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Insights into Pathways of Nitrous Oxide Generation from Novel Isotopologue Measurements
Get PDFThe accumulation of nitrous oxide (N2O) in the atmosphere is a significant manifestation of human perturbations of the nitrogen cycle. This thesis reports the development and first applications of a novel isotopic technique for characterizing nitrous oxide sources. Chapter 1 describes the development of methods to use the newly available technology of high- resolution dual-inlet multi-collector mass spectrometry to measure six isotopic parameters in nitrous oxide. It reports the standardization and initial biological application of these methods. Chapter 2 presents a model for the generation of isotope effects in an important N2O generating enzyme, the bacterial nitric oxide reductase; this model and published isotopic constraints are used to provide insights into the mechanism of that enzyme. Chapter 3 describes the six-dimensional isotopic characterization of nitrous oxide from bacterial denitrifiers, while Chapter 4 describes nitrous oxide generated by ammonia oxidizing bacteria.</p
Engineered Viral Vectors and Developed Tissue Clearing Methods for Single-cell Phenotyping in Whole Organs
Get PDFA central question in biology is how different cell types interact with each other and their native environment to form complex functional systems and networks. Although our ability to investigate this question has considerably expanded from the development of genetically encoded tools, some limitations still persist. For instance, we are limited in our ability to visualize the native three dimensional environments of whole organs. Additionally, it is challenging to efficiently deliver transgenes into difficult-to-target areas through direct-injections, such as the cardiac ganglia, or broadly distributed networks, such as the myenteric nervous system, which limits our ability to extensively study these areas. Therefore, tools and methods that overcome these limitations are needed. Towards this end, my thesis work has been focused on developing tools for single-cell resolution phenotyping in whole organs. I have been developing tissue clearing technologies to render whole organs transparent for optical interrogation and characterizing viral capsids and engineering viral vectors for noninvasive widespread gene delivery to the central and peripheral nervous system.
Tissue clearing techniques for three dimensional optical interrogation were invented over a century ago. However, these earlier methods used harsh organic chemicals and failed to retain the tissue’s native fluorescence or epitopes. These earlier methods eventually became incompatible to the hundreds of newly generated transgenic mouse lines that allowed for cell type-specific expression of fluorescent transgenes or to fluorescent labeling techniques, such as immunohistochemistry (IHC). The first part of my dissertation is aimed at addressing these limitations by further developing and standardizing a tissue clearing method that utilizes the vasculature to perfuse clearing reagents. This technique, called perfusion assisted agent release in situ (PARS) enables (i) whole organ clearing of soft tissue, (ii) preservation of native fluorescence, and (iii) preservation of epitopes compatible with IHC.
Although PARS allows us to optically investigate whole soft tissue organs, it is unsuitable for clearing bone tissue. The clearing of bone is important as it may provide optical access to delicate environments, such as the lymphatic vessels lining the dural sinuses beneath the skull that would otherwise be damaged through traditional methods. However, clearing bone tissue is challenging since it is composed of both soft (bone marrow) and hard (mineral) tissue. To overcome this challenge, I developed a clearing method that rendered intact bone tissue transparent by using EDTA to decalcify bones and by constructing a convective flow chamber to efficiently clear bones. This method, called Bone CLARITY, is able to preserve native fluorescence and epitopes. In order to demonstrate the utility of Bone CLARITY, I collaborated with colleagues to quantitatively access a rare and non-uniformly distributed population of osteoprogenitor cells in their native three dimensional environment. Bone CLARITY in conjunction with light-sheet microscope enabled the early detection of an increase to this osteoprogenitor population after administration of a novel anabolic drug, which may have been undetected with traditional techniques.
