Synthetic molecular machines for active self-assembly : prototype algorithms, designs, and experimental study

Computer science and electrical engineering have been the great success story of the twentieth century. The neat modularity and mapping of a language onto circuits has led to robots on Mars, desktop computers and smartphones. But these devices are not yet able to do some of the things that life takes for granted: repair a scratch, reproduce, regenerate, or grow exponentially fast–all while remaining functional.

This thesis explores and develops algorithms, molecular implementations, and theoretical proofs in the context of “active self-assembly” of molecular systems. The long-term vision of active self-assembly is the theoretical and physical implementation of materials that are composed of reconfigurable units with the programmability and adaptability of biology’s numerous molecular machines. En route to this goal, we must first find a way to overcome the memory limitations of molecular systems, and to discover the limits of complexity that can be achieved with individual molecules.

One of the main thrusts in molecular programming is to use computer science as a tool for figuring out what can be achieved. While molecular systems that are Turing-complete have been demonstrated [Winfree, 1996], these systems still cannot achieve some of the feats biology has achieved.

One might think that because a system is Turing-complete, capable of computing “anything,” that it can do any arbitrary task. But while it can simulate any digital computational problem, there are many behaviors that are not “computations” in a classical sense, and cannot be directly implemented. Examples include exponential growth and molecular motion relative to a surface.

Passive self-assembly systems cannot implement these behaviors because (a) molecular motion relative to a surface requires a source of fuel that is external to the system, and (b) passive systems are too slow to assemble exponentially-fast-growing structures. We call these behaviors “energetically incomplete” programmable behaviors. This class of behaviors includes any behavior where a passive physical system simply does not have enough physical energy to perform the specified tasks in the requisite amount of time.

As we will demonstrate and prove, a sufficiently expressive implementation of an “active” molecular self-assembly approach can achieve these behaviors. Using an external source of fuel solves part of the the problem, so the system is not “energetically incomplete.” But the programmable system also needs to have sufficient expressive power to achieve the specified behaviors. Perhaps surprisingly, some of these systems do not even require Turing completeness to be sufficiently expressive.

Building on a large variety of work by other scientists in the fields of DNA nanotechnology, chemistry and reconfigurable robotics, this thesis introduces several research contributions in the context of active self-assembly.

We show that simple primitives such as insertion and deletion are able to generate complex and interesting results such as the growth of a linear polymer in logarithmic time and the ability of a linear polymer to treadmill. To this end we developed a formal model for active-self assembly that is directly implementable with DNA molecules. We show that this model is computationally equivalent to a machine capable of producing strings that are stronger than regular languages and, at most, as strong as context-free grammars. This is a great advance in the theory of active self- assembly as prior models were either entirely theoretical or only implementable in the context of macro-scale robotics.

We developed a chain reaction method for the autonomous exponential growth of a linear DNA polymer. Our method is based on the insertion of molecules into the assembly, which generates two new insertion sites for every initial one employed. The building of a line in logarithmic time is a first step toward building a shape in logarithmic time. We demonstrate the first construction of a synthetic linear polymer that grows exponentially fast via insertion. We show that monomer molecules are converted into the polymer in logarithmic time via spectrofluorimetry and gel electrophoresis experiments. We also demonstrate the division of these polymers via the addition of a single DNA complex that competes with the insertion mechanism. This shows the growth of a population of polymers in logarithmic time. We characterize the DNA insertion mechanism that we utilize in Chapter 4. We experimentally demonstrate that we can control the kinetics of this re- action over at least seven orders of magnitude, by programming the sequences of DNA that initiate the reaction.

In addition, we review co-authored work on programming molecular robots using prescriptive landscapes of DNA origami; this was the first microscopic demonstration of programming a molec- ular robot to walk on a 2-dimensional surface. We developed a snapshot method for imaging these random walking molecular robots and a CAPTCHA-like analysis method for difficult-to-interpret imaging data.

