12023 research outputs found
Sort by
Geometry-Driven Model Reduction
Get PDFIn this thesis we bring discrete differential geometry to bear on model reduction, both in the context of data analysis and numerical simulation of physical phenomena.
First, we present a novel controllable as-isometric-as-possible embedding method for low- and high-dimensional geometric datasets through sparse matrix eigenanalysis. This approach is equally suitable for performing nonlinear dimensionality reduction on big data and nonlinear shape editing of 3D meshes and pointsets. At the core of our approach is the construction of a "multi-Laplacian" quadratic form that is assembled from local operators whose kernels only contain locally affine functions. Minimizing this quadratic form produces an embedding that best preserves all relative coordinates of points within their local neighborhoods. We demonstrate the improvements that our approach brings over existing nonlinear local manifold learning methods on a number of datasets, and formulate the first eigen-based as-rigid-as-possible shape deformation technique by applying our affine-kernel embedding approach to 3D data augmented with user-imposed constraints on select vertices.
Second, we introduce a new global manifold learning approach based on metric connection for generating a quasi-isometric, low-dimensional mapping from a sparse and irregular sampling of an arbitrary low-dimensional manifold embedded in a high-dimensional space. Our geometric procedure computes a low-dimensional embedding that best preserves all pairwise geodesic distances over the input pointset similarly to one of the staples of manifold learning, the Isomap algorithm, and exhibits the same strong resilience to noise. While Isomap relies on Dijkstra's shortest path algorithm to approximate geodesic distances over the input pointset, we instead propose to compute them through "parallel transport unfolding," a discrete form of Cartan's development, to offer robustness to poor sampling and arbitrary topology. Our novel approach to evaluating geodesic distances using discrete differential geometry results in a markedly improved robustness to irregularities and sampling voids. In particular, it does not suffer from Isomap's limitation to geodesically convex sampled domains. Moreover, it involves only simple linear algebra, significantly improves the accuracy of all pairwise geodesic distance approximations, and has the same computational complexity as Isomap. We also show that our connection-based distance estimation can be used for faster variants of Isomap such as Landmark-Isomap.
Finally, we introduce an operator-adapted multiresolution analysis for finite-element differential forms. From a given continuous, linear, bijective, and self-adjoint positive-definite operator L, a hierarchy of basis functions and associated wavelets for discrete differential forms is constructed in a fine-to-coarse fashion and in quasilinear time. The resulting wavelets are L-orthogonal across all scales, and can be used to obtain a Galerkin discretization of the operator with a block diagonal stiffness matrix composed of uniformly well-conditioned and sparse blocks. Because our approach applies to arbitrary differential p-forms, we can derive both scalar-valued and vector-valued wavelets that block diagonalize a prescribed operator. Our construction applies to various types of computational grids, offers arbitrary smoothness orders of basis functions and wavelets, and can accommodate linear differential constraints such as divergence-freeness. We also demonstrate the benefits of the operator-adapted multiresolution decomposition for coarse-graining and model reduction of linear and nonlinear partial differential equations.
We conclude with a short discussion on how future work in geometric model reduction may impact other related topics such as semi-supervised learning.</p
Intramolecular Hydrogen-shift Reactions of Peroxy Radicals
Get PDFStraight chain alkanes with more than five carbons, emitted in cities due to incomplete combustion and fuel evaporation, undergo atmospheric gas-phase oxidation with the hydroxyl radical to produce alkyl radicals. These alkyl radicals subsequently add O2, leading to the formation of peroxy radicals. Following further reaction of these radicals in urban areas, hydroxy-substituted peroxy radicals are formed. Previously, the fate of these peroxy radicals was assumed to be dominated by reaction with nitric oxide, a common air pollutant. Computational and experimental investigations of the oxidation mechanism of 2-hexanol, however, demonstrate that hydrogens α to the hydroxy group exhibit a significantly reduced energetic barrier toward intramolecular hydrogen shifts to the peroxy radical. The barrier reduction for these hydrogen shift reactions results in rate constants that are orders of magnitude larger than for alkyl hydrogens that lack α substitution. Due to significant reductions of nitric oxide emissions in North America, these rate constants are sufficiently large to suggest that this chemistry is competitive even in large cities, particularly during warm summer days. Gas-phase alkyl hydroperoxides, a class of compounds previously expected to exist in negligible quantities in cities, are major products of this chemistry.