Towards my second goal, I have been working on characterizing adeno-associated viruses (AAVs) for non-invasive widespread gene delivery across the central or peripheral nervous system. Through systemic delivery, these novel AAVs are able to efficiently deliver transgenes to (i) difficult-to-target areas, such as the dorsal root ganglia; (ii) cellular populations that are widely distributed across the mouse body, such as neurons in the myenteric nervous system, and (iii) through highly selective barriers, such as the blood-brain barrier. These viruses enable rapid expression of transgenes for perturbing and monitoring cellular circuits, or for potentially treating neurological diseases. In addition, I worked on engineering or validating several different gene regulatory elements to achieve cell type restricted expression in transgenic and non-transgenic animals with AAVs. These viral vectors may prove useful in rapidly testing newly developed genetic tools. Finally, I developed and characterized two different two-component viral vector systems to control the density of labeling when systemically delivering genes with our novel engineered viruses. I utilized this two-component system to perform single-cell morphology studies in the CNS and PNS. Collectively, these capsids and vectors expand the AAV toolbox and enable efficient and versatile gene delivery into the CNS and PNS of transgenic and non-transgenic animals.</p
P-Schemes and Deterministic Polynomial Factoring Over Finite Fields
Get PDFWe introduce a family of mathematical objects called P-schemes, where P is a poset of subgroups of a finite group G. A P-scheme is a collection of partitions of the right coset spaces H\G, indexed by H∈P, that satisfies a list of axioms. These objects generalize the classical notion of association schemes [BI84] as well as the notion of m-schemes [IKS09].
Based on P-schemes, we develop a unifying framework for the problem of deterministic factoring of univariate polynomials over finite field under the generalized Riemann hypothesis (GRH). More specifically, our results include the following:
We show an equivalence between m-scheme as introduced in [IKS09] and P-schemes in the special setting that G is an multiply transitive permutation group and P is a poset of pointwise stabilizers, and therefore realize the theory of m-schemes as part of the richer theory of P-schemes.
We give a generic deterministic algorithm that computes the factorization of the input polynomial ƒ(X) ∈ Fq[X] given a "lifted polynomial" ƒ~(X) of ƒ(X) and a collection F of "effectively constructible" subfields of the splitting field of ƒ~(X) over a certain base field. It is routine to compute ƒ~(X) from ƒ(X) by lifting the coefficients of ƒ(X) to a number ring. The algorithm then successfully factorizes ƒ(X) under GRH in time polynomial in the size of ƒ~(X) and F, provided that a certain condition concerning P-schemes is satisfied, for P being the poset of subgroups of the Galois group G of ƒ~(X) defined by F via the Galois correspondence. By considering various choices of G, P and verifying the condition, we are able to derive the main results of known (GRH-based) deterministic factoring algorithms [Hua91a; Hua91b; Ron88; Ron92; Evd92; Evd94; IKS09] from our generic algorithm in a uniform way.
We investigate the schemes conjecture in [IKS09] and formulate analogous conjectures associated with various families of permutation groups, each of which has applications on deterministic polynomial factoring. Using a technique called induction of P-schemes, we establish reductions among these conjectures and show that they form a hierarchy of relaxations of the original schemes conjecture.
We connect the complexity of deterministic polynomial factoring with the complexity of the Galois group G of ƒ~(X). Specifically, using techniques from permutation group theory, we obtain a (GRH-based) deterministic factoring algorithm whose running time is bounded in terms of the noncyclic composition factors of G. In particular, this algorithm runs in polynomial time if G is in Γk for some k=2O(√(log n), where Γk denotes the family of finite groups whose noncyclic composition factors are all isomorphic of subgroups of the symmetric group of degree k. Previously, polynomial-time algorithms for Γk were known only for bounded k.
We discuss various aspects of the theory of P-schemes, including techniques of constructing new P-schemes from old ones, P-schemes for symmetric groups and linear groups, orbit P-schemes, etc. For the closely related theory of m-schemes, we provide explicit constructions of strongly antisymmetric homogeneous m-schemes for m≤3. We also show that all antisymmetric homogeneous orbit 3-schemes have a matching for m≥3, improving a result in [IKS09] that confirms the same statement for m≥4.