Tissue engineering active biological machines : bio-inspired design, directed self-assembly, and characterization of muscular pumps simulating the embryonic heart

Biological machines are active devices that are comprised of cells and other biological components. These functional devices are best suited for physiological environments that support cellular function and survival. Biological machines have the potential to revolutionize the engineering of biomedical devices intended for implantation, where the human body can provide the required physiological environment. For engineering such cell-based machines, bio-inspired design can serve as a guiding platform as it provides functionally proven designs that are attainable by living cells. In the present work, a systematic approach was used to tissue engineer one such machine by exclusively using biological building blocks and by employing a bio-inspired design. Valveless impedance pumps were constructed based on the working principles of the embryonic vertebrate heart and by using cells and tissue derived from rats. The function of these tissue-engineered muscular pumps was characterized by exploring their spatiotemporal and flow behavior in order to better understand the capabilities and limitations of cells when used as the engines of biological machines.

The optoelectronic swept-frequency laser and its applications in ranging, three-dimensional imaging, and coherent beam combining of chirped-seed amplifiers

This thesis explores the design, construction, and applications of the optoelectronic swept-frequency laser (SFL). The optoelectronic SFL is a feedback loop designed around a swept-frequency (chirped) semiconductor laser (SCL) to control its instantaneous optical frequency, such that the chirp characteristics are determined solely by a reference electronic oscillator. The resultant system generates precisely controlled optical frequency sweeps. In particular, we focus on linear chirps because of their numerous applications. We demonstrate optoelectronic SFLs based on vertical-cavity surface-emitting lasers (VCSELs) and distributed-feedback lasers (DFBs) at wavelengths of 1550 nm and 1060 nm. We develop an iterative bias current predistortion procedure that enables SFL operation at very high chirp rates, up to 10^16 Hz/sec. We describe commercialization efforts and implementation of the predistortion algorithm in a stand-alone embedded environment, undertaken as part of our collaboration with Telaris, Inc. We demonstrate frequency-modulated continuous-wave (FMCW) ranging and three-dimensional (3-D) imaging using a 1550 nm optoelectronic SFL.

We develop the technique of multiple source FMCW (MS-FMCW) reflectometry, in which the frequency sweeps of multiple SFLs are "stitched" together in order to increase the optical bandwidth, and hence improve the axial resolution, of an FMCW ranging measurement. We demonstrate computer-aided stitching of DFB and VCSEL sweeps at 1550 nm. We also develop and demonstrate hardware stitching, which enables MS-FMCW ranging without additional signal processing. The culmination of this work is the hardware stitching of four VCSELs at 1550 nm for a total optical bandwidth of 2 THz, and a free-space axial resolution of 75 microns.

We describe our work on the tomographic imaging camera (TomICam), a 3-D imaging system based on FMCW ranging that features non-mechanical acquisition of transverse pixels. Our approach uses a combination of electronically tuned optical sources and low-cost full-field detector arrays, completely eliminating the need for moving parts traditionally employed in 3-D imaging. We describe the basic TomICam principle, and demonstrate single-pixel TomICam ranging in a proof-of-concept experiment. We also discuss the application of compressive sensing (CS) to the TomICam platform, and perform a series of numerical simulations. These simulations show that tenfold compression is feasible in CS TomICam, which effectively improves the volume acquisition speed by a factor ten.

We develop chirped-wave phase-locking techniques, and apply them to coherent beam combining (CBC) of chirped-seed amplifiers (CSAs) in a master oscillator power amplifier configuration. The precise chirp linearity of the optoelectronic SFL enables non-mechanical compensation of optical delays using acousto-optic frequency shifters, and its high chirp rate simultaneously increases the stimulated Brillouin scattering (SBS) threshold of the active fiber. We characterize a 1550 nm chirped-seed amplifier coherent-combining system. We use a chirp rate of 5*10^14 Hz/sec to increase the amplifier SBS threshold threefold, when compared to a single-frequency seed. We demonstrate efficient phase-locking and electronic beam steering of two 3 W erbium-doped fiber amplifier channels, achieving temporal phase noise levels corresponding to interferometric fringe visibilities exceeding 98%.

