Direct simulation of quantum dynamics in complex systems

Accurate simulation of quantum dynamics in complex systems poses a fundamental theoretical challenge with immediate application to problems in biological catalysis, charge transfer, and solar energy conversion. The varied length- and timescales that characterize these kinds of processes necessitate development of novel simulation methodology that can both accurately evolve the coupled quantum and classical degrees of freedom and also be easily applicable to large, complex systems. In the following dissertation, the problems of quantum dynamics in complex systems are explored through direct simulation using path-integral methods as well as application of state-of-the-art analytical rate theories.

The search for gravitational waves from the coalescence of black hole binary systems in data from the LIGO and Virgo detectors. Or: A dark walk through a random forest

The LIGO and Virgo gravitational-wave observatories are complex and extremely sensitive strain detectors that can be used to search for a wide variety of gravitational waves from astrophysical and cosmological sources. In this thesis, I motivate the search for the gravitational wave signals from coalescing black hole binary systems with total mass between 25 and 100 solar masses. The mechanisms for formation of such systems are not well-understood, and we do not have many observational constraints on the parameters that guide the formation scenarios. Detection of gravitational waves from such systems — or, in the absence of detection, the tightening of upper limits on the rate of such coalescences — will provide valuable information that can inform the astrophysics of the formation of these systems. I review the search for these systems and place upper limits on the rate of black hole binary coalescences with total mass between 25 and 100 solar masses. I then show how the sensitivity of this search can be improved by up to 40% by the the application of the multivariate statistical classifier known as a random forest of bagged decision trees to more effectively discriminate between signal and non-Gaussian instrumental noise. I also discuss the use of this classifier in the search for the ringdown signal from the merger of two black holes with total mass between 50 and 450 solar masses and present upper limits. I also apply multivariate statistical classifiers to the problem of quantifying the non-Gaussianity of LIGO data. Despite these improvements, no gravitational-wave signals have been detected in LIGO data so far. However, the use of multivariate statistical classification can significantly improve the sensitivity of the Advanced LIGO detectors to such signals.

Nanophotonic Light Trapping In Thin Solar Cells

Over the last several decades there have been significant advances in the study and understanding of light behavior in nanoscale geometries. Entire fields such as those based on photonic crystals, plasmonics and metamaterials have been developed, accelerating the growth of knowledge related to nanoscale light manipulation. Coupled with recent interest in cheap, reliable renewable energy, a new field has blossomed, that of nanophotonic solar cells.

In this thesis, we examine important properties of thin-film solar cells from a nanophotonics perspective. We identify key differences between nanophotonic devices and traditional, thick solar cells. We propose a new way of understanding and describing limits to light trapping and show that certain nanophotonic solar cell designs can have light trapping limits above the so called ray-optic or ergodic limit. We propose that a necessary requisite to exceed the traditional light trapping limit is that the active region of the solar cell must possess a local density of optical states (LDOS) higher than that of the corresponding, bulk material. Additionally, we show that in addition to having an increased density of states, the absorber must have an appropriate incoupling mechanism to transfer light from free space into the optical modes of the device. We outline a portfolio of new solar cell designs that have potential to exceed the traditional light trapping limit and numerically validate our predictions for select cases.

We emphasize the importance of thinking about light trapping in terms of maximizing the optical modes of the device and efficiently coupling light into them from free space. To further explore these two concepts, we optimize patterns of superlattices of air holes in thin slabs of Si and show that by adding a roughened incoupling layer the total absorbed current can be increased synergistically. We suggest that the addition of a random scattering surface to a periodic patterning can increase incoupling by lifting the constraint of selective mode occupation associated with periodic systems.

Lastly, through experiment and simulation, we investigate a potential high efficiency solar cell architecture that can be improved with the nanophotonic light trapping concepts described in this thesis. Optically thin GaAs solar cells are prepared by the epitaxial liftoff process by removal from their growth substrate and addition of a metallic back reflector. A process of depositing large area nano patterns on the surface of the cells is developed using nano imprint lithography and implemented on the thin GaAs cells.

