Water in silicate glasses

The speciation of water in a variety of hydrous silicate glasses, including simple and rhyolitic compositions, synthesized over a range of experimental conditions with up to 11 weight percent water has been determined using infrared spectroscopy. This technique has been calibrated with a series of standard glasses and provides a precise and accurate method for determining the concentrations of molecular water and hydroxyl groups in these glasses.

For all the compositions studied, most of the water is dissolved as hydroxyl groups at total water contents less than 3-4 weight percent; at higher total water contents, molecular water becomes the dominant species. For total water contents above 3-4 weight percent, the amount of water dissolved as hydroxyl groups is approximately constant at about 2 weight percent and additional water is incorporated as molecular water. Although there are small but measurable differences in the ratio of molecular water to hydroxyl groups at a given total water content among these silicate glasses, the speciation of water is similar over this range of composition. The trends in the concentrations of the H-bearing species in the hydrous glasses included in this study are similar to those observed in other silicate glasses using either infrared or NMR spectroscopy.

The effects of pressure and temperature on the speciation of water in albitic glasses have been investigated. The ratio of molecular water to hydroxyl groups at a given total water content is independent of the pressure and temperature of equilibration for albitic glasses synthesized in rapidly quenching piston cylinder apparatus at temperatures greater than 1000°C and pressures greater than 8 kbar. For hydrous glasses quenched from melts cooled at slower rates (i.e., in internally heated or in air-quench cold seal pressure vessels), there is an increase in the ratio of molecular water to hydroxyl group content that probably reflects reequilibration of the melt to lower temperatures during slow cooling.

Molecular water and hydroxyl group concentrations in glasses provide information on the dissolution mechanisms of water in silicate liquids. Several mixing models involving homogeneous equilibria of the form H_2O + O = 20H among melt species have been explored for albitic melts. These models can account for the measured species concentrations if the effects of non-ideal behavior or mixing of polymerized units are included, or by allowing for the presence of several different types of anhydrous species.

A thermodynamic model for hydrous albitic melts has been developed based on the assumption that the activity of water in the melt is equal to the mole fraction of molecular water determined by infrared spectroscopy. This model can account for the position of the watersaturated solidus of crystalline albite, the pressure and temperature dependence of the solubility of water in albitic melt, and the volumes of hydrous albitic melts. To the extent that it is successful, this approach provides a direct link between measured species concentrations in hydrous albitic glasses and the macroscopic thermodynamic properties of the albite-water system.

The approach taken in modelling the thermodynamics of hydrous albitic melts has been generalized to other silicate compositions. Spectroscopic measurements of species concentrations in rhyolitic and simple silicate glasses quenched from melts equilibrated with water vapor provide important constraints on the thermodynamic properties of these melt-water systems. In particular, the assumption that the activity of water is equal to the mole fraction of molecular water has been tested in detail and shown to be a valid approximation for a range of hydrous silicate melts and the partial molar volume of water in these systems has been constrained. Thus, the results of this study provide a useful thermodynamic description of hydrous melts that can be readily applied to other melt-water systems for which spectroscopic measurements of the H-bearing species are available.

Design strategies for ultra-high efficiency photovoltaics

While concentrator photovoltaic cells have shown significant improvements in efficiency in the past ten years, once these cells are integrated into concentrating optics, connected to a power conditioning system and deployed in the field, the overall module efficiency drops to only 34 to 36%. This efficiency is impressive compared to conventional flat plate modules, but it is far short of the theoretical limits for solar energy conversion. Designing a system capable of achieving ultra high efficiency of 50% or greater cannot be achieved by refinement and iteration of current design approaches.

This thesis takes a systems approach to designing a photovoltaic system capable of 50% efficient performance using conventional diode-based solar cells. The effort began with an exploration of the limiting efficiency of spectrum splitting ensembles with 2 to 20 sub cells in different electrical configurations. Incorporating realistic non-ideal performance with the computationally simple detailed balance approach resulted in practical limits that are useful to identify specific cell performance requirements. This effort quantified the relative benefit of additional cells and concentration for system efficiency, which will help in designing practical optical systems.