Spinal cord injury therapy through active learning

Therapy employing epidural electrostimulation holds great potential for improving therapy for patients with spinal cord injury (SCI) (Harkema et al., 2011). Further promising results from combined therapies using electrostimulation have also been recently obtained (e.g., van den Brand et al., 2012). The devices being developed to deliver the stimulation are highly flexible, capable of delivering any individual stimulus among a combinatorially large set of stimuli (Gad et al., 2013). While this extreme flexibility is very useful for ensuring that the device can deliver an appropriate stimulus, the challenge of choosing good stimuli is quite substantial, even for expert human experimenters. To develop a fully implantable, autonomous device which can provide useful therapy, it is necessary to design an algorithmic method for choosing the stimulus parameters. Such a method can be used in a clinical setting, by caregivers who are not experts in the neurostimulator's use, and to allow the system to adapt autonomously between visits to the clinic. To create such an algorithm, this dissertation pursues the general class of active learning algorithms that includes Gaussian Process Upper Confidence Bound (GP-UCB, Srinivas et al., 2010), developing the Gaussian Process Batch Upper Confidence Bound (GP-BUCB, Desautels et al., 2012) and Gaussian Process Adaptive Upper Confidence Bound (GP-AUCB) algorithms. This dissertation develops new theoretical bounds for the performance of these and similar algorithms, empirically assesses these algorithms against a number of competitors in simulation, and applies a variant of the GP-BUCB algorithm in closed-loop to control SCI therapy via epidural electrostimulation in four live rats. The algorithm was tasked with maximizing the amplitude of evoked potentials in the rats' left tibialis anterior muscle. These experiments show that the algorithm is capable of directing these experiments sensibly, finding effective stimuli in all four animals. Further, in direct competition with an expert human experimenter, the algorithm produced superior performance in terms of average reward and comparable or superior performance in terms of maximum reward. These results indicate that variants of GP-BUCB may be suitable for autonomously directing SCI therapy.

Geological evolution of two crustal scale shear zones. Part I. The Rand thrust complex, northwestern Mojave Desert, California. Part II. The Magdalena metamorphic core complex, north central Sonora, Mexico

The geology and structure of two crustal scale shear zones were studied to understand the partitioning of strain within intracontinental orogenic belts. Movement histories and regional tectonic implications are deduced from observational data. The two widely separated study areas bear the imprint of intense Late Mesozoic through Middle Cenozoic tectonic activity. A regional transition from Late Cretaceous-Early Tertiary plutonism, metamorphism, and shortening strain to Middle Tertiary extension and magmatism is preserved in each area, with contrasting environments and mechanisms. Compressional phases of this tectonic history are better displayed in the Rand Mountains, whereas younger extensional structures dominate rock fabrics in the Magdalena area.

In the northwestern Mojave desert, the Rand Thrust Complex reveals a stack of four distinctive tectonic plates offset along the Garlock Fault. The lowermost plate, Rand Schist, is composed of greenschist facies metagraywacke, metachert, and metabasalt. Rand Schist is structurally overlain by Johannesburg Gneiss (= garnet-amphibolite grade orthogneisses, marbles and quartzites), which in turn is overlain by a Late Cretaceous hornblende-biotite granodiorite. Biotite granite forms the fourth and highest plate. Initial assembly of the tectonic stack involved a Late Cretaceous? south or southwest vergent overthrusting event in which Johannesburg Gneiss was imbricated and attenuated between Rand Schist and hornblende-biotite granodiorite. Thrusting postdated metamorphism and deformation of the lower two plates in separate environments. A post-kinematic stock, the Late Cretaceous Randsburg Granodiorite, intrudes deep levels of the complex and contains xenoliths of both Rand Schist and mylonitized Johannesburg? gneiss. Minimum shortening implied by the map patterns is 20 kilometers.