In summary, our framework reduces the algorithmic problem of deterministic polynomial factoring over finite fields to a combinatorial problem concerning P-schemes, allowing us to not only recover most of the known results but also discover new ones. We believe progress in understanding P-schemes associated with various families of permutation groups will shed some light on the ultimate goal of solving deterministic polynomial factoring over finite fields in polynomial time.</p
Nonlinear Optics in Chip-based Microresonators and their Applications
Get PDFOptical micro-resonators have been studied for decades as a platform to investigate optical physics, and to miniaturize bulky optical systems. In the last decade, optical frequency combs, which have revolutionized the precision measurement of time and frequency, have been demonstrated in optical micro-resonators via the combined effect of parametric oscillation and cascaded four-wave mixing. More recently, soliton mode-locking has made possible low-noise/reproducible generation of these miniature combs (microcombs). In this thesis, we demonstrated the generation of soliton microcombs from silica wedge disk micro-resonators and the characteristics of the soliton microcombs are described. We also applied soliton microcombs to dual-comb spectroscopy and distance measurement (LIDAR) for the first time. Also, ways to improve spectral resolution, signal-to-noise ratio, and spectral coverage are discussed. In addition to soliton microcombs, a novel spiral resonator is studied as a stable optical frequency reference. Combined with a frequency comb, this new type of chip-based reference cavity is also applied to generate stable microwaves via optical frequency division. Lastly, we generated a stimulated Brillouin laser (SBL) from the optical micro-resonator and its phonon-limited linewidth is studied. Application of the SBL for rotation measurement is also demonstrated. This thesis is organized into six chapters. Throughout the thesis, the implication and potential of my PhD work toward chip-based advanced optics system are discussed.</p
Effective Toughness of Heterogeneous Materials
Get PDFComposite materials are widely used because of their extraordinary performance. It is understood that the heterogeneity / microstructure can dramatically affect the effective behavior of materials. Although there is a well-developed theory for this relation in elasticity, there is no similar theory in fracture mechanics. Therefore, we use theoretical, numerical, and experimental approaches to study the relationship between heterogeneity / microstructure and the effective fracture behavior in this thesis.
We use the surfing boundary condition, a boundary condition that ensures the macroscopic steady crack growth, and then define the effective toughness of heterogeneous materials as the peak energy release rate during crack propagation. We also use the homogenization theory to prove that the effective J-integral in heterogeneous materials is well defined, and that it can be calculated by the homogenized stress and strain field.
In order to study the relationship between heterogeneities and effective toughness, we first use the semi-analytical method under the assumption of small elastic contrast to study selected examples. For strong heterogeneities, we use the phase field fracture method to study the crack propagation numerically. We then optimize the microstructure with respect to effective stiffness and effective toughness in a certain class of microgeometries. We show that it is possible to significantly enhance toughness without significant loss of stiffness. We also design materials with asymmetric toughness.
We develop a new experimental configuration that can measure the effective toughness of specimens with arbitrary heterogeneities. We confirm through preliminary tests that the heterogeneities can enhance the effective toughness.
Besides study the effective toughness of heterogeneous materials, we also study a model problem of peeling a thin sheet from a heterogeneous substrate. We develop a methodology to systematically optimize microstructure.</p
Mathematical Modeling of Electronic Systems: From Oscillators to Multipliers
Get PDFThe ubiquity of electronics in modern technology is undeniable. Although it is not feasible to design or analyze circuits in an exhaustively detailed fashion, it is still imperative that circuit design engineers understand the pertinent physical tradeoffs and are able to think at the appropriate level of mathematical abstraction. This thesis presents several mathematical modeling techniques of common electronic systems.
First, we derive, ab initio, a general analytical model for the behavior of electrical oscillators under injection without making any assumptions about the type of oscillator or the size or shape of the injection. This model provides novel insights into the phenomena of injection locking and pulling while subsuming existing theories found in the literature. Next, we focus on the familiar scenario of an inductor-capacitor (LC) oscillator locked to a sinusoidal signal. An exact analysis of this circuit is carried out for an arbitrary injection strength and frequency, a task which has not been executed to fruition in the existing literature. This analysis intuitively illuminates the fundamental physics underlying the synchronization of electrical harmonic oscillators, and it generalizes the notion of the lock range for such oscillators into separate necessary and sufficient conditions. We then turn to the classical estimate of the bandwidth of a linear time-invariant (LTI) system via the sum of its zero-value time constants (ZVTs), and we show that this sum can actually be used to tightly bound the bandwidth—both from above and from below—in addition to simply estimating it. Finally, we look at a natural generalization of the Gilbert cell topology: an analog multiplier for an arbitrary number of inputs; we then analyze its large- and small-signal characteristics as well as its frequency response.