A quantitative investigation of the solar modulation of cosmic-ray protons and helium nuclei

The differential energy spectra of cosmic-ray protons and He nuclei have been measured at energies up to 315 MeV/nucleon using balloon- and satellite-borne instruments. These spectra are presented for solar quiet times for the years 1966 through 1970. The data analysis is verified by extensive accelerator calibrations of the detector systems and by calculations and measurements of the production of secondary protons in the atmosphere.

The spectra of protons and He nuclei in this energy range are dominated by the solar modulation of the local interstellar spectra. The transport equation governing this process includes as parameters the solar-wind velocity, V, and a diffusion coefficient, K(r,R), which is assumed to be a scalar function of heliocentric radius, r, and magnetic rigidity, R. The interstellar spectra, j_D, enter as boundary conditions on the solutions to the transport equation. Solutions to the transport equation have been calculated for a broad range of assumed values for K(r,R) and j_D and have been compared with the measured spectra.

It is found that the solutions may be characterized in terms of a dimensionless parameter, ψ(r,R) = ^∞∫_r V dr'/(K(r',R). The amount of modulation is roughly proportional to ψ. At high energies or far from the Sun, where the modulation is weak, the solution is determined primarily by the value of ψ (and the interstellar spectrum) and is not sensitive to the radial dependence of the diffusion coefficient. At low energies and for small r, where the effects of adiabatic deceleration are found to be large, the spectra are largely determined by the radial dependence of the diffusion coefficient and are not very sensitive to the magnitude of ψ or to the interstellar spectra. This lack of sensitivity to j_D implies that the shape of the spectra at Earth cannot be used to determine the interstellar intensities at low energies.

Values of ψ determined from electron data were used to calculate the spectra of protons and He nuclei near Earth. Interstellar spectra of the form j_D α (W - 0.25m)^-2.65 for both protons and He nuclei were found to yield the best fits to the measured spectra for these values of ψ, where W is the total energy and m is the rest energy. A simple model for the diffusion coefficient was used in which the radial and rigidity dependence are separable and K is independent of radius inside a modulation region which has a boundary at a distance D. Good agreement was found between the measured and calculated spectra for the years 1965 through 1968, using typical boundary distances of 2.7 and 6.1 A.U. The proton spectra observed in 1969 and 1970 were flatter than in previous years. This flattening could be explained in part by an increase in D, but also seemed to require that a noticeable fraction of the observed protons at energies as high at 50 to 100 MeV be attributed to quiet-time solar emission. The turnup in the spectra at low energies observed in all years was also attributed to solar emission. The diffusion coefficient used to fit the 1965 spectra is in reasonable agreement with that determined from the power spectra of the interplanetary magnetic field (Jokipii and Coleman, 1968). We find a factor of roughly 3 increase in ψ from 1965 to 1970, corresponding to the roughly order of magnitude decrease in the proton intensity at 250 MeV. The change in ψ might be attributed to a decrease in the diffusion coefficient, or, if the diffusion coefficient is essentially unchanged over that period (Mathews et al., 1971), might be attributed to an increase in the boundary distance, D.

Cosmic Explosions: Observations Of Infant Hydrogen-Free Supernovae Towards An Understanding Of Their Parent Systems

Radiation in the first days of supernova explosions contains rich information about physical properties of the exploding stars. In the past three years, I used the intermediate Palomar Transient Factory to conduct one-day cadence surveys, in order to systematically search for infant supernovae. I show that the one-day cadences in these surveys were strictly controlled, that the realtime image subtraction pipeline managed to deliver transient candidates within ten minutes of images being taken, and that we were able to undertake follow-up observations with a variety of telescopes within hours of transients being discovered. So far iPTF has discovered over a hundred supernovae within a few days of explosions, forty-nine of which were spectroscopically classified within twenty-four hours of discovery.