Some low angle faults of the Rand Thrust Complex formed or were reactivated between Late Cretaceous and Early Miocene time. South-southwest directed mylonites derived from Johannesburg Gneiss are commonly overprinted by less penetrative north-northeast vergent structures. Available kinematic information at shallower structural levels indicates that late disturbance(s) culminated in northward transport of the uppermost plate. Persistence of brittle fabrics along certain structural horizons suggests a possible association of late movement(s) with regionally known detachment faults. The four plates were juxtaposed and significant intraplate movements had ceased prior to Early Miocene emplacement of rhyolite porphyry dikes.

In the Magdalena region of north central Sonora, components of a pre-Middle Cretaceous stratigraphy are used as strain markers in tracking the evolution of a long lived orogenic belt. Important elements of the tectonic history include: (1) Compression during the Late Cretaceous and Early Tertiary, accompanied by plutonism, metamorphism, and ductile strain at depth, and thrust driven? syntectonic sedimentation at the surface. (2) Middle Tertiary transition to crustal extension, initially recorded by intrusion of leucogranites, inflation of the previously shortened middle and upper crustal section, and surface volcanism. (3) Gravity induced development of a normal sense ductile shear zone at mid crustal levels, with eventual detachment and southwestward displacement of the upper crustal stratigraphy by Early Miocene time.

Elucidation of the metamorphic core complex evolution just described was facilitated by fortuitous preservation of a unique assemblage of rocks and structures. The "type" stratigraphy utilized for regional correlation and strain analysis includes a Jurassic volcanic arc assemblage overlain by an Upper Jurassic-Lower Cretaceous quartz pebble conglomerate, in turn overlain by marine strata with fossiliferous Aptian-Albian limestones. The Jurassic strata, comprised of (a) rhyolite porphyries interstratified with quartz arenites, (b) rhyolite cobble conglomerate, and (c) intrusive granite porphyries, are known to rest on Precambrian basement north and east of the study area. The quartz pebble conglomerate is correlated with the Glance Conglomerate of southeastern Arizona and northeastern Sonora. The marine sequence represents part of an isolated arm? of the Bisbee Basin.

Crosscutting structural relationships between the pre-Middle Cretaceous supracrustal section, younger plutons, and deformational fabrics allow the tectonic sequence to be determined. Earliest phases of a Late Cretaceous-Early Tertiary orogeny are marked by emplacement of the 78 ± 3 Ma Guacomea Granodiorite (U/Pb zircon, Anderson et al., 1980) as a sill into deep levels of the layered Jurassic series. Subsequent regional metamorphism and ductile strain is recorded by a penetrative schistosity and lineation, and east-west trending folds. These fabrics are intruded by post-kinematic Early Tertiary? two mica granites. At shallower crustal levels, the orogeny is represented by north directed thrust faulting, formation of a large intermontane basin, and development of a pronounced unconformity. A second important phase of ductile strain followed Middle Tertiary? emplacement of leucogranites as sills and northwest trending dikes into intermediate levels of the deformed section (surficial volcanism was also active during this transitional period to regional extension). Gravitational instabilities resulting from crustal swelling via intrusion and thermal expansion led to development of a ductile shear zone within the stratigraphic horizon occupied by a laterally extensive leucogranite sill. With continued extension, upper crustal brittle normal faults (detachment faults) enhanced the uplift and tectonic denudation of this mylonite zone, ultimately resulting in southwestward displacement of the upper crustal stratigraphy.