Efforts to improve the quality of the solar cells themselves focused on the development of tunable lattice constant epitaxial templates. Initially intended to enable lattice matched multijunction solar cells, these templates would enable increased flexibility in band gap selection for spectrum splitting ensembles and enhanced radiative quality relative to metamorphic growth. The III-V material family is commonly used for multijunction solar cells both for its high radiative quality and for the ease of integrating multiple band gaps into one monolithic growth. The band gap flexibility is limited by the lattice constant of available growth templates. The virtual substrate consists of a thin III-V film with the desired lattice constant. The film is grown strained on an available wafer substrate, but the thickness is below the dislocation nucleation threshold. By removing the film from the growth substrate, allowing the strain to relax elastically, and bonding it to a supportive handle, a template with the desired lattice constant is formed. Experimental efforts towards this structure and initial proof of concept are presented.

Cells with high radiative quality present the opportunity to recover a large amount of their radiative losses if they are incorporated in an ensemble that couples emission from one cell to another. This effect is well known, but has been explored previously in the context of sub cells that independently operate at their maximum power point. This analysis explicitly accounts for the system interaction and identifies ways to enhance overall performance by operating some cells in an ensemble at voltages that reduce the power converted in the individual cell. Series connected multijunctions, which by their nature facilitate strong optical coupling between sub-cells, are reoptimized with substantial performance benefit.

Photovoltaic efficiency is usually measured relative to a standard incident spectrum to allow comparison between systems. Deployed in the field systems may differ in energy production due to sensitivity to changes in the spectrum. The series connection constraint in particular causes system efficiency to decrease as the incident spectrum deviates from the standard spectral composition. This thesis performs a case study comparing performance of systems over a year at a particular location to identify the energy production penalty caused by series connection relative to independent electrical connection.

Self-healing Techniques for RF and mm-Wave Transmitters and Receivers

With continuing advances in CMOS technology, feature sizes of modern Silicon chip-sets have gone down drastically over the past decade. In addition to desktops and laptop processors, a vast majority of these chips are also being deployed in mobile communication devices like smart-phones and tablets, where multiple radio-frequency integrated circuits (RFICs) must be integrated into one device to cater to a wide variety of applications such as Wi-Fi, Bluetooth, NFC, wireless charging, etc. While a small feature size enables higher integration levels leading to billions of transistors co-existing on a single chip, it also makes these Silicon ICs more susceptible to variations. A part of these variations can be attributed to the manufacturing process itself, particularly due to the stringent dimensional tolerances associated with the lithographic steps in modern processes. Additionally, RF or millimeter-wave communication chip-sets are subject to another type of variation caused by dynamic changes in the operating environment. Another bottleneck in the development of high performance RF/mm-wave Silicon ICs is the lack of accurate analog/high-frequency models in nanometer CMOS processes. This can be primarily attributed to the fact that most cutting edge processes are geared towards digital system implementation and as such there is little model-to-hardware correlation at RF frequencies.

All these issues have significantly degraded yield of high performance mm-wave and RF CMOS systems which often require multiple trial-and-error based Silicon validations, thereby incurring additional production costs. This dissertation proposes a low overhead technique which attempts to counter the detrimental effects of these variations, thereby improving both performance and yield of chips post fabrication in a systematic way. The key idea behind this approach is to dynamically sense the performance of the system, identify when a problem has occurred, and then actuate it back to its desired performance level through an intelligent on-chip optimization algorithm. We term this technique as self-healing drawing inspiration from nature's own way of healing the body against adverse environmental effects. To effectively demonstrate the efficacy of self-healing in CMOS systems, several representative examples are designed, fabricated, and measured against a variety of operating conditions.

We demonstrate a high-power mm-wave segmented power mixer array based transmitter architecture that is capable of generating high-speed and non-constant envelope modulations at higher efficiencies compared to existing conventional designs. We then incorporate several sensors and actuators into the design and demonstrate closed-loop healing against a wide variety of non-ideal operating conditions. We also demonstrate fully-integrated self-healing in the context of another mm-wave power amplifier, where measurements were performed across several chips, showing significant improvements in performance as well as reduced variability in the presence of process variations and load impedance mismatch, as well as catastrophic transistor failure. Finally, on the receiver side, a closed-loop self-healing phase synthesis scheme is demonstrated in conjunction with a wide-band voltage controlled oscillator to generate phase shifter local oscillator (LO) signals for a phased array receiver. The system is shown to heal against non-idealities in the LO signal generation and distribution, significantly reducing phase errors across a wide range of frequencies.

