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Open Access Publications from the University of California

Scholarly Works (22 results)

  • Thesis
  • Peer Reviewed
UC Berkeley Electronic Theses and Dissertations (2018)

It is well-known that internal wave breaking is the principle cause of ocean mixing. The latter plays a role in shaping global climate and ocean ecology. To understand how internal wave loses instability and possibly breaks, in this thesis I present some new findings on the instability mechanisms of internal gravity waves due to wave-wave/topography interactions.

Parametric Subharmonic Instability (PSI) is one of the most important mechanisms that transfer energy from tidally-generated long internal waves to short steep waves. Breaking of these short waves results in diapycnal mixing through which oceanic abyssal stratification is maintained. It has long been believed that PSI is strongest between a primary internal wave and perturbative waves of half the frequency of the primary wave. Here, I rigorously show that this is not the case. Specifically, I show that neither the initial growth rate nor the maximum long-term amplification occur at the half frequency, and demonstrate that the dominant subharmonic waves have much longer wavelengths than previously thought.

Next I show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently transfers the energy of an internal wave to its higher harmonics. I show that, in fact, there are a countably infinite number of such unstable waves. For the harmonic-generation resonance to take place, the nonlinear terms in the free surface boundary condition play a pivotal role, and the instability does not occur in a linearly-stratified fluid if a simplified boundary condition such as a rigid lid or a linearized boundary condition is employed. Harmonic-generation resonance presented here provides a mechanism for the transfer of internal wave energy to the higher-frequency part of the spectrum hence affecting, potentially significantly, the evolution of the internal waves spectrum.

Following the work on harmonic generations of internal waves, we show that monochromatic internal gravity waves in a stratified ocean can continuously descend to smaller scales of higher wave numbers after being reflected from no-penetration boundaries, provided their second harmonics satisfy dispersion relation. The wave with wave number $k$ and frequency $\omega$ first generate its second harmonic due to the non-linearity in the momentum equation and the free surface boundary. Then the resonant interaction of the parent wave with its second harmonic gives rise to a $(3k, \omega)$ wave upon reflection, starting from which a series of triad resonances continuously form in the vicinity of the frequency $\omega$ or $2\omega$. The energy of the internal wave is sent to waves with higher and higher wave numbers. The mechanism potentially explains how part of internal wave energy converts from large scales to that of turbulent mixing near reflecting boundaries, such as ocean ridges and steep continental slopes.

Internal waves mainly arise from wind disturbing the upper ocean mixed layer and barotropic tide flowing over topographic features in the ocean. I report a mechanism for conversion of tidal energy to internal gravity waves, through baratropic tidal currents interacting with ambient internal waves. The newly-generated internal waves have the same wave length as the ambient waves and frequencies higher by the tidal frequency. I show that they grow exponentially in time and continuously extract energy from the tidal currents. The mechanism exists in any stratified ocean with smooth density profiles and is only possible if a nonlinear free surface is taken into account. I show that for a typical water depth of 4000 m and density stratification 5\% in the Pacific Ocean, the energy flux from baratropic tide to plane internal waves via this mechanism can reach order of 1MWm$^{-1}$. It therefore can be significant enough to account for a fraction of the 1TW total tidal energy loss in the open deep ocean.

Ocean mixing has been seen increased where there is rough bottom topography in the ocean. I show in theory that, in a two dimensional domain, with a free surface taken into account, the interaction between an internal wave and corrugated bottom topography can efficiently generate a series of co-directional internal waves with higher wave numbers. As a result, the internal wave energy can be transferred to smaller scales where internal wave is more prone to breaking and being dissipated.

    Cover page: Instability of Internal Gravity Waves from Wave-wave/topography Interactions
    • Thesis
    • Peer Reviewed
    UC Berkeley Electronic Theses and Dissertations (2012)

    In this dissertation, the problem of flexible demand management under time-varying prices is studied. This generic problem has many applications, which usually have multiple periods in which decisions on satisfying demand need to be made, and prices in these periods are time-varying. Examples of such applications include multi-period procurement problem, operating room scheduling, and user-end demand scheduling in the Smart Grid, where the last application is used as the main motivating story throughout the dissertation.