Strains associated with the two ductile deformation events have been successfully partitioned through a multifaceted analysis. R_f/Ø measurements on various markers from the "type" stratigraphy allow a gradient representing cumulative strain since Middle Cretaceous time to be determined. From this gradient, noncoaxial strains accrued since emplacement of the leucogranites may be removed. Irrotational components of the postleucogranite strain are measured from quartz grain shapes in deformed granites; rotational components (shear strains) are determined from S-C fabrics and from restoration of rotated dike and vein networks. Structural observations and strain data are compatable with a deformation path of: (1) coaxial strain (pure shear?), followed by (2) injection of leucogranites as dikes (perpendicular to the minimum principle stress) and sills (parallel to the minimum principle stress), then (3) southwest directed simple shear. Modeling the late strain gradient as a simple shear zone permits a minimum displacement of 10 kilometers on the Magdalena mylonite zone/detachment fault system. Removal of the Middle Tertiary noncoaxial strains yields a residual (or pre-existing) strain gradient representative of the Late Cretaceous-Early Tertiary deformation. Several partially destrained cross sections, restored to the time of leucogranite emplacement, illustrate the idea that the upper plate of the core complex bas been detached from a region of significant topographic relief. 50% to 100% bulk extension across a 50 kilometer wide corridor is demonstrated.

Late Cenozoic tectonics of the Magdalena region are dominated by Basin and Range style faulting. Northeast and north-northwest trending high angle normal faults have interacted to extend the crust in an east-west direction. Net extension for this period is minor (10% to 15%) in comparison to the Middle Tertiary detachment related extensional episode.

Active interaction control for civil structures

This thesis presents a civil engineering approach to active control for civil structures. The proposed control technique, termed Active Interaction Control (AIC), utilizes dynamic interactions between different structures, or components of the same structure, to reduce the resonance response of the controlled or primary structure under earthquake excitations. The primary control objective of AIC is to minimize the maximum story drift of the primary structure. This is accomplished by timing the controlled interactions so as to withdraw the maximum possible vibrational energy from the primary structure to an auxiliary structure, where the energy is stored and eventually dissipated as the external excitation decreases. One of the important advantages of AIC over most conventional active control approaches is the very low external power required.

In this thesis, the AIC concept is introduced and a new AIC algorithm, termed Optimal Connection Strategy (OCS) algorithm, is proposed. The efficiency of the OCS algorithm is demonstrated and compared with two previously existing AIC algorithms, the Active Interface Damping (AID) and Active Variable Stiffness (AVS) algorithms, through idealized examples and numerical simulations of Single- and Multi-Degree-of Freedom systems under earthquake excitations. It is found that the OCS algorithm is capable of significantly reducing the story drift response of the primary structure. The effects of the mass, damping, and stiffness of the auxiliary structure on the system performance are investigated in parametric studies. Practical issues such as the sampling interval and time delay are also examined. A simple but effective predictive time delay compensation scheme is developed.

The application of trimethylsilyl diazomethane to the synthesis of optically active pyrazolines and related studies

The 1,3-dipolar cycloadditions of trimethylsilyl diazomethane with camphorsultam-derived acrylates are reported as a means for the efficient synthesis of optically active pyrazolines. Trimethylsilyl diazomethane is a safe, commercially available diazoalkane which provides Δ¹-pyrazolines 1n good yield and diastereoselectivity when camphorsultam-derived acrylates are used as the reaction dipolarophiles . These initial cycloadducts are subsequently converted to stable, characterizable Δ²-pyrazolines upon desilylation.

A manifold of reactions that can be applied to these Δ²-pyrazolines has been developed which includes pyrazoline reduction, N-N bond reduction, addition to the pyrazoline C=N by mild carbon nucleophiles, and both solvolytic and reductive chiral auxiliary removal. Additionally, it has been demonstrated that the pyrazoline reduction products can take part in peptide coupling reactions that allow for the pyrazolidines to serve as proline-like molecules. The development of this methodology is a general solution to the problem of highly substituted, functionalized pyrazoline synthesis. Importantly, the pyrazolines thus provided have been demonstrated to be amenable to reactions that add to their value as synthetic intermediates.