Further oxidation of alkyl hydroperoxides leads to the formation of hydroperoxy-substituted peroxy radicals. The chemistry of such peroxy radicals is evaluated through the oxidation of 2-hydroperoxy-2-methylpentane. Experimental observations confirm the previously reported computational result that these peroxy radicals rapidly isomerize by intramolecular hydrogen shift of the hydroperoxide hydrogen. This isomerization occurs on timescales that are much faster than those of bimolecular reaction in essentially all regions of the troposphere. As a consequence of the isomerization, one peroxy radical isomer produced in the oxidation of 2-hydroperoxy-2-methylpentane exhibits an α hydroperoxide hydrogen shift. This reaction rate constant is similar to that reported for the α hydroxy hydrogen shift in the 2-hexanol system.
Alkoxy radicals produced in the oxidation of 2-hydroperoxy-2-methylpentane are similarly shown to undergo a very rapid hydrogen shift of the hydroperoxide hydrogen. One of these shifts results in a peroxy radical that exhibits an α hydroxy hydrogen shift. Thus, the rapid scrambling of hydroperoxy-subsituted alkoxy and peroxy radicals is a key process that can enable additional unimolecular pathways that are otherwise inaccessible. This chemistry has the potential to introduce significant mechanistic complexity and, due to the rapid nature of the reactions, cannot be neglected even under typical "high NO" conditions employed in chamber studies.</p
Phototherapeutic Devices for the Treatment of Diabetic Retinopathy
Get PDFDiabetic retinopathy is a microvascular disease of the retina and a leading cause of vision loss worldwide. In the non-proliferative phase, diabetes-induced degradation of the retinal blood supply leads to edema and progressive tissue hypoxia. In response, the retinal tissue expresses proangiogenic growth factors (e.g. vascular endothelial growth factor), which drive proliferation of aberrant blood vessels within the eye. These poorly formed vessels leak fluid and blood cells into the eye and grow into the vitreous, which puts traction on the retina and leads to detachment. Given the hypoxic etiology, retinal oxygen tension and metabolism have received considerable attention. Dark-adapted conditions drive the retina to a significantly lower oxygen tension compared to light- adapted conditions as rod cells consume more energy in order to boost sensitivity. While tolerable in the healthy retina, it has been hypothesized that increased nightly metabolism overwhelms the compromised oxygen supply in the diabetic retina, leading to hypoxia and pathological vascular endothelial growth factor expression.
This thesis develops ocular devices that shine light onto the retina to modulate rod metabolism, reducing oxygen demand and mitigating nightly hypoxia. The phototherapeutic effect is characterized through mathematical modeling of retinal metabolism and in vivo testing. Implantable phototherapy devices are designed, fabricated, and evaluated. This thesis also develops overnight phototherapeutic contact lenses utilizing radioluminescence, chemiluminescence, and electroluminescence approaches. Phototherapy holds promise as a non-invasive, preventative therapy for the treatment of hypoxic retinal diseases such as diabetic retinopathy.</p
Mechanistic Bases for Privileged Capture and Unidirectional Targeting of Tail-Anchored Proteins by the Get3 ATPase
Get PDFC-terminal tail-anchored membrane proteins (TAs) are targeted post-translationally to the endoplasmic reticulum (ER) in eukaryotic cells mainly through the Guided entry of tail-anchored protein (GET) pathway. Here we use biochemical and biophysical approaches to shed further mechanistic insight into how the central chaperone, the Get3 ATPase, is able to capture TA substrates in a privileged manner and provide unidirectional targeting to the ER.
