Melting and Structural Transformations of Carbonates and Hydrous Phases in Earth's Mantle.

This dissertation addresses questions about carbon and hydrogen transport and storage in the mantle through experimental investigations of the melting behaviors of carbonates under high pressure and phase stability of dense hydrous germanate. In Chapter II, a new technique was developed to measure melting temperatures at high pressures by monitoring the sudden change of capacitive current through ionic compounds upon melting. In Chapter III, the melting curve of NaCl up to 20 GPa was measured using the capacitive current technique. New results are consistent with previous data on melting temperature of NaCl up to 6.5 GPa, thus validating the accuracy of capacitive current based measurement. In Chapter IV, we measured the melting curve of CaCO3 between 3 and 22 GPa. The melting temperature of CaCO3 was found to decrease between 7 and 15 GPa and then increase with pressure between 15 and 21 GPa. The negative melting slope was attributed to the melt/solid density crossover at 7 GPa and the positive melting slope at higher pressures can be explained by calcite V to aragonite phase transition at 15 GPa. The melting curve of CaCO3 may cross a hot adiabatic geotherm at the transition zone depth in an upwelling setting, producing carbonate melt in the transition zone. In Chapter V, the melting curves of two more carbonates, Na2CO3 and K2CO3, were measured between 3 and 20 GPa. Above 9 GPa the melting temperature of K2CO3 was found to increase with pressure at a much higher rate than Na2CO3. Results from high pressure in situ X-ray diffraction experiments indicated two solid phase transitions of K2CO3 at ~3 and ~9 GPa, respectively. In Chapter VI, the stability of three new dense hydrous magnesium germanate (DHMG) minerals were reported on the basis of phase equilibrium experiments using in situ synchrotron X-ray diffraction and hydrothermal diamond anvil cell. One of them was determined as germanate analogue of phase D, and the other two were likely germanium analogues of superhdrous B and phase H.PHDGeologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111435/1/zeyuli_1.pd

Natural Model Reduction for Kinetic Equations

A promising approach to investigating high-dimensional problems is to identify their intrinsically low-dimensional features, which can be achieved through recently developed techniques for effective low-dimensional representation of functions such as machine learning. Based on available finite-dimensional approximate solution manifolds, this paper proposes a novel model reduction framework for kinetic equations. The method employs projections onto tangent bundles of approximate manifolds, naturally resulting in first-order hyperbolic systems. Under certain conditions on the approximate manifolds, the reduced models preserve several crucial properties, including hyperbolicity, conservation laws, entropy dissipation, finite propagation speed, and linear stability. For the first time, this paper rigorously discusses the relation between the H-theorem of kinetic equations and the linear stability conditions of reduced systems, determining the choice of Riemannian metrics involved in the model reduction. The framework is widely applicable for the model reduction of many models in kinetic theory.Comment: 46 page

Rhoticity in Chinese English: An experimental investigation on the realization of the variant (r) in an Expanding Circle variety

The realization of postvocalic /r/ has been frequently examined in both diachronic and synchronic research on world Englishes, showing a multitude of linguistic and extra-linguistic factors to modulate the degree of rhoticity. Since rhoticity is one of the most important indices of variation across Englishes, it forms an instructive phonological marker to investigate the dynamics of norm formation in emerging varieties. While the Inner and Outer Circle varieties have been extensively studied, there is fairly little research on the variable realization of postvocalic /r/ in the Expanding Circle Englishes. Here, we fill this gap with a study on the degree of rhoticity by highly proficient users of an EFL variety emerging in China, college English teachers, who are pertinent norm providers for EFL learners. We provide a multivariate analysis of phonological and sociolinguistic factors conditioning the degree of rhoticity in Chinese English on the basis of speech production data from 13 participants. Results show that Chinese English is best categorized as marginally rhotic. Concerning the patterning of phonological variables, it aligns more with Inner Circle than Outer Circle Englishes, albeit with significant inter- and intra-speaker variability. We discuss the competing roles of norm orientation, substrate influence, and other relevant variables therein

Lax Equivalence for Hyperbolic Relaxation Approximations

This paper investigates the zero relaxation limit for general linear hyperbolic relaxation systems and establishes the asymptotic convergence of slow variables under the unimprovable weakest stability condition, akin to the Lax equivalence theorem for hyperbolic relaxation approximations. Despite potential high oscillations, the convergence of macroscopic variables is established in the strong $L^\infty_t L^2_x$ sense rather than the sense of weak convergence, time averaging, or ensemble averaging.Comment: 32 page