Transition metal clusters supported by multinucleating ligand frameworks as models of biological active sites

This dissertation describes efforts to model biological active sites with small molecule clusters. The approach used took advantage of a multinucleating ligand to control the structure and nuclearity of the product complexes, allowing the study of many different homo- and heterometallic clusters. Chapter 2 describes the synthesis of the multinucleating hexapyridyl trialkoxy ligand used throughout this thesis and the synthesis of trinuclear first row transition metal complexes supported by this framework, with an emphasis on tricopper systems as models of biological multicopper oxidases. The magnetic susceptibility of these complexes were studied, and a linear relation was found between the Cu-O(alkoxide)-Cu angles and the antiferromagnetic coupling between copper centers. The triiron(II) and trizinc(II) complexes of the ligand were also isolated and structurally characterized.

Chapter 3 describes the synthesis of a series of heterometallic tetranuclear manganese dioxido complexes with various incorporated apical redox-inactive metal cations (M = Na⁺, Ca²⁺, Sr²⁺, Zn²⁺, Y³⁺). Chapter 4 presents the synthesis of heterometallic trimanganese(IV) tetraoxido complexes structurally related to the CaMn₃ subsite of the oxygen-evolving complex (OEC) of Photosystem II. The reduction potentials of these complexes were studied, and it was found that each isostructural series displays a linear correlation between the reduction potentials and the Lewis acidities of the incorporated redox-inactive metals. The slopes of the plotted lines for both the dioxido and tetraoxido clusters are the same, suggesting a more general relationship between the electrochemical potentials of heterometallic manganese oxido clusters and their “spectator” cations. Additionally, these studies suggest that Ca²⁺ plays a role in modulating the redox potential of the OEC for water oxidation.

Chapter 5 presents studies of the effects of the redox-inactive metals on the reactivities of the heterometallic manganese complexes discussed in Chapters 3 and 4. Oxygen atom transfer from the clusters to phosphines is studied; although the reactivity is kinetically controlled in the tetraoxido clusters, the dioxido clusters with more Lewis acidic metal ions (Y³⁺ vs. Ca²⁺) appear to be more reactive. Investigations of hydrogen atom transfer and electron transfer rates are also discussed.

Appendix A describes the synthesis, and metallation reactions of a new dinucleating bis(N-heterocyclic carbene)ligand framework. Dicopper(I) and dicobalt(II) complexes of this ligand were prepared and structurally characterized. A dinickel(I) dichloride complex was synthesized, reduced, and found to activate carbon dioxide. Appendix B describes preliminary efforts to desymmetrize the manganese oxido clusters via functionalization of the basal multinucleating ligand used in the preceding sections of this dissertation. Finally, Appendix C presents some partially characterized side products and unexpected structures that were isolated throughout the course of these studies.

Aperiodic structures in optics and integrated optics and the transverse Bragg reflector laser

The first part of this work describes the uses of aperiodic structures in optics and integrated optics. In particular, devices are designed, fabricated, tested and analyzed which make use of a chirped grating corrugation on the surface of a dielectric waveguide. These structures can be used as input-output couplers, multiplexers and demultiplexers, and broad band filters.

Next, a theoretical analysis is made of the effects of a random statistical variation in the thicknesses of layers in a dielectric mirror on its reflectivity properties. Unlike the intentional aperiodicity introduced in the chirped gratings, the aperiodicity in the Bragg reflector mirrors is unintentional and is present to some extent in all devices made. The analysis involved in studying these problems relies heavily on the coupled mode formalism. The results are compared with computer experiments, as well as tests of actual mirrors.

The second part of this work describes a novel method for confining light in the transverse direction in an injection laser. These so-called transverse Bragg reflector lasers confine light normal to the junction plane in the active region, through reflection from an adjacent layered medium. Thus, in principle, it is possible to guide light in a dielectric layer whose index is lower than that of the surrounding material. The design, theory and testing of these diode lasers are discussed.

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.

Multilayer Active Shell Mirrors

This thesis presents a novel active mirror technology based on carbon fiber composites and replication manufacturing processes. Multiple additional layers are implemented into the structure in order to provide the reflective layer, actuation capabilities and electrode routing. The mirror is thin, lightweight, and has large actuation capabilities. These features, along with the associated manufacturing processes, represent a significant change in design compared to traditional optics. Structural redundancy in the form of added material or support structures is replaced by thin, unsupported lightweight substrates with large actuation capabilities.