    The current grid is experiencing an upgrade with lots of new designs. What is of particular interest is the idea of passing time-varying prices that reflect electricity market conditions to end users as incentives for load shifting. One key component, consequently, is the demand management system at the user-end. The objective of the system is to find the optimal trade-off between cost saving and discomfort increment resulted from load shifting. In this dissertation, we approach this problem from the following aspects: (1) construct a generic model, solve for Pareto optimal solutions, and analyze the robust solution that optimizes the worst-case payoffs, (2) extend to a distribution-free model for multiple types of demand (appliances), for which an approximate dynamic programming (ADP) approach is developed, and (3) design other efficient algorithms for practical purposes of the flexible demand management system.

    We first construct a novel multi-objective flexible demand management model, in which there are a finite number of periods with time-varying prices, and demand arrives in each period. In each period, the decision maker chooses to either satisfy or defer outstanding demand to minimize costs and discomfort over a certain number of periods. We consider both the deterministic model, models with stochastic demand or prices, and when only partial information about the stochastic demand or prices is known. We first analyze the stochastic optimization problem when the objective is to minimize the expected total cost and discomfort, then since the decision maker is likely to be risk-averse, and she wants to protect herself from price spikes, we study the robust optimization problem to address the risk-aversion of the decision maker. We conduct numerical studies to evaluate the price of robustness.

    Next, we present a detailed model that manages multiple types of flexible demand in the absence of knowledge regarding the distributions of related stochastic processes. Specifically, we consider the case in which time-varying prices with general structures are offered to users, and an energy management system for each household makes optimal energy usage, storage, and trading decisions according to the preferences of users. Because of the uncertainties associated with electricity prices, local generation, and the arrival processes of demand, we formulate a stochastic dynamic programming model, and outline a novel and tractable ADP approach to overcome the curses of dimensionality. Then, we perform numerical studies, whose results demonstrate the effectiveness of the ADP approach.

    At last, we propose another approximation approach based on Q-learning. In addition, we also develop another decentralization-based heuristic. Both the Q-learning approach and the heuristic make necessary assumptions on the knowledge of information, and each of them has unique advantages. We conduct numerical studies on a testing problem. The simulation results show that both the Q-learning and the decentralization based heuristic approaches work well. Lastly, we conclude the paper with some discussions on future extension directions.