Transmission matrices and lumped parameter models for continuous systems

The use of transmission matrices and lumped parameter models for describing continuous systems is the subject of this study. Non-uniform continuous systems which play important roles in practical vibration problems, e.g., torsional oscillations in bars, transverse bending vibrations of beams, etc., are of primary importance.

A new approach for deriving closed form transmission matrices is applied to several classes of non-uniform continuous segments of one dimensional and beam systems. A power series expansion method is presented for determining approximate transmission matrices of any order for segments of non-uniform systems whose solutions cannot be found in closed form. This direct series method is shown to give results comparable to those of the improved lumped parameter models for one dimensional systems.

Four types of lumped parameter models are evaluated on the basis of the uniform continuous one dimensional system by comparing the behavior of the frequency root errors. The lumped parameter models which are based upon a close fit to the low frequency approximation of the exact transmission matrix, at the segment level, are shown to be superior. On this basis an improved lumped parameter model is recommended for approximating non-uniform segments. This new model is compared to a uniform segment approximation and error curves are presented for systems whose areas very quadratically and linearly. The effect of varying segment lengths is investigated for one dimensional systems and results indicate very little improvement in comparison to the use of equal length segments. For purposes of completeness, a brief summary of various lumped parameter models and other techniques which have previously been used to approximate the uniform Bernoulli-Euler beam is a given.

Optimum linear coding for additive noise systems using information feedback

The feedback coding problem for Gaussian systems in which the noise is neither white nor statistically independent between channels is formulated in terms of arbitrary linear codes at the transmitter and at the receiver. This new formulation is used to determine a number of feedback communication systems. In particular, the optimum linear code that satisfies an average power constraint on the transmitted signals is derived for a system with noiseless feedback and forward noise of arbitrary covariance. The noisy feedback problem is considered and signal sets for the forward and feedback channels are obtained with an average power constraint on each. The general formulation and results are valid for non-Gaussian systems in which the second order statistics are known, the results being applicable to the determination of error bounds via the Chebychev inequality.

I. Quantal effects in biochemical cooperativity and a proposed mechanism for the differentiation of calcium signaling in synaptic plasticity. II. Evolutionary algorithms for the optimization of methods in computational chemistry

In Part 1 of this thesis, we propose that biochemical cooperativity is a fundamentally non-ideal process. We show quantal effects underlying biochemical cooperativity and highlight apparent ergodic breaking at small volumes. The apparent ergodic breaking manifests itself in a divergence of deterministic and stochastic models. We further predict that this divergence of deterministic and stochastic results is a failure of the deterministic methods rather than an issue of stochastic simulations.

Ergodic breaking at small volumes may allow these molecular complexes to function as switches to a greater degree than has previously been shown. We propose that this ergodic breaking is a phenomenon that the synapse might exploit to differentiate Ca$^{2+}$ signaling that would lead to either the strengthening or weakening of a synapse. Techniques such as lattice-based statistics and rule-based modeling are tools that allow us to directly confront this non-ideality. A natural next step to understanding the chemical physics that underlies these processes is to consider \textit{in silico} specifically atomistic simulation methods that might augment our modeling efforts.

In the second part of this thesis, we use evolutionary algorithms to optimize \textit{in silico} methods that might be used to describe biochemical processes at the subcellular and molecular levels. While we have applied evolutionary algorithms to several methods, this thesis will focus on the optimization of charge equilibration methods. Accurate charges are essential to understanding the electrostatic interactions that are involved in ligand binding, as frequently discussed in the first part of this thesis.

Dynamics of non-Abelian Aharonov-Bohm systems

This thesis examines several examples of systems in which non-Abelian magnetic flux and non-Abelian forms of the Aharonov-Bohm effect play a role. We consider the dynamical consequences in these systems of some of the exotic phenomena associated with non-Abelian flux, such as Cheshire charge holonomy interactions and non-Abelian braid statistics. First, we use a mean-field approximation to study a model of U(2) non-Abelian anyons near its free-fermion limit. Some self-consistent states are constructed which show a small SU(2)-breaking charge density that vanishes in the fermionic limit. This is contrasted with the bosonic limit where the SU(2) asymmetry of the ground state can be maximal. Second, a global analogue of Chesire charge is described, raising the possibility of observing Cheshire charge in condensedmatter systems. A potential realization in superfluid He-3 is discussed. Finally, we describe in some detail a method for numerically simulating the evolution of a network of non-Abelian (S₃) cosmic strings, keeping careful track of all magnetic fluxes and taking full account of their non-commutative nature. I present some preliminary results from this simulation, which is still in progress. The early results are suggestive of a qualitatively new, non-scaling behavior.