Specifically, we first show in Chapter 2 that Get3 dynamically samples open and closed conformations as a "protean clamp". Binding of TA substrates induces Get3 to sample more open conformations that causes Get3 to dissociate from the cytosolic regulatory Get4/5 complex, hydrolyze ATP, and become primed to interact with the Get1/2 membrane receptors. Therefore, a TA substrate acts as the switch for unidirectional targeting, transitioning Get3 from a "TA-loading mode" to a "membrane targeting mode". Next, in Chapter 3, we show that a small, conserved alpha-helical lid motif, known as α8, lining the substrate binding groove is necessary for Get3 to efficiently capture TA substrates in a privileged manner over competing off-pathway chaperones.</p
Atmospheric Peroxy Radical Chemistry Studied by Infrared Kinetic Spectroscopy
Get PDFPeroxy radical (RO2) chemistry plays a central role in atmospheric science. RO2 radicals control the oxidative capacity of the atmosphere and are key intermediates in the cycling of ozone in the troposphere in regions where levels of nitrogen oxides (NOx ≡ NO + NO2) are high. In more remote regions of the Earth where NOx concentrations are low, RO2 loss is dominated by reaction with hydroperoxy (HO2) and other peroxy radicals, leading to removal of reactive radicals from the troposphere. However, for certain species of RO2, reaction with HO2 can also propagate radical chemistry by recycling hydroxyl (OH) radicals, a primary oxidant in the atmosphere. Both HO2 and OH radicals play important roles in atmospheric oxidation reactions. Accurate characterization of various RO2 reactions that contribute to consuming and recycling HOx (HOx ≡ HO2 + OH) are instrumental for understanding the effects of atmospheric composition on climate forcing, air quality, and the global ozone budget.
My thesis work used laboratory studies to characterize gas phase organic peroxy radical (RO2) reactions that are relevant to atmospheric chemistry. The main body of my work focused on studying the self reactions of HO2 and RO2 as well as their cross reactions (HO2 + RO2) using a time-resolved experimental technique called Infrared Kinetic Spectroscopy (IRKS), which combines infrared (IR) and ultraviolet (UV) absorption spectroscopy. Perfect isolation of one specific reaction is generally difficult or impossible due to radical recycling and secondary chemistry, which leads to numerous reactions occurring simultaneously. Thus, although laboratory studies provide controlled environments to study these reactions, the accuracy of the results are highly dependent on the experiment's selectivity and sensitivity to specific transient species. In this work, a new mid-IR (MIR) laser was implemented into the existing apparatus for measuring OH radicals. In addition to UV absorption spectroscopy, the IRKS apparatus was equipped for selective detection of HO2 and OH radicals in the near-IR (NIR) and MIR, respectively.
The kinetics and product yields of a reaction are two important factors for assessing the impact of these reactions on the atmosphere. IRKS was used to study the kinetics of the self reactions of acetylperoxy (CH3C(O)O2) and acetonylperoxy (CH3C(O)CH2O2), as well as their reactions with HO2. The OH and O3 yields from the reaction of HO2 + CH3C(O)O2 were also measured, providing the first parametrization of the temperature dependence of the OH product channel. The temperature dependence of the HO2 self reaction kinetics was re-investigated to resolve discrepancies in the results previously reported in the literature. Furthermore, this work identified and characterized rate enhancement effects on the HO2 self reaction by the adducts of HO2 formed from the reaction of HO2 with methanol (CH3OH), acetaldehyde (CH3CHO), and acetone (CH3C(O)CH3), which were used as radical precursors for HO2, CH3C(O)O2, and CH3C(O)CH2O2, respectively.