      Cover page: Flexible Demand Management under Time-Varying Prices
      • Article
      • Peer Reviewed
      UCLA Previously Published Works (2017)
      Bioorthogonal chemistry has had a major impact on the study of biological processes in vivo. Biomolecules of interest can be tracked by using probes and reporters that do not react with cellular components and do not interfere with metabolic processes in living cells. Much time and effort has been devoted to the screening of potential bioorthogonal reagents experimentally. This Account describes how our groups have performed computational screening of reactivity and mutual orthogonality. Our collaborations with experimentalists have led to the development of new and useful reactions. Dozens of bioorthogonal cycloadditions have been reported in the literature in the past few years, but as interest in tracking multiple targets arises, our computational screening has gained importance for the discovery of new mutually orthogonal bioorthogonal cycloaddition pairs. The reactivities of strained alkenes and alkynes with common 1,3-dipoles such as azides, along with mesoionic sydnones and other novel 1,3-dipoles, have been explored. Studies of "inverse-electron-demand" dienes such as triazines and tetrazines that have been used in bioorthogonal Diels-Alder cycloadditions are described. The color graphics we have developed give a snapshot of whether reactions are fast enough for cellular applications (green), adequately reactive for labeling (yellow), or only useful for synthesis or do not occur at all (red). The colors of each box give an instant view of rates, while bar graphs provide an analysis of the factors that control reactivity. This analysis uses the distortion/interaction or activation strain model of cycloaddition reactivity developed independently by our group and that of F. Matthias Bickelhaupt in The Netherlands. The model analyzes activation barriers in terms of the energy required to distort the reactants to the transition state geometry. This energy, called the distortion energy or activation strain, constitutes the major component of the activation energy. The strong bonding interaction between the termini of the two reactants, which we call the interaction energy, overcomes the distortion energy and leads to the new bonds in the products. This Account describes how we have analyzed and predicted bioorthogonal cycloaddition reactivity using the distortion/interaction model and how our experimental collaborators have employed these insights to create new bioorthogonal cycloadditions. The graphics we use document and predict which combinations of cycloadditions will be useful in bioorthogonal chemistry and which pairs of reactions are mutually orthogonal. For example, the fast reaction of 5-phenyl-1,2,4-triazine and a thiacycloheptyne will not interfere with the other fast reaction of 3,6-diphenyl-1,2,4,5-tetrazine and a cyclopropene. No cross reactions will occur, as these are very slow reactions.
        Cover page: Bioorthogonal Cycloadditions: Computational Analysis with the Distortion/Interaction Model and Predictions of Reactivities
        • Article
        • Peer Reviewed
        UCLA Previously Published Works (2016)
        Density functional theory (DFT) calculations and experiments in tandem led to discoveries of new reactivities and selectivities involving bioorthogonal sydnone cycloadditions. Dibenzocyclooctyne derivatives (DIBAC and BARAC) were identified to be especially reactive dipolarophiles, which undergo the (3 + 2) cycloadditions with N-phenyl sydnone with the rate constant of up to 1.46 M-1 s-1. Most significantly, the sydnone-dibenzocyclooctyne and norbornene-tetrazine cycloadditions were predicted to be mutually orthogonal. This was validated experimentally and used for highly selective fluorescence labeling of two proteins simultaneously.
          Cover page: Discovery of new mutually orthogonal bioorthogonal cycloaddition pairs through computational screening.
          • Article
          • Peer Reviewed
          UCLA Previously Published Works (2016)
          Density functional theory (DFT) calculations and experiments in tandem led to discoveries of new reactivities and selectivities involving bioorthogonal sydnone cycloadditions. Dibenzocyclooctyne derivatives (DIBAC and BARAC) were identified to be especially reactive dipolarophiles, which undergo the (3+2) cycloadditions with N-phenyl sydnone with the rate constant of up to 1.46 M-1 s-1. Most signifcantly, the sydnone-dibenzocyclooctyne and norbornene-tetrazine cycloadditions were predicted to be mutually orthogonal. This was validated experimentally and used for highly selective fluorescence labeling of two proteins simultaneously.
            Cover page: Discovery of new mutually orthogonal bioorthogonal cycloaddition pairs through computational screening
            • Article
            • Peer Reviewed
            UCLA Previously Published Works (2023)
            Prized for their ability to generate chemical complexity rapidly, catalytic carbon-hydrogen (C-H) activation and functionalization reactions have enabled a paradigm shift in the standard logic of synthetic chemistry. Directing group strategies have been used extensively in C-H activation reactions to control regio- and enantioselectivity with transition metal catalysts. However, current methods rely heavily on coordination with nitrogen and/or oxygen atoms in molecules and have therefore been found to exhibit limited generality in asymmetric syntheses. Here, we report enantioselective C-H activation with unsaturated hydrocarbons directed by phosphorus centres to rapidly construct libraries of axially chiral phosphines through dynamic kinetic resolution. High reactivity and enantioselectivity are derived from modular assembly of an iridium catalyst with an endogenous phosphorus atom and an exogenous chiral phosphorus ligand, as confirmed by detailed experimental and computational studies. This reaction mode significantly expands the pool of enantiomerically enriched functional phosphines, some of which have shown excellent efficiency for asymmetric catalysis.
