Supernova remnants are the lasting interactions of shock waves that develop in the wake of supernovae. These remnants, especially those in our galaxy and our companion galaxies, allow us to study supernovae for thousands of years after the initial stellar explosions. Remnants that are formed from Ia supernovae, which are the explosions and complete annihilation of white dwarf stars, are of particular interest due to the explosions’ value as standard candles in cosmological studies. The shock waves in these young supernova remnants offer an unparalleled look into the physical processes that take place there, especially since these shocks are often simpler to study than shocks with strong radiative components that are present in remnants that are formed from the core-collapse supernovae of massive stars. I will detail the work of my kinematic study of the second youngest remnant in the Large Magellanic Cloud, 0509−67.5, which has been confirmed to be the result of a Ia supernova. Chapter 2 details the proper motion measurements made on the forward shock of this remnant, which has led to many key results. I was able to use the results of ii the global shock speed in the remnant to measure the density of neutral hydrogen in the ambient medium into which these shocks expand. In addition, I use the measurements of the shock speed for select portions of the forward shock to search for signatures of efficient cosmic-ray acceleration. Hydrodynamic simulations are then employed to constrain the age and ambient medium density of 0509−67.5, as well as to place limits on the compression factor at the immediate location of the blast wave. Chapter 3 uses the proper motion results from chapter 2 to determine possible asymmetries in the expansion of the remnant for the eastern and western limbs. These measurements are then used as constraints in hydrodynamic simulations to assess the possible dynamical offset of the explosion site compared to the geometric center of 0509−67.5 that we observe today. I find a continuum of possible offsets, which are sensitive to assumptions that are made about the evolutionary history of the remnant, and use the uncertainties in these calculations to determine the area in which to search for a leftover progenitor companion star in the event that the explosion resulted from a single-degenerate system. The stars within this search area are explored with a multi-band photometric study, wherein we determine the mass ranges for these candidates. Chapter four concludes this thesis, recapping the main results from chapters 2 and 3, and highlights the future projects I will carry out that are motivated by my findings in this comprehensive study of the supernova remnant 0509−67.5.

This dissertation seeks to understand ferroelectric domains, which can be viewed as networks of topological structural vortices, in a new class of materials called multiferroic hexagonal manganites RMnO3 (h-RMnO3) with R = rare earths, Y, In and Sc. From an experimental standpoint with solid theoretical background, we will briefly introduce improper ferroelectricity and topological defects in general in chapter 1. Then we start our discussion by reviewing the origin of the topological defect (vortex) in multiferroic material (h-RMnO3) and its self-organized domain network, which will act to motivate the work. We will also discuss the origin of self electric poling effect, self-organized criticality (SOC), and a rare phenomenon - vortex core fragmentation in chapter 2. This will be followed by chapter 3 which mainly discusses the manipulation of topological vortex by applying an external shear strain. The force on vortices in h-RMnO3 generated by shear strain is analogous to the Magnus force that moves superfluid vortices in the direction transverse to the superfluid current. Chapter 4 starts with a brief introduction to the Kibble-Zurek Mechanism (KZM), which is the theoretical background of the connection between cosmology and condensed matter physics. It turns out that multiferroic h-RMnO3 is an excellent test bed for KZM through the study of defect formation, emergent continuous symmetry, and Higgs condensation of the disorder field. In the remaining chapter, we extend our scope from the standard vortex to its "dual description"  – partially undistorted antipolar (PUA) vortex. Then we will end this dissertation with a summary of the results and future research directions, which actually open a new path to understand the fundamental properties of this new class of materials.

The star formation histories (SFHs) of galaxies have long been approximated by simple parametric forms while estimating quantities like stellar masses, star formation rates and ages. However, there is considerable diversity seen among galaxy SFHs in cosmological simulations, and individual SFHs are variable across a range of timescales corresponding to the various physical processes that govern star formation. With higher S/N multiwavelength Spectral Energy Distributions (SEDs) from broadband photometry and sophisticated analysis tools, we develop the Dense Basis SED fitting method (Iyer & Gawiser 2017) to reconstruct the SFHs of individual galaxies with uncertainties. Applying this method to CANDELS data, we reconstruct the SFHs of nearly 50,000 galaxies across a wide range of redshifts. An updated version of the method (Iyer et al. 2019) uses Gaussian Processes to create smooth SFHs that are independent of any choice of functional form, with a flexible number of parameters that recover the maximum amount of information from individual SEDs. Using this method, we estimate the number and duration of major star formation episodes in a galaxy's past, in addition to quantifying the evolution of galaxy SFHs with mass, morphology, and redshift. The distribution of SFHs at a particular epoch constrains feedback and wind strengths modeled in simulations of galaxy evolution. (Iyer et al. 2018) uses SFHs as trajectories in SFR-M* space to probe the previously inaccessible low-mass, high-redshift regime of the SFR-M* correlation. This new technique of SFH reconstruction allows us to probe a wide range of quantities that were previously inaccessible through SED fitting, creating new possibilities of probing galaxy formation and evolution at high redshifts.

