Strange attractors in periodically-kicked degenerate Hopf bifurcations

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a new multi-parameter version of the theory of rank one maps developed by Wang and Young.Comment: 16 page

Approach to equilibrium for the stochastic NLS

We study the approach to equilibrium, described by a Gibbs measure, for a system on a $d$-dimensional torus evolving according to a stochastic nonlinear Schr\"odinger equation (SNLS) with a high frequency truncation. We prove exponential approach to the truncated Gibbs measure both for the focusing and defocusing cases when the dynamics is constrained via suitable boundary conditions to regions of the Fourier space where the Hamiltonian is convex. Our method is based on establishing a spectral gap for the non self-adjoint Fokker-Planck operator governing the time evolution of the measure, which is {\it uniform} in the frequency truncation $N$. The limit $N\to\infty$ is discussed.Comment: 15 p

Improvement of random vibration theory site response analysis

Random Vibration Theory (RVT) site response analysis is a standard in seismic hazard analysis for nuclear facilities to compute the dynamic response of soil deposits. However, studies have shown that the RVT analysis predicts site amplification at natural site frequencies that are considerably larger than the time series (TS) analysis. The objectives of this research are to identify improvements to the current approaches used in RVT site response analysis and to incorporate these improvements so that the discrepancy between RVT and TS site amplification are reduced. This research first investigates a critical part of the RVT approach – the peak factor, defined as the peak to root-mean-square (rms) ratio of a signal. It is shown that by accounting for the statistical dependence between peaks, the peak factor model developed by Vanmarcke (1975) is superior to the model developed by Cartwright and Longuet-Higgins (1956) when applied to seismic site response analysis. The use of the Vanmarcke peak factor model reduces the RVT site amplification at the natural site frequencies and makes the RVT amplification more similar to the TS analysis. This research also investigates the duration used in the computation of the rms value from the Fourier Amplitude Spectrum. It is shown that by accounting for the influence of the dynamic site response on the duration of the oscillator response, the RVT analysis generally predicts site amplification within +/- 10% of TS analysis. To apply the modification of duration to RVT without the use of time series, a duration model is developed that empirically predicts the change of duration at the ground surface due to site response. In the last part of the research, the improved RVT approach, which utilizes the Vanmarcke (1975) peak factor and incorporates the change in duration due to site response, is applied to more complex and realistic shear wave velocity profiles and for strain-compatible properties associated with equivalent-linear analysis. The site amplification results indicate that the improved RVT site response analysis generally works well to reduce the discrepancy between RVT and TS amplification for a wide range of situations.Civil, Architectural, and Environmental Engineerin

Forward optimization and real-time model adaptation with applications to portfolio management, indifference valuation and optimal liquidation

The goal of this thesis is to introduce a new, alternative approach to deal with model uncertainty and “real-time” model revisions and, in turn, develop a comparative study with existing approaches in the context of various applications in financial mathematics. This new approach is based on the forward performance criteria which adapt in a time-consistent way to “real-time” model revisions. The novelty is that these revisions are genuinely “model-free” in that they occur in “real-time”, without any modeling pre-commitment. For example, in the context of optimal liquidation (see Chapter 3 and Chapter 4), there is no a priori model for the evolution of the market impact parameter λ. It is rather assumed that this parameter switches at predictable times, to values only observable at the switching times. As such, the model revisions capture the evolving reality and allow for considerable flexibility. This forward approach thus incorporates “real-time” model revisions and is, therefore, close to adaptive optimization. On the other hand, it produces, by construction, time-consistent policies and is, thus, close to the classical optimization with model(s) pre-commitment. In other words, it can be thought as a hybrid approach that accommodates dynamic model changes while preserving time-consistency. We apply the forward approach with “real-time” model revisions in four distinct problems: portfolio management in discrete and continuous settings (binomial and lognormal, respectively), indifference valuation in lognormal models and optimal liquidation in the continuous time Almgren-Chriss model. We produce closed form solutions and characterize the optimal policies and optimal criteria. As the analysis shows, one needs to solve various sequential “inverse” optimal investment problems with random coefficients, corresponding to model revisions in real-time. We develop a comparative study with the classical settings. A main novelty is the introduction of two performance metrics which measure the discrepancies between the actual performance, and the projected or the true optimal performances under the various criteria and behavior. We study these metrics for various scenaria, related to favorable and non-favorable market changes, and compare their performance. These metrics resemble the notion of “regret”, which is now considered in a more dynamic and “real-time” manner. Among others, we show that the regret of the forward decision maker is always zero, independently of the upcoming model changes. In what follows, we describe each application separately. For each application, we introduce the model, the forward and classical criteria, construct the corresponding solutions and policies, and compare them in detailMathematic

