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Integrated Nonlinear Photonic Devices
Get PDFChip-scale nonlinear optics can provide important new functions in communications, frequency metrology and spectroscopy. Optical microcavities enhance nonlinear optical effects through resonant recirculation. This recirculation dramatically reduces the required power in applications and also lowers signal noise. A key figure-of-merit is the optical Q factor, which provides a dimensionless scale of optical storage time within the microcavity. In this thesis, a novel integrated ultra-high-Q microcavity with Q as high as 230 million is presented. The device is applied to demonstrate multiple functions including electronic-rate soliton microcomb generation and stimulated Brillouin laser operation. For soliton generation, the resonator must be engineered to produce optical mode families that feature anomalous dispersion. This engineering is applied to generate solitons at wavelengths of 1064 nm and 778 nm. Systems-on-a-chip applications of these devices are discussed including compact optical synthesizers, optical clocks and rotation sensors. Finally, a compact array of silica ridge waveguides is described and applied for efficient and coherent ultraviolet-to-visible comb generation by dispersive-wave generation. Unlike other devices used to broaden spectra such as micro-structured fibers, these arrays provide a wide range of emission wavelength choices on a single chip. The arrays can also enable mode-locked lasers to attain greatly extended spectral reach for spectroscopy, bioimaging, tomography and metrology
Optimal Controller Synthesis for Nonlinear Systems
Get PDFOptimal controller synthesis is a challenging problem to solve. However, in many applications such as robotics, nonlinearity is unavoidable. Apart from optimality, correctness of the system behaviors with respect to system specifications such as stability and obstacle avoidance is vital for engineering applications. Many existing techniques consider either the optimality or the correctness of system behavior. Rarely, a tool exists that considers both. Furthermore, most existing optimal controller synthesis techniques are not scalable because they either require ad-hoc design or they suffer from the curse of dimensionality.
This thesis aims to close these gaps by proposing optimal controller synthesis techniques for two classes of nonlinear systems: linearly solvable nonlinear systems and hybrid nonlinear systems. Linearly solvable systems have associated Hamilton- Jacobi-Bellman (HJB) equations that can be transformed from the original nonlinear partial differential equation (PDE) into a linear PDE through a logarithmic transformation. The first part of this thesis presets two methods to synthesize optimal controller for linearly solvable nonlinear systems. The first technique uses a hierarchy of sums-of-square programs to compute a sequence of suboptimal controllers that have non-increasing suboptimality for first exit and finite horizon problems. This technique is the first systematic approach to provide stability and suboptimal performance guarantees for stochastic nonlinear systems in one framework. The second technique uses the low rank tensor decomposition framework to solve the linear HJB equation for first exit, finite horizon, and infinite horizon problems. This technique scale linearly with dimensions, alleviating the curse of dimensionality and enabling us to solve the linear HJB equation for a quadcopter model that is a twelve-dimensional system on a personal laptop. A new algorithm is proposed for a key step in the controller synthesis algorithm to solve the ill-conditioning issue that arises in the original algorithm. A MATLAB toolbox that implements the algorithms is developed, and the performance of these algorithms is illustrated by a few engineering examples.
Apart from stability, in many applications, more complex specifications such as obstacle avoidance, reachability, and surveillance are required. The second part of the thesis describes methods to synthesize optimal controllers for hybrid nonlinear systems with quantitative objectives (i.e., minimizing cost) and qualitative objectives (i.e., satisfying specifications). This thesis focuses on two types of qualitative objectives, regular objectives, and ω-regular objectives. Regular objectives capture bounded time behavior such as reachability, and ω-regular objectives capture long term behavior such as surveillance. For both types of objectives, an abstraction-refinement procedure that preserves the cost is developed. A two-player game is solved on the product of the abstract system and the given objectives to synthesize the suboptimal controller for the hybrid nonlinear system. By refining the abstract system, the algorithms are guaranteed to converge to the optimal cost and return the optimal controller if the original systems are robust with respect to the initial states and the optimal controller inputs. The proposed technique is the first abstraction-refinement based technique to combine both quantitative and qualitative objectives into one framework. A Python implementation of the algorithms are developed, and a few engineering examples are presented to illustrate the performance of these algorithms.</p
Interplay of Proton Transfer, Electron Transfer and Proton-Coupled Electron Transfer in Transition Metal Mediated Nitrogen Fixation
Get PDFMitigation of the hydrogen evolution reaction (HER) is a key challenge in selective small molecule reduction catalysis, including the nitrogen (N2) reduction reactions (N2RR) using H+/e- currency. Here we explore, via DFT calculations, three iron model systems, P3EFe (E = B, Si, C), known to mediate both N2RR and HER, but with different selectivity depending on the identity of the auxiliary ligand. It is shown that the respective efficiencies of these systems for N2RR trend with the predicted N–H bonds strengths of two putative hydrazido intermediates of the proposed catalytic cycle, P3EFe(NNH2)+ and P3EFe(NNH2). Bimolecular proton-coupled electron transfer (PCET) from intermediates with weak N–H bonds is posited as a major source of H2 instead of more traditional scenarios that proceed via metal hydride intermediates and proton transfer/electron transfer (PT/ET) pathways.