Dusty star-forming galaxies (DSFGs) are some of the most luminous and rapidly star-forming systems in the Universe. However, the large dust content present in these galaxies absorbs the optical light produced from stars and re-radiates it out to longer wavelengths, primarily in the infrared. As a result, this population of galaxies that are forming stars at rates of up 1000 M_sun/year were missed in surveys that looked only in the optical regime. The true nature of these galaxies did not start to come to light until the late 1990s when they were discovered in large numbers in submillimeter surveys. In this thesis, I present results on the 30 brightest DSFGs among a larger sample first identified in the Atacama Cosmology Telescope 470 deg² equatorial field survey observed at 148, 218, and 277 GHz. In Chapter 2, I present a detailed analysis from Northern Extended Millimeter Array (NOEMA) CO data of ACT J0209, a strongly-lensed source. In Chapter 3, I present a similar preliminary analysis on an additional source, ACT J2029, that combines the use of both NOEMA and Hubble Space Telesope (HST) data. In Chapter 4, I present a more sample-wide analysis by including additional NOEMA data and Submillimeter Array (SMA) data to characterize the physical properties of the sample. And finally in Chapter 5, I discuss future prospects for both the subsample of 30 DSFGs and the parent DSFG sample.

Modern galaxy formation and evolution models are able to match the statistical properties of galaxy populations across most of cosmic history. However, detailed observations and sophisticated analytical methods are still needed to test theoretical predictions in extreme scenarios, where the complex interplay of gas accretion, star formation, galaxy interactions, feedback, and other physical processes can have compounded impacts on interstellar medium properties. I discuss results from new far-infrared and submillimeter observations of star-forming galaxies in four massive galaxy clusters at redshifts 0.3 ≲ z ≲ 1.1. Despite being surrounded by hot intracluster plasma, some cluster members are able to retain their cold gas reservoirs, and have high dust-obscured star formation rates. I find that the prevalence of star-forming cluster galaxies increases with increasing redshift. I also present results from integral field spectroscopy, centered on the Paα line, targeting a sample of rare, low-redshift, compact starbursts that strongly resemble z ~ 3 Lyman break galaxies (LBGs). H2 ro-vibrational emission is measured for the first time in either distant LBGs or their low-z analogs. Warm molecular gas and ionized gas properties suggest that star formation feedback is the dominant excitation mechanism in these systems. I also find that, compared to typical nearby star-forming galaxies, LBG analogs are characterized by high velocity dispersions and low ordered-to-disordered velocity ratios. LBG analogs deviate from kinematic scaling relations such as the stellar mass and baryonic Tully-Fisher relations; their anomalously low kinematic support may be attributed to their small physical sizes. Finally, I optimize a deep convolutional neural network (CNN) to predict the gas-phase metallicities of typical low-z star-forming galaxies from three-band optical imaging. The trained CNN is not only able to accurately estimate metallicity, but also can reconstruct the empirical mass-metallicity relation with zero additional scatter. These results imply that multi-color morphological features are important for understanding the connection between galaxies' stellar mass assembly and chemical enrichment histories.

Concerning the early evolution history of our universe and distant galaxies that are expected to be uncovered with future telescopes, we present a collection of comprehensive, physically-backed forecasts for galaxy populations across cosmic time and their interaction with the cosmic environment. Our predictions cover galaxies spanning a remarkably wide range of mass and redshift, for which we provide a large variety of physical and observable properties, and from which we derive the production rate of energetic photons and the subsequent reionization history. These pre-eminent results are achieved with a custom-built modelling pipeline based on the versatile Santa Cruz semi-analytic model for galaxy formation and the new model components introduced in this work. This efficient modelling pipeline established an effective link between the ‘ground-level’ galaxy formation physics and the ‘top-level’ cosmological-scale observables, which also enables controlled experiments that help pinpoint the set of physical processes that have leading effects on cosmological events and quantifying their impacts. This work demonstrates the enormous potential of using semi-analytic models to inform the planning of optimal survey strategies, support scientific rationale for observing programs, and facilitate physical interpretation for observed objects. In anticipation of the soon-to-be-launched James Webb Space Telescope, a portion of our predictions are tailored to explore its capability on detecting faint, distant galaxies and on constraining key galaxy formation physics.