Finally, the improved sensitivity of the IRKS apparatus enabled the investigation of fast reaction kinetics. The rate constants of Cl atoms with CH3OH and CH3CHO were measured over a wide range of temperatures. The results were consistent with previously reported values in the literature and additionally validated assumptions that had been made regarding the temperature independence of these reactions. The temperature and pressure dependences of the OH yield from the reaction of CH3CO with O2 were also studied to resolve current discrepancies in the literature. The yield of HO2 from this reaction was also directly measured for the first time. </p
Exploring Microscopic Thermal Transport Properties of Molecular Crystals with Simulations and Experiments
Get PDFPolymers are widely used in applications due to their diverse and controllable properties in many physical domains. However, polymers have not historically been used in applications for which a high thermal conductivity is required as bulk polymers are typically thermal insulators. However, research in recent decades on a handful of highly oriented or semi-crystalline polymers has shown the potential for dramatically increased uniaxial thermal conductivity by factors exceeding 100. This dramatic increase in thermal conductivity is because heat is conducted by atomic vibrations along the covalently bonded polymer backbone rather than across chains by weak van der Waals bonds as in unoriented polymers. While it is known that polymers can be processed to yield these properties, much remains unknown about the microscopic transport properties of atomic vibrations in these materials and the true upper limits to thermal conductivity. In this thesis, we address these knowledge gaps by using a combination of simulations and experiments to investigate thermal conduction in semi-crystalline and crystalline polymers.
First, we present molecular dynamics simulations of a perfect polymer crystal, polynorbornene. While polymer crystals studied typically exhibit substantially enhanced thermal conductivities above those of the amorphous form, polynorbornene exhibits a glass-like thermal conductivity of less than 1 Wm-1K-1 even as a perfect crystal. This unusual behavior occurs despite the polymer satisfying many of the conventional criteria for high thermal conductivity. Using our simulations, we show that the origin of this unusual behavior is excessively anharmonic bonds and a complex unit cell.
Second, we move to experimental studies of thermal transport in polymers. A key requirement to perform materials science is a method to routinely and easily characterize the property of interest in diverse samples. For polymers, this property is typically the in-plane thermal conductivity. This property turns out to be surprisingly difficult to measure using conventional thermal characterization methods. In this work, we adapt transient grating spectroscopy (TG), a well-known method in the chemistry community, to perform in-plane thermal conductivity measurements of polymer films. TG can resolve the in-plane thermal anisotropy of a sample without any physical contact and at tunable length scales, a substantial advance in capability over all prior characterization methods. We extend the application of TG to probe sub-µm length scales, and we successfully apply the technique to numerous poor quality polymer samples as well as thin films.
Finally, we exploit the capability of TG to probe thermal conduction over sub-µm length scales to provide the first experimentally resolved microscopic transport properties of atomic vibrations in semi-crystalline polyethylene (PE). Despite the intense interest over decades in PE due to its high intrinsic thermal conductivity, no experimental measurement has yet been able to directly probe the heat-carrying phonons, leading to many questions about the relevant scattering mechanisms and absolute upper limits of thermal conductivity in real samples. Using TG, we present the first observation of quasi-ballistic thermal transport at sub-µm length scales, from which we obtain the phonon mean free path spectra of a semi-crystalline PE sample. Further, we pair these results with Small-Angle X-ray Scattering measurements to show that thermal phonons propagate ballistically within and across nanocrystalline domains, contrary to the conventional viewpoint. These results provide an unprecedented microscopic view of thermal transport in polymer crystals that was previously experimentally inaccessible.</p
The Many Roles of the Nitrogenase Iron Protein
Get PDFNitrogenase is the only known enzyme capable of reducing atmospheric nitrogen (N2) into ammonia (NH3) for incorporation into cellular material. N2 reduction by nitrogenase is accomplished by sequential electron transfer between two component proteins: the substrate reductase (the MoFe-protein), and a specialized low-potential electron donor (the Fe-protein). The MoFe-protein contains the active site for nitrogen reduction, the FeMocofactor (FeMo-co). During nitrogen reduction, each Fe-protein dimer docks onto the MoFe-protein, transferring electrons to an intermediate cluster (P-cluster), and ultimately to the FeMo-co.