Studies on our most efficient molecular iron catalyst, [P3BFe]+, reveal that the interaction of acid and reductant, Cp*2Co, is critical to achieve high efficiency for NH3, leading to the demonstration of electrocatalytic N2RR. Stoichiometric reactivity shows that Cp*2Co is required to observe productive N–H bond formation with anilinium triflate acids under catalytic conditions. A study of substituted anilinium triflate acids demonstrates a strong correlation between pKa and the efficiency for NH3, which DFT studies attribute to the kinetics and thermodynamics of Cp*2Co protonation. These results contribute to the growing body of evidence suggesting that metallocenes should be considered as more than single electron transfer reagents in the proton-coupled reduction of small molecule substrates and that ring-functionalized metallocenes, believed to be intermediates on the background HER pathway, can play a critical role in productive bond-forming steps.</p
Coarse-Grained Simulation Approaches for Protein Integration and Translocation via the Sec Translocon
Get PDFThis thesis describes coarse-grained approaches for simulating the co-translational integration and translocation of proteins via the Sec translocon, which is a key step in the biogenesis of membrane and secretory proteins. We present a coarse-grained simulation approach that is capable of simulating minute-timescale dynamics while retaining sufficient chemical and structural detail to capture sequence-specific interactions. The model is validated through comparison to existing experimental data and applied to characterize the forces that act on nascent proteins and drive successful integration and translocation. We also apply coarse-grained simulations of the integration of multi-spanning membrane proteins to understand the effect of sequence modifications on expression levels. We uncover the link between integration efficiency and observed expression levels for membrane proteins, and utilize coarse-grained simulations to predict sequence modifications that improve heterologous overexpression.</p
Molybdenum Para-Terphenyl Diphosphine Complexes
Get PDFThis dissertation describes studies exploring the coordination chemistry and reactivity of molybdenum complexes bearing a flexible and redox non-innocent para-terphenyl diphosphine ligand. Within this context, transformations relevant to energy storage and conversion, fundamental structure function studies, and unusual group transfer reactivity are presented.
Chapter 2 accounts the ability of Mo para-terphenyl diphosphine complexes to catalyze extensive ammonia borane dehydrogenation, releasing greater than two equiv. of hydrogen (H2). Initially believed to be a frontrunner as a high energy density H2 storage medium, AB is a Lewis acid/base adduct that features both hydridic B–H bond and protic N–H bonds. As a highly reactive molecule, the controlled dehydrogenation of AB, accessing ≥ 2 of the 3 stored equiv. of H2, is uncommon. We disclose a catalytic system, utilizing an earth-abundant metal, that is capable of such reactivity. The mechanism by which the catalysis proceeds is dependent on the oxidation state of the precatalyst, with MoII proceeding through a II/IV cycle and Mo0 proceeding through a 0/II cycle. Several Mo hydride complexes were characterized in conjunction with this work. Importantly, the ability of the para-terphenyl diphosphine ancillary ligand to support a range of Mo oxidation states and coordination numbers was established, a feature that provides a foundation for the work presented in subsequent chapters.
In Chapter 3, new features of the para-terphenyl diphosphine ligand were discovered, namely facilitation of electron loading that subsequently leads to small molecule functionalization and cleavage. From the Mo dicarbonyl complex described in Chapter 2, stepwise reduction affords Mo0, Mo-II, and Mo-III compounds, all of which were characterized both structurally and by a variety of spectroscopies. The latter two complexes were demonstrated to react with silyl electrophiles, instigating deoxygenative reductive coupling of the bound CO ligands to a metal-free C2O1 fragment. This remarkable four-electron process was studied in detail, characterizing twelve different reaction intermediates, including rare examples of bis(siloxy)carbyne, terminal carbide, and mixed dicarbyne motifs. The cleavage of a bound carbon monoxide (CO), subsequent coupling, and spontaneous product release was an unprecendented sequence of chemical transformations, the detailed mechanistic study of which provides valuable precedent for catalyses for the conversion of C1 oxygenates to multicarbon products.