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Nonlinear oscillations in discrete and continuous systems

The first thesis topic is a perturbation method for resonantly coupled nonlinear oscillators. By successive near-identity transformations of the original equations, one obtains new equations with simple structure that describe the long time evolution of the motion. This technique is related to two-timing in that secular terms are suppressed in the transformation equations. The method has some important advantages. Appropriate time scalings are generated naturally by the method, and don't need to be guessed as in two-timing. Furthermore, by continuing the procedure to higher order, one extends (formally) the time scale of valid approximation. Examples illustrate these claims. Using this method, we investigate resonance in conservative, non-conservative and time dependent problems. Each example is chosen to highlight a certain aspect of the method.

The second thesis topic concerns the coupling of nonlinear chemical oscillators. The first problem is the propagation of chemical waves of an oscillating reaction in a diffusive medium. Using two-timing, we derive a nonlinear equation that determines how spatial variations in the phase of the oscillations evolves in time. This result is the key to understanding the propagation of chemical waves. In particular, we use it to account for certain experimental observations on the Belusov-Zhabotinskii reaction.

Next, we analyse the interaction between a pair of coupled chemical oscillators. This time, we derive an equation for the phase shift, which measures how much the oscillators are out of phase. This result is the key to understanding M. Marek's and I. Stuchl's results on coupled reactor systems. In particular, our model accounts for synchronization and its bifurcation into rhythm splitting.

Finally, we analyse large systems of coupled chemical oscillators. Using a continuum approximation, we demonstrate mechanisms that cause auto-synchronization in such systems.

Analog VLSI-based, neuromorphic sensorimotor systems: modeling the primate oculomotor system

Using neuromorphic analog VLSI techniques for modeling large neural systems has several advantages over software techniques. By designing massively-parallel analog circuit arrays which are ubiquitous in neural systems, analog VLSI models are extremely fast, particularly when local interactions are important in the computation. While analog VLSI circuits are not as flexible as software methods, the constraints posed by this approach are often very similar to the constraints faced by biological systems. As a result, these constraints can offer many insights into the solutions found by evolution. This dissertation describes a hardware modeling effort to mimic the primate oculomotor system which requires both fast sensory processing and fast motor control. A one-dimensional hardware model of the primate eye has been built which simulates the physical dynamics of the biological system. It is driven by analog VLSI circuits mimicking brainstem and cortical circuits that control eye movements. In this framework, a visually-triggered saccadic system is demonstrated which generates averaging saccades. In addition, an auditory localization system, based on the neural circuits of the barn owl, is used to trigger saccades to acoustic targets in parallel with visual targets. Two different types of learning are also demonstrated on the saccadic system using floating-gate technology allowing the non-volatile storage of analog parameters directly on the chip. Finally, a model of visual attention is used to select and track moving targets against textured backgrounds, driving both saccadic and smooth pursuit eye movements to maintain the image of the target in the center of the field of view. This system represents one of the few efforts in this field to integrate both neuromorphic sensory processing and motor control in a closed-loop fashion.

A dynamical systems analysis of vortex pinch-off

Vortex rings constitute the main structure in the wakes of a wide class of swimming and flying animals, as well as in cardiac flows and in the jets generated by some moss and fungi. However, there is a physical limit, determined by an energy maximization principle called the Kelvin-Benjamin principle, to the size that axisymmetric vortex rings can achieve. The existence of this limit is known to lead to the separation of a growing vortex ring from the shear layer feeding it, a process known as `vortex pinch-off', and characterized by the dimensionless vortex formation number. The goal of this thesis is to improve our understanding of vortex pinch-off as it relates to biological propulsion, and to provide future researchers with tools to assist in identifying and predicting pinch-off in biological flows.