Color-Kinematics Duality with Minimal Deformation: Two-Loop Four-Gluon Amplitudes in Pure Yang-Mills Revisited

The conjectured duality between color and kinematics has significantly advanced our understanding of both gauge and gravitational theories. However, constructing numerators that manifest the color-kinematics (CK) duality, even for the two-loop four-gluon amplitude in pure Yang-Mills, has been challenging. In this paper, we revisit this amplitude and show that the difficulty of applying CK duality can be overcome by introducing a simple deformation. Our approach distinguishes itself from previous studies by maximizing the use of off-shell CK duality while maintaining a compact ansatz. In particular, the deformation we introduce satisfies a subset of off-shell dual Jacobi relations. The resulting numerators are presented in $d$-dimensionally Lorentz invariant local form and are applicable to all helicities of external gluons. The solution we provide can be directly employed to construct the corresponding gravitational amplitude through double copy. Our findings suggest a novel and efficient strategy for constructing high-loop gauge and gravitational amplitudes using CK duality.Comment: 24 pages, 11 figure

Value Added of Teachers in High-Poverty Schools and Lower-Poverty Schools

This paper examines whether teachers in schools serving students from high-poverty backgrounds are as effective as teachers in schools with more advantaged students. The question is important. Teachers are recognized as the most important school factor affecting student achievement, and the achievement gap between disadvantaged students and their better off peers is large and persistent. Using student-level microdata from 2000-2001 to 2004-2005 from Florida and North Carolina, the authors compare the effectiveness of teachers in high-poverty elementary schools (>70% FRL students) with that of teachers in lower-poverty elementary schools

High Order Numerical Homogenization for Dissipative Ordinary Differential Equations

We propose a high order numerical homogenization method for dissipative ordinary differential equations (ODEs) containing two time scales. Essentially, only first order homogenized model globally in time can be derived. To achieve a high order method, we have to adopt a numerical approach in the framework of the heterogeneous multiscale method (HMM). By a successively refined microscopic solver, the accuracy improvement up to arbitrary order is attained providing input data smooth enough. Based on the formulation of the high order microscopic solver we derived, an iterative formula to calculate the microscopic solver is then proposed. Using the iterative formula, we develop an implementation to the method in an efficient way for practical applications. Several numerical examples are presented to validate the new models and numerical methods.Comment: 29 pages, 8 figure

Realized volatility and absolute return volatility: a comparison indicating market risk

Measuring volatility in financial markets is a primary challenge in the theory and practice of risk management and is essential when developing investment strategies. Although the vast literature on the topic describes many different models, two nonparametric measurements have emerged and received wide use over the past decade: realized volatility and absolute return volatility. The former is strongly favored in the financial sector and the latter by econophysicists. We examine the memory and clustering features of these two methods and find that both enable strong predictions. We compare the two in detail and find that although realized volatility has a better short-term effect that allows predictions of near-future market behavior, absolute return volatility is easier to calculate and, as a risk indicator, has approximately the same sensitivity as realized volatility. Our detailed empirical analysis yields valuable guidelines for both researchers and market participants because it provides a significantly clearer comparison of the strengths and weaknesses of the two methods.ZZ, ZQ, BL thank "Econophysics and Complex Networks" fund number R-144-000-313-133 from National University of Singapore (www.nus.sg). TT thanks Japan Society for the Promotion of Science Grant (www.jsps.go.jp/english/e-grants/) Number 25330047. HES thanks Defense Threat Reduction Agency (www.dtra.mil) (Grant HDTRA-1-10-1-0014, Grant HDTRA-1-09-1-0035) and National Science Foundation (www.nsf.gov) (Grant CMMI 1125290). ZZ thanks Chinese Academy of Sciences (english.cas.cn) Grant Number Y4FA030A01. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. (R-144-000-313-133 - National University of Singapore; 25330047 - Japan Society for the Promotion of Science Grant; HDTRA-1-10-1-0014 - Defense Threat Reduction Agency; HDTRA-1-09-1-0035 - Defense Threat Reduction Agency; CMMI 1125290 - National Science Foundation; Y4FA030A01 - Chinese Academy of Sciences)Published versio