              Cover page: Atroposelective hydroarylation of biaryl phosphines directed by phosphorus centres.
              • Article
              • Peer Reviewed
              UCLA Previously Published Works (2014)
              Substituted cyclopropenes have recently attracted attention as stable "mini-tags" that are highly reactive dienophiles with the bioorthogonal tetrazine functional group. Despite this interest, the synthesis of stable cyclopropenes is not trivial and their reactivity patterns are poorly understood. Here, the synthesis and comparison of the reactivity of a series of 1-methyl-3-substituted cyclopropenes with different functional handles is described. The rates at which the various substituted cyclopropenes undergo Diels-Alder cycloadditions with 1,2,4,5-tetrazines were measured. Depending on the substituents, the rates of cycloadditions vary by over two orders of magnitude. The substituents also have a dramatic effect on aqueous stability. An outcome of these studies is the discovery of a novel 3-amidomethyl substituted methylcyclopropene tag that reacts twice as fast as the fastest previously disclosed 1-methyl-3-substituted cyclopropene while retaining excellent aqueous stability. Furthermore, this new cyclopropene is better suited for bioconjugation applications and this is demonstrated through using DNA templated tetrazine ligations. The effect of tetrazine structure on cyclopropene reaction rate was also studied. Surprisingly, 3-amidomethyl substituted methylcyclopropene reacts faster than trans-cyclooctenol with a sterically hindered and extremely stable tert-butyl substituted tetrazine. Density functional theory calculations and the distortion/interaction analysis of activation energies provide insights into the origins of these reactivity differences and a guide to the development of future tetrazine coupling partners. The newly disclosed cyclopropenes have kinetic and stability advantages compared to previously reported dienophiles and will be highly useful for applications in organic synthesis, bioorthogonal reactions, and materials science.
                Cover page: Synthesis and Reactivity Comparisons of 1‐Methyl‐3‐Substituted Cyclopropene Mini‐tags for Tetrazine Bioorthogonal Reactions
                • Article
                • Peer Reviewed
                UCLA Previously Published Works (2017)
                The design, synthesis, and evaluation of bifunctional linchpins, conformationally anchored on six-membered rings to achieve efficient [1,5]-Brook rearrangements involving vinyl silanes have been achieved. The restrained linchpins were subsequently exploited in type II anion relay chemistry (ARC) to permit both alkylations and Pd-mediated cross-coupling reactions (CCR) of sp2 stabilized carbanions. DFT calculations were then employed to understand the mechanism and reactivity trends of [1,4]- and [1,5]-vinyl Brook rearrangements to provide insight on the role of the required copper reagent and the substrate geometry.
                  Cover page: Type II Anion Relay Chemistry: Conformational Constraints To Achieve Effective [1,5]-Vinyl Brook Rearrangements
                  • Article
                  • Peer Reviewed
                  UCLA Previously Published Works (2016)
                  A reusable silicon-based transfer agent (1) has been designed, synthesized, and validated for effective room-temperature palladium-catalyzed cross-coupling reactions (CCRs) of aryl and heteroaryl chlorides with readily accessible aryl lithium reagents. The crystalline, bench-stable siloxane transfer agent (1) is easily prepared via a one-step protocol. Importantly, this "green" CCR protocol circumvents prefunctionalization, isolation of organometallic cross-coupling partners, and/or stoichiometric waste aside from LiCl. DFT calculations support a σ-bond metathesis mechanism during transmetalation and lead to insights on the importance of the CF3 groups.
                    Cover page: Design, Synthesis, and Validation of an Effective, Reusable Silicon-Based Transfer Agent for Room-Temperature Pd-Catalyzed Cross-Coupling Reactions of Aryl and Heteroaryl Chlorides with Readily Available Aryl Lithium Reagents
                    • Article
                    • Peer Reviewed
                    UCLA Previously Published Works (2021)
                    Experiments indicate that a catalytic amount of CuI plays an important role in the siloxane-mediated Pd-catalyzed cross-coupling reactions with the direct use of organolithium reagents. Addition of organolithium to the siloxane transfer agent generates an organosilicon intermediate. DFT calculations indicate that CuI initially accelerates the Si-Pd(II) transmetalation of the organosilicon intermediate by the formation of CuI2 -. Subsequently, CuI2 - works as a shuttle between the Si-Cu(I) and Cu(I)-Pd(II) transmetalation processes.
                      Cover page: The role of CuI in the siloxane-mediated Pd-catalyzed cross-coupling reactions of aryl iodides with aryl lithium reagents
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