Chapter 4 discusses continuations of this work in an attempt to model Fischer-Tropsch catalysis with higher fidelity. To this end, the silyl electrophiles used in the fundamental studies in Chapter 3 needed to be replaced with protons. Addition of protons to the super-reduced Mo complexes resulted in formal arene hydrogenation; no evidence for C–O functionalization was obtained. These diene-linked complexes; however, provided an opportunity to explore how the nature of the basal π-system effects CO catenation chemistry and ultimately led to the preparation of a Mo-bound C3O3 unit derived entirely from CO. Reactivity with protons was likewise explored for downstream intermediates. Carbide protonation yields a stable methylidyne carbonyl complex, that, upon treatment with hydride, forms a methylidene. Comparison to a silyl-bearing model system suggests that subsequent carbene carbonylation affords enthenone.
Chapter 5 and 6 focus on the synthesis and reactivity of Mo(IV) terminal pnictogen complexes isoelectronic to the carbyne and carbide complexes prepared in Chapters 3 and 4. Chapter 5 describes successful N–C bond formation through N– transfer to CO from a MoII anionic nitride precursor. In Chapter 6, the first example of a terminal transition metal phosphide with d-electrons was prepared via a 4 e– oxidative group transfer. This species can undergo a single-electron oxidation, providing, at low temperatures, an unstable Mo(V) phosphide cation that studied extensively by CW and pulse EPR techniques. Upon warming, P–P bond formation is evidenced by chemical trapping and characterization of coupling byproducts. Related phosphinidene (Mo=PR), phosphide (Mo-PR2), and dinuclear μ-phosphido compounds are also reported. In a collaboration with Mr. Yohei Ueda and Dr. Masa Hirahara these complexes were explored for proton reduction reactivity. Isotopic labeling suggests formation of a dinuclear μ-phosphinidene upon treatment with acid, and a bimetallic hydride μ-phosphide was accessed from reaction with hydride.
The final chapters of this dissertation are focused on the reduction of carbon dioxide (CO2). Chapter 7 presents a fundamental study involving Lewis acid (LA) aditives, that demonstrates the importance of kinetic stabilization, and not just thermodynamic activation, in productive small molecule functionalization chemistry. Upon addition of LAs, well-defined adducts are formed with Mo-bound CO2. Protonation results in C–O bond cleavage, utilizing two electrons from the metal center to reduce CO2 to CO and H2O. Though the degree of CO2 activation trends well as a function of Lewis acidity, the residence time of the bound CO2, reported via the rate of CO2 self-exchange, is shown to correlate to the degree of C–O scission. Chapter 8 looks at CO2 reactivity with E–H bonds, describing first stoichiometric reactivity with silanes. In this system, CO2 is reduced to CO and silanol; mechanistic studies suggest a pathway that involves oxygen atom transfer to silane from a transient Mo oxo. In a collaboration with Dr. Naoki Shida, CO2 hydrogenation was explored, with demonstration of bidirectional catalysis in addition to detailed studies investigating the elementary steps of both formate formation and formic acid dehydrogenation.</p
Studying the Extragalactic Background Light with the Second Cosmic Infrared Background ExpeRiment, CIBER-2
Get PDFFluctuations in the extragalactic background light trace emission from the entire history of galaxy formation, including emission from early luminous sources prior to the reionization of the universe. The formation of the first luminous objects represents an important transition in the evolution of the universe from its smooth initial state to the clumpy, highly ordered state observable today. However, these objects are faint and diffuse and not well studied; direct observations of their emission are needed to constrain current numerical simulations of the nonlinear evolution of the early universe. A number of recent near-infrared measurements show excess spatial power at large angular scales inconsistent with models of z < 5 emission from galaxies. These measurements have been interpreted as arising from either redshifted emission of early luminous objects, such as stellar and quasar emission from the epoch of reionization, or the combined intra-halo light from stars thrown out of more recent galaxies during merging activity at lower redshifts. Though astrophysically distinct, both interpretations arise from faint, low surface brightness source populations that are difficult to detect except by statistical approaches using careful observations with suitable instruments. The key to determining the source of these background anisotropies will be wide-field imaging measurements spanning multiple bands from the optical to the near-infrared.