Our observations of infant Type Ia supernovae provide evidence for both the single-degenerate and double-degenerate progenitor channels. On the one hand, a low-velocity Type Ia supernova iPTF14atg revealed a strong ultraviolet pulse within four days of its explosion. I show that the pulse is consistent with the expected emission produced by collision between the supernova ejecta and a companion star, providing direct evidence for the single degenerate channel. By comparing the distinct early-phase light curves of iPTF14atg to an otherwise similar event iPTF14dpk, I show that the viewing angle dependence of the supernova-companion collision signature is probably responsible to the difference of the early light curves. I also show evidence for a dark period between the supernova explosion and the first light of the radioactively-powered light curve. On the other hand, a peculiar Type Ia supernova iPTF13asv revealed strong near-UV emission and absence of iron in the spectra within the first two weeks of explosion, suggesting a stratified ejecta structure with iron group elements confined to the slow-moving part of the ejecta. With its total ejecta mass estimated to exceed the Chandrasekhar limit, I show that the stratification and large mass of the ejecta favor the double-degenerate channel.

In a separate approach, iPTF found the first progenitor system of a Type Ib supernova iPTF13bvn in the pre-explosion HST archival mages. Independently, I used the early-phase optical observations of this supernova to constrain its progenitor radius to be no larger than several solar radii. I also used its early radio detections to derive a mass loss rate of 3e-5 solar mass per year for the progenitor right before the supernova explosion. These constraints on the physical properties of the iPTF13bvn progenitor provide a comprehensive data set to test Type Ib supernova theories. A recent HST revisit to the iPTF13bvn site two years after the supernova explosion has confirmed the progenitor system.

Moving forward, the next frontier in this area is to extend these single-object analyses to a large sample of infant supernovae. The upcoming Zwicky Transient Facility with its fast survey speed, which is expected to find one infant supernova every night, is well positioned to carry out this task.

Real-time load-side control of electric power systems

Two trends are emerging from modern electric power systems: the growth of renewable (e.g., solar and wind) generation, and the integration of information technologies and advanced power electronics. The former introduces large, rapid, and random fluctuations in power supply, demand, frequency, and voltage, which become a major challenge for real-time operation of power systems. The latter creates a tremendous number of controllable intelligent endpoints such as smart buildings and appliances, electric vehicles, energy storage devices, and power electronic devices that can sense, compute, communicate, and actuate. Most of these endpoints are distributed on the load side of power systems, in contrast to traditional control resources such as centralized bulk generators. This thesis focuses on controlling power systems in real time, using these load side resources. Specifically, it studies two problems.

(1) Distributed load-side frequency control: We establish a mathematical framework to design distributed frequency control algorithms for flexible electric loads. In this framework, we formulate a category of optimization problems, called optimal load control (OLC), to incorporate the goals of frequency control, such as balancing power supply and demand, restoring frequency to its nominal value, restoring inter-area power flows, etc., in a way that minimizes total disutility for the loads to participate in frequency control by deviating from their nominal power usage. By exploiting distributed algorithms to solve OLC and analyzing convergence of these algorithms, we design distributed load-side controllers and prove stability of closed-loop power systems governed by these controllers. This general framework is adapted and applied to different types of power systems described by different models, or to achieve different levels of control goals under different operation scenarios. We first consider a dynamically coherent power system which can be equivalently modeled with a single synchronous machine. We then extend our framework to a multi-machine power network, where we consider primary and secondary frequency controls, linear and nonlinear power flow models, and the interactions between generator dynamics and load control.

(2) Two-timescale voltage control: The voltage of a power distribution system must be maintained closely around its nominal value in real time, even in the presence of highly volatile power supply or demand. For this purpose, we jointly control two types of reactive power sources: a capacitor operating at a slow timescale, and a power electronic device, such as a smart inverter or a D-STATCOM, operating at a fast timescale. Their control actions are solved from optimal power flow problems at two timescales. Specifically, the slow-timescale problem is a chance-constrained optimization, which minimizes power loss and regulates the voltage at the current time instant while limiting the probability of future voltage violations due to stochastic changes in power supply or demand. This control framework forms the basis of an optimal sizing problem, which determines the installation capacities of the control devices by minimizing the sum of power loss and capital cost. We develop computationally efficient heuristics to solve the optimal sizing problem and implement real-time control. Numerical experiments show that the proposed sizing and control schemes significantly improve the reliability of voltage control with a moderate increase in cost.