Strikingly, the Fe-protein has another critical role in nitrogen fixation. The Fe-protein is required for the biosynthesis of the two unique metalloclusters of the MoFe-protein: the Pcluster [8Fe:7S] and the active site FeMo-co ([Mo:7Fe:9S:C]-R-homocitrate) cluster. During FeMo-co-cluster maturation, the Fe-protein forms a complex with NifEN, a scaffolding protein homologous to the MoFe-protein, catalyzing the final step in the FeMoco biosynthesis. Studies indicate that the Fe-protein catalyzes insertion of molybdenum and R-homocitrate into an all-iron FeMo-co precursor in a reductant and nucleotide dependent manner. The remaining questions about the cellular functions of the Fe-protein include how the Fe-protein interacts with other maturation proteins in distinct (or similar) ways compared to the MoFe-protein, and how the Fe-protein contributes to the activation and insertion of molybdenum into the FeMo-co.</p
Applications of the Enantioselective Allylic Alkylation Toward the Synthesis of Complex Natural Products
Get PDFThe Stoltz group, and moreover the synthetic community at large, has long been interested in the development of methods for the synthesis of enantioenriched all-carbon quaternary stereocenters. This thesis present three projects all unified by the development and use of the palladium-catalyzed decarboxylative allylic alkylation to synthesize enantioenriched all-carbon quaternary stereocenter containing cyclopentanones as well as the natural product total synthesis.</p
Nonlinear Physics in Soliton Microcombs
Get PDFLike rulers of light, optical frequency combs consist of hundreds to millions of coherent laser lines, which are capable of measuring time and frequency with the highest degree of accuracy. Used to rely on table-top mode-locked lasers, optical frequency combs have been recently realized in a miniaturized form, namely the microcomb, using monolithic microresonators. Besides a reduction of footprint, microcombs could also achieve parity with traditional frequency combs in performance by mode-locking through the formation of "light bullets" called dissipative Kerr solitons. These soliton microcombs not only serve as a unique platform to study nonlinear physics, but also offer scalable and cost-effective solutions to many groundbreaking applications, spanning spectroscopy to time standards. In this thesis I will trace the physical origin of soliton microcombs, followed by their experimental realization in high-Q silica microresonators. The impact of several nonlinear process on solitons will be discussed, which leads to novel soliton systems, e.g., Stokes solitons and counter-propagating solitons. Utilizing these nonlinear properties, we show that soliton microcombs can be adapted for high-precision spectroscopic applications. In the end, a real-time method for monitoring transient behavior of solitons will be presented
Towards High Performance Robotic Actuation
Get PDFThe main objective of this thesis is to enable development of high performance actuation for legged, limbed and mobile robots. Due to the fact that such robots need to support their own weight, their actuators need to be light weight, compact and efficient. Furthermore, a dynamics analysis, shows that the actuators' design may have significant impact on a robot's dynamics sensitivity. These consideration motivate improvements in all actuator design aspects.
First, the application-specific design of outer rotor motors with concentrated windings is considered. It is shown that an intrinsic design trade-off exists between a motor's copper loss, core loss and mass, which allows development of motors with superior performance for a particular application. The three main application categories of interest are: electric vehicles, drones and robotic joints. Due to their outstanding torque density, high pole count outer rotor motors are analysed in terms of their design and optimization for robotic applications. Motor design scaling modes are also described in order to outline the main challenges in the implementation of high torque motors.
Next, the design of gearboxes for robotic actuation is discussed. A novel type of high reduction Bearingless Planetary Gearbox is introduced which allows large range of reduction ratios to be achieved in a compound planetary stage. In this concept, all gear components float in an unconstrained manner as the planet carrier is substituted with a secondary sun gear. The advantages of the Bearingless Planetary Gearbox over current approaches in terms of improved robustness, load distribution, manufacturability, and assembly are outlined.
Finally, analysis, design, and prototyping of rotary planar springs for rotary series elastic actuators is described. A mathematical model, based on curved beam theory, that allows rapid design, analysis, and comparison of rotary springs is developed. Mass reduction techniques based on composite arm structures are introduced and internal arm contact modeling is presented. Motivated by strain energy density analysis, an optimization based spring design approach is developed that allows significant increase in the torque and torque density.</p