The Cosmic Infrared Background ExpeRiment 2 (CIBER-2) will measure spatial anisotropies in the extragalactic infrared background caused by cosmological structure using six broad spectral bands. The experiment uses three 2048 x 2048 Hawaii-2RG near-infrared arrays in three cameras coupled to a single 28.5 cm telescope housed in a reusable sounding rocket-borne payload. A small portion of each array will also be combined with a linear-variable filter to make absolute measurements of the spectrum of the extragalactic background with high spatial resolution for deep subtraction of Galactic starlight. The large field of view and multiple spectral bands make CIBER-2 unique in its sensitivity to fluctuations predicted by models of lower limits on the luminosity of the first stars and galaxies and in its ability to distinguish between primordial and foreground anisotropies. This work encompasses the scientific motivation for CIBER-2 and describes details of the instrument design and verification prior to flight.</p
Structural and Functional Characterization of the Escherichia coli MetNI Methionine Transporter
Get PDFDespite the ubiquitous role of ATP Binding Cassette (ABC) importers in nutrient uptake, only the E. coli maltose and vitamin B12 ABC transporters have been structurally characterized in multiple conformations relevant to the alternating access transport mechanism. To complement our previous structure determination of the E. coli MetNI methionine importer partner in the inward facing conformation (Kadaba et al. Science 321, 250-253, 2008), we have explored conditions stabilizing the outward facing conformation. Using two variants, the Walker B E166Q mutation with ATP and EDTA to stabilize MetNI in the ATP-bound conformation, and the N229A variant of the binding protein MetQ to disrupt methionine binding as shown in this work, a high affinity MetNIQ complex was formed with a dissociation constant measured to be 27 nM. We then solved a 2.95 Å resolution crystal structure of the outward-facing conformation of the MetNI transporter, in complex with its binding protein, MetQ. The structure sheds light on how the C-regulatory domains regulate transport activity by rearrangement of a hydrogen bonding network between their interfaces in two different conformations. Structure of the substrate-free homologous MetQ from N. meningitides was also resolved using the N-to-A mutation (N238A). Superimposition of the substrate-bound, substrate-free (homologous model) MetQ and the binding protein MetQ in complex with its MetNI transporter (complexed MetQ) reveals unexpected structural features of the complexed MetQ, indicates a different substrate delivery mechanism for the MetNI transporter. These structural insights, coupled with thermodynamic binding constant and in vivo transport studies, support an unconventional transport mechanism for the Type-I methionine ABC importer
Super Pivotal Categories, Fermion Condensation, and Fermionic Topological Phases
Get PDFWe describe a systematic way of producing fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain an emergent fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions, and condensing pairs of physical and emergent fermions. There are two distinct types of objects in fermionic theories, which we call “m-type” and “q-type” particles. The endomorphism algebras of q-type particles are complex Clifford algebras, and they have no analogues in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations in fermionic topological phases. We then prove a series of results relating data in condensed theories to data in their parent theories; for example, if C is a modular tensor category containing a fermion, then the tube category of the condensed theory satisfies Tube(C/ψ) ≅ C × C/ψ. We also study how modular transformations, fusion rules, and coherence relations are modified in the fermionic setting, prove a fermionic version of the Verlinde dimension formula, construct a commuting projector lattice Hamiltonian for fermionic theories, and write down a fermionic version of the Turaev-Viro-Barrett-Westbury state sum.</p
Development of Tensor Network Algorithms for Studying Classical and Quantum Many-Body Systems
Get PDFThe field of tensor networks, kicked off in 1992 by Steve White's invention of the spectacularly successful density matrix renormalization group (DMRG) algorithm, has exploded in popularity in recent years. Tensor networks are poised to play a role in helping us solve some of the greatest open physics problems of our time, such as understanding the nature of high-temperature superconductivity and illuminating a theory of quantum gravity. DMRG and extensions based on a class of variational states known as tensor network states have been indispensable tools in helping us understand both numerically and theoretically the properties of complicated classical and quantum many-body systems. However, practical challenges to these techniques still remain, and algorithmic developments are needed before tensor network algorithms can be applied to more physics problems. In this thesis we present a variety of recent advancements to tensor network algorithms.
