we conclude that substantial gains in performance over traditional systems are possible. In particular, it is possible to extract a greater percentage of peak theoretical performance from some heterogeneous systems when compared to x86 architectures.

This thesis aims to improve our understanding of the early stages of massive star formation and of the physical properties of interstellar clouds. To achieve this, I have used submillimeter continuum dust emission data obtained by the Balloon-borne Large Aperture submillimeter Telescope (BLAST) in the first science flight in 2005, with a 2-m telescope operating simultaneously at 250, 350, and 500 micron. Unfortunately, BLAST produced images of about 3'3 resolution due to an uncharacterized optical problem. In Chapter~2, I discuss implementation of the Lucy-Richardson (L-R) method of deconvolution to restore BLAST images to near diffraction limited resolution. Its performance and convergence have been extensively analyzed through simulations and comparison of deconvolved images with available high-resolution maps. In Chapter~3, I study diverse phenomena in the Cygnus~X region associated with high mass star-formation. To interpret the BLAST emission more fully and place the compact sources in context, archival data cubes of 13CO line emission from KOSMA, MIPS images from the Spitzer Legacy Survey of this region, and 21-cm radio continuum emission from the Canadian Galactic Plane Survey have been used. Utilizing available ancillary multi-wavelength observations, the influence of OB stars and stellar clusters on Cygnus~X has been studied,revisiting the well-known DR HII regions and their surroundings in the light of submillimeter continuum dust emission and CO line emission. An effort has been made to assess the evolutionary sequence of the compact sources (spatial extent of about 1~pc) on the basis of L-M diagram and subsequently to relate this sequence to independent empirical evidence and theory. Using multi-resolution observations, evidence for hierarchical substructures within molecular clouds has been examined. Finally, in Chapter~4, a multi-wavelength power spectrum analysis of the large scale brightness fluctuations in the Galactic plane is presented. This analysis has been used to assess the level of cirrus noise which limits the detection of faint sources. A characteristic power law exponent of about -2.7 has been obtained for sub-regions of Aquila and Cygnus~X. The observed relative amplitudes of power spectra at different wavelengths have been related through a spectral energy distribution, thereby determining a characteristic temperature for the Galactic diffuse emission.

In this thesis I present near-infrared detections of the thermal emission of a number of hot Jupiters and likely transit depth differences from different wavelength observations of a super-Earth. I have pioneered ``Staring Mode'' using the Wide-field Infrared Camera on the Canada-France-Hawaii Telescope to achieve the most accurate photometry to-date in the near-infrared from the ground. I also discuss avenues that should allow one to achieve even more accurate photometry in the future. Using WIRCam on CFHT my collaborators and I have detected the thermal emission of the following hot Jupiters: TrES-2b and TrES-3b in Ks-band, WASP-12b in the J, H \& Ks-bands, and WASP-3b in the Ks-band on two occasions. Near-infrared detections of the thermal emission of hot Jupiters are important, because the majority of these planets' blackbodies peak in this wavelength range; near-infrared detections allow us to obtain the most model-independent constraints on these planets' atmospheric characteristics, their temperature-pressure profiles with depth and an estimate of their bolometric luminosities. With these detections we are able to answer such questions as: how efficiently these planets redistribute heat to their nightsides, if they're being inflated by tidal heating, whether there's any evidence that one of these planets is precessing, and whether another experiences extreme weather and violent storms? My collaborators and I have also observed several transits of the super-Earth GJ 1214b. We find a deeper transit depth in one of our near-infrared bands than the other. This is likely indicative of a spectral absorption feature. For the differences in the transit depth to be as large as we observed, the atmosphere of GJ 1214b must have a large scale height, low mean molecular weight and thus have a hydrogen/helium dominated atmosphere. Given that other researchers have not found similar transit depth differences, we also discuss the most likely atmospheric makeup for this planet that results from a combination of all the observations to date. Lastly, by searching for long-term linear trends in radial velocity data, I constrain the theory that most hot Jupiters migrated to their present positions via the Kozai mechanism with tidal heating.

The lifetime of a Giant Molecular Cloud (GMC) and the total mass of stars that form within it are crucial to the understanding of star formation rates across a whole galaxy. In particular, the stars within a GMC may dictate its disruption and the quenching of further star formation. Indeed, observations show that the Milky Way contains GMCs with extensive expanding bubbles while the most massive stars are still alive. Simulating entire GMCs is challenging, due to the large variety of physics that needs to be included, and the computational power required to accurately simulate a GMC over tens of millions of years. Using the radiative-magneto-hydrodynamic code Enzo, I have run many simulations of GMCs. I obtain robust results for the fraction of gas converted into stars and the lifetimes of the GMCs: (A) In simulations with no stellar outputs (or ``feedback''), clusters form at a rate of 30% of GMC mass per free fall time; the GMCs were not disrupted but contained forming stars. (B) Including ionization gas pressure or radiation pressure into the simulations, both separately and together, the star formation was quenched at between 5% and 21% of the original GMC mass. The clouds were fully disrupted within two dynamical times after the first cluster formed. The radiation pressure contributed the most to the disruption of the GMC and fully quenched star formation even without ionization. (C) Simulations that included supernovae showed that they are not dynamically important to GMC disruption and have only minor effects on subsequent star formation. (D) The inclusion of a few micro Gauss magnetic field across the cloud slightly reduced the star formation rate but accelerated GMC disruption by reducing bubble shell disruption and leaking. These simulations show that new born stars quench further star formation and completely disrupt the parent GMC. The low star formation rate and the short lifetimes of GMCs shown here can explain the low star formation rate across the whole galaxy.