Throughout, we will demonstrate how infusing physical intuition with mathematical rigor whilst seeking a balance between detailed analysis and abstract modularity results in models that are conceptually insightful, sufficiently accurate, and computationally feasible.</p
Disentangling Spatiotemporal Signals in Global Atmospheric Methane Columns
Get PDFMethane is a major driver of atmospheric chemistry and a powerful radiative forcing agent. Thus, explaining tropospheric methane trends over the last two decades is critical for the scientific understanding of the global carbon cycle as well as the ability to predict future consequences on the climate and biosphere. Tropospheric concentrations of methane have been increasing, but the growth rate in the last two decades has been extremely variable. Long-term trends in atmospheric methane concentrations and short-term fluctuations in its growth rate are not well understood because its surface emissions and chemical loss are poorly constrained. The ranges of uncertainties for estimates of methane sources and sinks are considerably broad due to the complexity of both natural and anthropogenic fluxes and the heterogeneity of their timescales. This research takes a multifaceted approach to constraining methane fluxes and determining the causes of interannual and long-term variability by developing and synthesizing measurements, integrating methane observations with tracers of tropospheric advection, and assessing systematic biases in chemical transport models. This work synthesizes satellite, aircraft, and surface measurements, including a newly developed dataset of tropospheric column-averaged dry-air mole fractions from Fourier Transform Spectrometer (FTS) instruments within the Total Carbon Column Observing Network (TCCON). Assimilating measurements into the GEOS-Chem chemical transport model, the sensitivities of the temporal and spatial distributions of methane to changes in the distributions of sources and sinks are evaluated. We demonstrate that systematic biases in model stratospheres alias into assimilation of total column methane, masking measurement-model mismatch in tropospheric seasonality. This work also investigates the influence of large-scale transport to the spatial distribution, and in particular the interhemispheric and meridional gradients, of methane
Atom-Light Interactions in a Photonic Crystal Waveguide
Get PDFNew opportunities for optical physics emerge from the integration of cold atoms with nanophotonic devices. Due to their small optical loss and tight field confinement, these nanoscale dielectric devices are capable of mediating strong atom-light interactions and open new avenues for quantum transport and quantum many-body phenomena. In particular, coupling atoms to the band edge of a photonic crystal waveguide (PCW) provides a unique platform for generating tunable range coherent atom-atom interactions which are mediated by the guided mode photons
Differential Bandgap Solar Cell Analysis
No full textThis thesis proposes and analyzes a new solar cell design. The base electrode of the new
photovoltaic is composed of several electrically isolated nanolattices suspended on top of
each other. Doped semiconductors are then deposited onto the beams of this electrode,
forming isolated p-n junctions. The deposition thicknesses of one of the doped
semiconductors is varied along the height of the device, creating a multi-junction solar cell.
The charge ca rrier dynamics in an amorphous silicon- and germanium-based device are
simulated, and the efficiency is found to be a factor of four greater than a conventional
planar structure with similar parameters. The main components of this photovoltaic's
fabrication process are developed and analyzed. Specifically, suspended and electrically
isolated lattice electrodes made of carbon are built. The electrical conductivity of the
carbon is shown to be similar to that of indium-tin oxide. The electrode material is
determined to be a mix of amorphous and glassy carbon. Different methods of radiofrequency
sputter deposition are used to deposit spatially dependent layer thicknesses of
semiconductors onto the lattice beams. The spatial dependence is shown to be
approximately linearly dependent on the height dimension of the lattice