First we describe a DMRG-like algorithm for noninteracting fermions. Noninteracting fermions, naturally being gapless and therefore having high levels of entanglement, are actually a challenging setting for standard DMRG algorithms, and we believe this new algorithm can help with tensor network calculations in that setting.
Next we explain a new algorithm called the variational uniform matrix product state (VUMPS) algorithm that is a DMRG-like algorithm that works directly in the thermodynamic limit, improving upon currently available MPS-based methods for studying infinite 1D and quasi-1D quantum many-body systems.
Finally, we describe a variety of improvements to algorithms for contracting 2D tensor networks, a common problem in tensor network algorithms, for example for studying 2D classical statistical mechanics problems and 2D quantum many-body problems with projected entangled pair states (PEPS). One is a new variant of the corner transfer matrix renormalization group (CTMRG) algorithm of Nishino and Okunishi that improves the numerical stability for contracting asymmetric two-dimensional tensor networks compared to the most commonly used method. Another is the application of the VUMPS algorithm to contracting 2D tensor networks. The last is a new alternative to CTMRG, where the tensors are solved for with eigenvalue equations instead of a power method, which we call the fixed point corner method (FPCM). We present results showing the transfer matrix VUMPS algorithm and FPCM significantly improve upon the convergence time of CTMRG. We expect these algorithms will play an important role in expanding the set of 2D classical and 2D quantum many-body problems that can be addressed with tensor networks.</p
Experimental and Numerical Studies of Cavities, Flows, and Waves in Arched Flux Ropes
Get PDFThis dissertation details various studies of arched flux ropes using both scalable laboratory experiments and numerical simulations. This work can be divided into three major classes: studies of flux rope motion and shape, development of supporting simulations, and development of new experimental diagnostics.
The primary scientific results in this work are the characterization of new mechanisms for flux rope motion and morphology. These studies are done on two separate experiments, the single loop and double loop, which produce arched flux ropes with non-dimensional evolution equivalent to solar prominences. Measurements taken on these experiments characterize three flux rope mechanisms: (1) how variation in a flux rope minor radius can drive axial flows and collimation, (2) how non-uniform axial density can perturb flux rope shape and inhibit the kink instability, and (3) how changing flux rope current can repel background plasma and form density cavities around the flux rope. These mechanisms are each relevant to a different aspect of solar prominences: the collimation mechansim (1) can explain why solar loops are denser and more collimated than expected, the work on density perturbations (2) puts a higher limit on prominence stability, and the cavity mechanism (3) provides the first model to explain why coronal mass ejections (CMEs) are observed to have a three part structure.
Two numerical simulations were developed in support of the experiments: a 3D magnetohydrodynamic (MHD) simulation of the single loop experiment and a 3D spline model simulating flux ropes as interacting current carrying wires. The MHD simulation uses the solver module from the Los Alamos COMPutational Astrophysics Simulation Suite (LA-COMPASS) to evolve B, v, rho, and P on a 96^3 Cartesian grid using the dimensionless ideal MHD equations. The resulting simulation has excellent agreement with experimental observations in shape, velocity, and magnetic field and quantitatively reproduces the mechanisms (2,3) observed in the single loop experiment. The spline simulation models the flux ropes experiments as plasma systems of thin current paths in a 3D space with no background plasma. This model is shown to be useful for reproducing flux rope evolution, testing new experimental configurations, evaluating the magnetic fields generated from complex 3D current paths, and testing the robustness of analytic flux rope models.
The last body of work concerns the development of two novel diagnostics: a high frequency (1-100 MHz) wave probe designed to measure both the magnetic field B, and current density J, of passing waves and a high frequency (100 MHz) 1D coded aperture camera. The wave probe consists of four 3-axis Bdot-probes arranged in a tetrahedron. This additional spatial resolution allows the calculation of both J and the wavevector k. Measurements taken by this probe on the plasma jet experiment identify short whistler wave pulses emitted from magnetic reconnection events. These waves are identified by measurements of the background conditions, the wave polarization, and comparisons with the theoretical whistler dispersion relation. The pulses also occur simultaneously with bursts of X-ray emissions, indicating that non-MHD physics (i.e. two-fluid or kinetic effects) are important during the reconnection event. The coded aperture camera is a fast (100MHz) 1D visible light system developed as a prototype for imaging plasma experiments in the EUV/X-ray bands. In the low signal limit, the system demonstrates 40-fold increase in throughput and a signal-to-noise gain of ~7 over that of a pinhole camera of equivalent parameters.</p