A co-translational ubiquitination pathway for quality control of newly synthesized proteins

textPrevious studies indicated that 6%-30% of newly synthesized proteins are rapidly degraded by the ubiquitin-proteasome system. This has generally been assumed to occur post-translationally, following failure of chaperone-assisted folding mechanisms. However, the extent and significance of co-translational quality control remains largely unknown. In investigations of ISG15, an interferon-induced ubiquitin-like protein, our lab found that ISG15 is conjugated to a very broad spectrum of newly synthesized proteins. The major ligase for ISG15, Herc5, co-fractionated with polysomes, and further studies indicated that the processes of translation and ISGylation were closely coupled. Here, I employ an in vitro run-off translation system and puromycin labeling experiments to demonstrate that nascent polypeptides are ISGylated within active translation complexes, providing direct support for the co-translational mechanism for ISG15 conjugation. Approaches developed for studying co-translational ISGylation were subsequently used to examine co-translational ubiquitination (CTU), which we hypothesized might be important in quality control of newly synthesized proteins. Consistent with this, I found that the pathway for degradation of newly synthesized proteins was initiated while proteins were being translated, with ubiquitination of actively translating nascent polypeptides. CTU is a conserved and robust pathway from yeast to mammals, with 5-6% of total nascent polypeptides being ubiquitinated in S. cerevisiae, and 12-15% in human cells. CTU products contained primarily K48-linked polyubiquitin chains, consistent with a proteasomal targeting function. Although nascent chains previously have been shown to be ubiquitinated within stalled and defective translation complexes (referred to here as CTU [superscript S]), nascent chain ubiquitination also occurred within active translation complexes (CTU [superscript A]). CTU [superscript A] accounted for approximately two-thirds of total CTU (CTU[superscript T]) in human cells and approximately half of CTU[superscript T] in yeast cells. CTU[superscript A] was increased in response to agents that induce protein misfolding, whereas CTU[superscript S] was increased in response to agents that led to translational misreading or stalling. These results indicate that ubiquitination of nascent chains occurs in two contexts and define CTU[superscript A] as a component of a quality control system that marks proteins for destruction before their synthesis is complete. Finally, decreased translation fidelity is thought to lead to the accumulation of misfolded proteins and hasten the aging process. As CTU is a pathway for quality control of newly synthesized proteins, I explored whether CTU plays a protective role during the replicative aging process in budding yeast. Consistent with previous reports using human cells, I found that newly synthesized proteins are a major source of proteasome substrates under non-stressed conditions. Transient proteasome inhibition (using MG132) led to a decrease of yeast replicative life span (RLS), whereas simultaneous treatment with cycloheximide, a translation inhibitor, suppressed this effect. Deletion of Ltn1, the major E3 ligase of the CTU[superscript S] pathway, also shortened the RLS of yeast. Together, these results provide a preliminary set of evidence supporting the hypothesis that the quality of newly synthesized proteins is an important determinant of aging.Microbiolog

Circumcision as a kinship ritual in ancient Israel

This dissertation argues that circumcision functions as a kinship ritual in the non-Priestly, narrative texts of the Hebrew Bible. Secondarily, by showing the continuity between non-Priestly and Priestly conceptualizations of circumcision, this study challenges the prevailing categorization of circumcision as a ritual that only acquired significance during the exilic and postexilic periods. Chapter 1 reviews the history of modern biblical scholarship on circumcision in the Hebrew Bible and explains the basis of the scholarly separation between non-Priestly and Priestly views of circumcision. Additionally, this chapter also discusses and evaluates various views of the function of circumcision in the Hebrew Bible. Chapter 2 presents the critical theoretical basis for the primary claim of this dissertation: that circumcision functions as a kinship ritual in ancient Israel. The chapter introduces Nancy Jay’s theory of the gendered nature of blood sacrifice and shows how it can be productively applied to the study of circumcision in the Hebrew Bible. The chapter argues for the kinship-oriented nature of both circumcision and blood sacrifice, taking into account not only biblical evidence but relevant anthropological data as well. Chapters 3–5 are a literary, historical-critical analysis of three non-Priestly, narrative passages regarding circumcision in the Hebrew Bible (Gen 34; Exod 4:24–26; Josh 5:2–9). Each chapter discusses previous scholarship concerning the function of circumcision in the passage before showing how circumcision is best explained as a kinship ritual in each passage. Chapter 6 focuses on three Priestly texts concerning circumcision (Gen 17; Exod 12:43–49; Lev 12:3) and shows how they too present circumcision as a kinship ritual. In doing so, the chapter suggests that there is more continuity between non-Priestly and Priestly presentations of circumcision than typically acknowledged. Chapter 7 concludes the dissertation, summarizes its main claims and arguments, and suggests a couple of directions for future research.Middle Eastern Studie