To this end, we introduce a method for identifying pinch-off in starting jets using the Lagrangian coherent structures in the flow, and apply this criterion to an experimentally generated starting jet. Since most naturally occurring vortex rings are not circular, we extend the definition of the vortex formation number to include non-axisymmetric vortex rings, and find that the formation number for moderately non-axisymmetric vortices is similar to that of circular vortex rings. This suggests that naturally occurring vortex rings may be modeled as axisymmetric vortex rings. Therefore, we consider the perturbation response of the Norbury family of axisymmetric vortex rings. This family is chosen to model vortex rings of increasing thickness and circulation, and their response to prolate shape perturbations is simulated using contour dynamics. Finally, the response of more realistic models for vortex rings, constructed from experimental data using nested contours, to perturbations which resemble those encountered by forming vortices more closely, is simulated using contour dynamics. In both families of models, a change in response analogous to pinch-off is found as members of the family with progressively thicker cores are considered. We posit that this analogy may be exploited to understand and predict pinch-off in complex biological flows, where current methods are not applicable in practice, and criteria based on the properties of vortex rings alone are necessary.

Interplay of martensitic phase transformation and plastic slip in polycrystals

Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.

We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.

We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.

Theoretical studies of novel organic systems : biradicals, polyradicals, and conducting polymers

Chapter 1

Cyclobutanediyl has been studied in both its singlet and triplet states by ab initio electronic structure theory. The triplet, which is the ground state of the molecule, exists in both C_(2h) and C_(2v) forms, which interconvert via a C_s transition state. For the singlet, only a C_(2h) form is found. It passes, via a C_s transition state, onto the C_(2v) surface on which bicyclobutane is the only minimum. The ring-flipping (inversion) process in bicyclobutane includes the singlet biradical as an intermediate, and involves a novel, nonleast motion pathway. Semiclassical periodic orbit theory indicates that the various minima on both the singlet and triplet surfaces can interconvert via quantum mechanical tunneling.

Chapter 2

The dimethylenepolycyclobutadienes (n) are the non-Kekulé analogues of the classical acenes. Application of a variety of theoretical methods reveals several novel features of such structures. Most interesting is the emergence of a parity rule. When n is even, n is predicted to be a singlet, with n disjoint NBMOs. When n is odd, theory predicts a triplet ground state with (n+1) NBMOs that are not fully disjoint.

Chapter 3

Bi(cyclobutadienyl) (2), the cyclobutadiene analogue of biphenyl, and its homologues tri- (3) and tetra(cyclobutadienyl) (4) have been studied using electronic structure theory. Ab initio calculations on 2 reveal that the central bond is a true double bond, and that the structure is best thought of as two allyl radicals plus an ethylene. The singlet and triplet states are essentially degenerate. Trimer 3 is two allyls plus a dimethylenecyclobutanediyl, while 4 is two coplanar bi(cyclobutadienyl) units connected by a single bond. For both 3 and 4, the quintet, triplet, and singlet states are essentially degenerate, indicating that they are tetraradicals. The infinite polymer, polycyclobutadiene, has been studied by HMO, EHCO, and VEH methods. Several geometries based on the structures of 3 and 4 have been studied, and the band structures are quite intriguing. A novel crossing between the valence and conduction bands produces a small band gap and a high density of states at the Fermi level.

Chapter 4

At the level of Hückel theory, polyfulvene has a HOCO-LUCO degeneracy much like that seen in polyacetylene. Higher levels of theory remove the degeneracy, but the band gap (E_g) is predicted to be significantly smaller than analogous structures such as polythiophene and polypyrrole at the fulvenoid geometry. An alternative geometry, which we have termed quinoid, is also conceivable for polyfulvene, and it is predicted to have a much larger E_g. The effects of benzannelation to produce analogues of polyisothianaphthene have been evaluated. We propose a new model for such structures based on conventional orbital mixing arguments. Several of the proposed structures have quite interesting properties, which suggest that they are excellent candidates for conducting polymers.

Chapter 5

Theoretical studies of polydimethylenecyclobutene and polydiisopropylidene- cyclobutene reveal that, because of steric crowding, they cannot achieve a planar, fully conjugated structure in either their undoped or doped states. Rather, the structure consists of essentially orthogonal hexatriene units. Such a structure is incompatible with conventional conduction mechanisms involving polarons and bipolarons.

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.

Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.