Several studies motivated by the desire to improve as-manufactured figure quality are performed. Firstly, imperfections in thin CFRP laminates and their effect on post-cure shape errors are studied. Numerical models are developed and compared to experimental measurements on flat laminates. Techniques to mitigate figure errors for thicker laminates are also identified. A method of properly integrating the reflective facesheet onto the front surface of the CFRP substrate is also presented. Finally, the effect of bonding multiple initially flat active plates to the backside of a curved CFRP substrate is studied. Figure deformations along with local surface defects are predicted and characterized experimentally. By understanding the mechanics behind these processes, significant improvements to the overall figure quality have been made.

Studies related to the actuation response of the mirror are also performed. The active properties of two materials are characterized and compared. Optimal active layer thicknesses for thin surface-parallel schemes are determined. Finite element simulations are used to make predictions on shape correction capabilities, demonstrating high correctabiliity and stroke over low-order modes. The effect of actuator saturation is studied and shown to significantly degrade shape correction performance.

The initial figure as well as actuation capabilities of a fully-integrated active mirror prototype are characterized experimentally using a Projected Hartmann test. A description of the test apparatus is presented along with two verification measurements. The apparatus is shown to accurately capture both high-amplitude low spatial-frequency figure errors as well as those at lower amplitudes but higher spatial frequencies. A closed-loop figure correction is performed, reducing figure errors by 94%.

Signatures of Topological Superconductors

Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors.

The proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity.

This system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction.

As we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means.

Apart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.

Heterometallic Complexes as Models of Enzymatic Active Sites

This dissertation describes studies on two multinucleating ligand architectures: the first scaffold was designed to support tricopper complexes, while the second platform was developed to support tri- and tetrametallic clusters.

In Chapter 2, the synthesis of yttrium (and lanthanide) complexes supported by a tripodal ligand framework designed to bind three copper centers in close proximity is described. Tricopper complexes were shown to react with dioxygen in a 1:1 [Cu₃]/O₂ stoichiometry to form intermediates in which the O–O bond was fully cleaved, as characterized via UV-Vis spectroscopy and determination of the reaction stoichiometry. Pre-arrangement of the three Cu centers was pivotal to cooperative O₂ activation, as mono-copper complexes reacted differently with dioxgyen. The reactivity of the observed intermediates was studied with various substrates (reductants, O-atom acceptors, H-atom donors, Brønsted acids) to determine their properties. In Chapter 3, the reactivity of the same yttrium-tricopper complex with nitric oxide was explored. Reductive coupling to form a trans-hyponitrite complex (characterized by X-ray crystallography) was observed via cooperative reactivity by an yttrium and a copper center on two distinct tetrametallic units. The hyponitrite complex was observed to release nitrous oxide upon treatment with a Brønsted acid, supporting its viability as an intermediate in nitric oxide reduction to nitrous oxide.

In Chapter 4, a different multinucleating ligand scaffold was employed to synthesize heterometallic triiron clusters containing one oxide and one hydroxide bridges. The effects of the redox-inactive, Lewis acidic heterometals on redox potential was studied by cyclic voltammetry, unveiling a linear correlation between redox potential and heterometal Lewis acidity. Further studies on these complexes showed that the Lewis acidity of the redox-inactive metals also affected the oxygen-atom transfer reactivity of these clusters. Comparisons of this reactivity with manganese systems, collaborative efforts to reassign the structures of related manganese oxo-hydroxo clusters, and synthetic attempts to access related dioxo clusters are also described.

In Appendix A, ongoing efforts to synthesize new clusters supported by the same multinucleating ligand platform are described. Studies of novel approaches towards ligand exchange in tetrametallic clusters and incorporation of new supporting and bridging ligand motifs in trinuclear complexes are presented.