Using an array of multi-wavelength data, we examine a variety of astrophysical problems with gravitational lensing. First, we seek to understand the mass distribution of an early-type galaxy with an analysis of the lens Q0957+561. We dissect the lens galaxy into luminous and dark components, and model the environment using results from weak lensing. Combining constraints from newly-discovered lensed images and stellar population models we find the lens has a density profile which is shallower than isothermal, unlike those of typical early-type galaxies. Finally, using the measured time delay between the quasar images we find the Hubble constant to be H₀=79.3^+6.7_-8.5 km s^-1 Mpc^-1. One intriguing application of lensing is to exploit the lens magnification boost to study high-redshift objects in greater detail than otherwise possible. Here, we analyze the mid-infrared properties of two lensed z~2 star-forming galaxies, SDSS J120602.09+514229.5 and SDSS J090122.37+181432.3, using Spitzer/IRS spectra to study their rest-frame ~ 5-12 micron emission. Both systems exhibit strong polycyclic aromatic hydrocarbon (PAH) features in the spectra, indicating strong star formation and the absence of significant AGN activity. For SDSS J090122.37+181432.3, this detection belies that inferred from optical measurements, indicating mid-IR spectroscopy provides key information needed to understand the properties of high-redshift star-forming galaxies. While lensing provides measurements of the macroscopic properties of lens systems, it can also shed light on small-scale structure of galaxies. To identify and understand lens substructure, we examine the multi-wavelength properties of flux ratios for six lenses. Variations of the flux ratios with wavelength can be used to study the lensed quasars and the small-scale mass distribution of lens galaxies. We detect strong multi-wavelength variations in the lenses HE 0435-1223 and SDSS 0806+2006. For HE 0435-1223, we study its substructure with a series of lens models which add clumps of mass near the lensed images. We detect the presence of a clump near image A, with a mass of log(M_A(<Rein))=7.68^+0.92_-0.85. We also find support for a second clump, near image B, with mass log(M_B(<Rein))=6.6^+1.02_-1.52, although evidence for this clump is not decisive. Using Monte Carlo simulations, we connect these clumps to their associated populations, finding the mass fraction in substructure to be > 0.00092.

My graduate studies involved three broad classes of problems, each of which are presented in different chapters of this thesis. The first two parts of my work were related to studying dynamics of biochemical networks. I studied a mean-field/stochastic model of epigenetic chromatin silencing in yeast. The model gives rise to different dynamical behaviors possible within the same molecular model and provides qualitative predictions that are being investigated experimentally. In another part of my work, I studied a model of segment polarity network in Drosophila and analyzed the parameter space of the system. I particularly studied the relation between the geometry of parameter space and the robustness of the network. I will show that, in addition to the volume, the geometry of this region has important consequences for the robustness and the fragility of a network. A major part of my PhD work involved applications of high-throughput sequencing technologies for extracting information at the genomic level. I present SOPRA, a new algorithm for exploiting the mate pair information for assembly of short reads. I have successfully applied SOPRA to real data and were able to assemble scaffolds of significant length with very few errors introduced in the process.

Using a combination of numerical and analytical techniques, I present characterizations of ferroelectric materials in bulk, thin-film and nanostructure geometries. My results have impact on ongoing research and on design for nanodevices. Size-dependent effects in ferroelectrics are important due to their long-range electrostatic interactions; thus their dielectric properties depend on electromechanical boundary conditions. In my first study, I address the effects of strain on the measured properties of thin-film (TF) ferroelectrics. It has been suggested that the observed suppression of many TF dielectric characteristics implies underlying strain gradients in the film. I show that the same effects can be explained by a simpler model with homogeneous strain, and I suggest a “smoking gun” benchtop probe. The quantum paraelectric-ferroelectric transition (QPFT) is the topic of my second study. Using methods including finite-size scaling and self-consistent Gaussian theory, I calculate the classical-quantum crossover in the dielectric susceptbility and the resulting temperature-pressure phase diagram; comparison with current experiment is excellent and predictions are made for future measurements. Here, temperature can be considered a “finite-size effet” in time, and previous results on the QPFT using diagrammatic techniques are recovered and extended using this approach. Recent synthesis of artificially structured oxides with “checkerboard” patterning at the nanoscale has been reported, and this serves as motivation for my third study. Here, I use first-principles methods to characterize an atomic-scale BiFeO3-BiMnO3 nanocheckerboard, and find that it has properties that are distinctive from those of either parent compound. More specifically, it has both a spontaneous polarization and magnetization, and also displays a magnetostructural effect. My work on this prototypical multiferroic nanocheckerboard motivates further theoretical and experimental studies of new heterostructures with properties that are geometrically induced.