Theoretical and numerical study on adhesive interactions between graphene and substrate

This dissertation presents a set of theoretical and numerical studies on adhesive interactions between monolayer graphene membranes and their substrates. Both continuum mechanics models and molecular dynamics simulations are developed to investigate deformation of graphene membranes depending on the adhesive interactions with the substrates. First, a numerical study on snap transitions of gas-filled graphene blisters is presented, based on a continuum model combining a nonlinear plate theory with a nonlinear traction–separation relation. The numerical results may be used in conjunction with experiments for quantitative characterization of the interfacial properties of graphene and other two-dimensional (2D) membrane materials. Next, a statistical mechanics analysis on thermal rippling of monolayer graphene supported on a rigid substrate is presented and compared with molecular dynamics simulations to reveal the entropic effects of thermal rippling on van der Waals interactions between graphene and the substrate. While the amplitude of thermal rippling is reduced by the adhesive interactions, the entropic contribution of thermal rippling leads to an effective repulsion, thus reducing the effective adhesion. Moreover, the effect of a biaxial pre-strain in graphene is considered, and a buckling instability is predicted at a critical compressive strain that depends on both the temperature and the adhesive interactions. This motivates a systematic study on morphological transitions of monolayer graphene on a substrate under uniaxial compressive strain, from rippling to wrinkling/buckling and to folding. The presence of water at the interface has significant influence on the adhesive interactions between graphene and its substrate. Molecular dynamics simulations are performed to study the interactions between graphene and a wet substrate that is covered by a thin layer of water. Four stages of the traction-separation relations are identified and they are analyzed approximately by simple continuum models. When the thickness of water layer is below 1 nm, the water molecules form discrete monolayer or bilayer structures, leading to different traction-separation behaviors. Finally, with a finite number of water molecules trapped between a monolayer graphene and its substrate, water-filled graphene blisters form spontaneously. Based on molecular dynamics simulations and a simple theoretical model, the work of adhesion for the graphene/substrate interface may be estimated by measuring the aspect ratios of the graphene blisters. Unlike gas-filled graphene blisters in previous studies, the shape and size of the water-filled graphene blister depend on the wetting properties of graphene and the substrate. The results on wet adhesion and water-filled blisters can be readily extended to other 2D materials.Engineering Mechanic

Phase-driven optomechanics in exotic photonic media

Integrated photonics provide unique advantages in tailoring and enhancing optical forces. Recent advancements in integrated photonics have introduced many novel phenomena and exotic photonic media, such as photonic topological insulator, negative index material, photonic crystals, 2D material, and strongly-modulated time-dynamic systems. In my dissertation, I theoretically and numerically explore the novel properties and applications of optical forces in these systems. We propose guided-wave photonic pulling forces in photonic crystal waveguides. Photonic crystal waveguides offer great capability to define the mode properties, and can incorporate complex trajectories, leading to unprecedented flexibility and robustness compared to previous works in free space or in longitudinally uniform waveguides. With response theory, a virtual work approach, we establish general rules to tailor optical forces in periodic structures involved with photonic crystals: pulling forces arise from negative gradients in the phase responses of the outgoing modes, which corresponds to forward scattering on the Bloch band diagram with unit cell function corrections. We devise robust forward scattering, first, using topologically protected nonreciprocal chiral edge states, second, using backward (i.e. negative index) waves in a reciprocal system. The structures are tailored to accommodate only the necessary modes, which largely benefits the robustness. With these, we numerically demonstrate long range pulling forces on arbitrary particles through sharp corners. Our work paves the way towards sophisticated optical manipulation with single laser beam. We next explore the implication and applicability of momentum conservation in periodic media, which has been unclear due to the inhomogeneity and strong near field. We first quantify the linear momentum flux of Bloch modes under discrete translational symmetry, which is further understood from their plane wave composition. We then demonstrate through varies examples that the change in momentum flux predicts a total force distributed to both the scatterer and the media. However, one still need response theory to predict the forces on individual objects. Using response theory, we can predict more general forms of optical forces. We numerically demonstrate optical motoring effect due to singularity in the phase responses, and strong optical forces between graphene sheets due to large gradients in the phase responses. In particular, by combining the strong forces in graphene guided-wave system and the exceptional elastic properties of graphene, we can get an SBS gain that is four orders of magnitude stronger than in a silicon step-index waveguide, which may lead to smaller devices for RF signal processing.Physic