Numerical Determination of Critical Mach number of a Three-Element Airfoil in Unbounded Flow and in Ground Effect

The critical Mach number is an important property of airfoils on aerodynamics. When the freestream Mach number exceeds the critical Mach number, shock will appear on the aircraft and cause a huge loss of energy. Lift decreases sharply and drag increases dramatically. We usually hope to increase the critical Mach number and delay the occurrence of shock so that the aircraft can fly with a higher speed and carry more weight. In this thesis, the main task is to determine the critical Mach number of multi-element airfoil 30P30N in unbounded flow and in ground effect. Commercial software ICEM is employed to generate mesh. ANSYS Fluent is conducted to compute flow filed. The compressible The Reynolds-averaged Navier - Stokes equations (or RANS equations) with the Spalart-Allmaras Turbulence Model are solved in flow field. The results are discussed in three parts. Firstly the results lead to the determination of the critical Mach number of 30P30N airfoil in unbounded flow and compare it with the critical Mach number of single element airfoil RAE2822. In addition, the evolution of aerodynamics of 30P30N airfoil from unbounded flow to ground effect is displayed and the reasons are analyzed. Finally, the determination of the critical Mach number at different ride heights in ground effect is shown and a clear change in the critical Mach number can be seen

Advancing Microdata Privacy Protection: A Review of Synthetic Data

Synthetic data generation is a powerful tool for privacy protection when considering public release of record-level data files. Initially proposed about three decades ago, it has generated significant research and application interest. To meet the pressing demand of data privacy protection in a variety of contexts, the field needs more researchers and practitioners. This review provides a comprehensive introduction to synthetic data, including technical details of their generation and evaluation. Our review also addresses the challenges and limitations of synthetic data, discusses practical applications, and provides thoughts for future work

Finite elements for symmetric and traceless tensors in three dimensions

We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes. This complex includes vector fields and symmetric and traceless tensor fields, interlinked through the conformal Killing operator, the linearized Cotton-York operator, and the divergence operator, respectively. This leads to discrete versions of transverse traceless (TT) tensors and York splits in general relativity. We provide bubble complexes and investigate supersmoothness to facilitate the construction. We show the exactness of the finite element complex on contractible domains.Comment: 44 pages, 1 figur

State-dependent Modeling of Default Rates

Risk-weight function is the most popular formula for banking regulations used to calculate the amount of backup deposit that banks need to hold in order to bear extraordinary losses. The model behind the formula was introduced by Vasicek in 2002. In that paper, there are several intuitively appealing assumptions which are oversimplified. The most unrealistic assumption made by Vasicek is that correlations among each unit do not depend on the overall market environment. Metzler (2020) has developed a generalized version of the Vasicek model to relax this assumption, which is called the state-dependent model. The model includes a parameter to allow the market correlations to change in a systematic way based on the overall economic level. We apply an EM algorithm that produces consistent estimates of the model parameters proposed by Metzler (2000). We also explore some properties of the model. The model involves an independence assumption, which assumes that the default rate for each time is independent with each other. But according to the plots of the historical data, that assumption is obviously violated. In order to relax the independence assumption, we bring a dependence structure to the model with respect to time by using time series to model the so-called systematic risk factor $M$. By doing so, we bring the forecasting ability to the model and verify its accuracy in the empirical study. The results suggest that the model we proposed shows some advantages compared with the classic auto-regression models. We also demonstrate that the model we proposed can be treated as a general extension of the classic auto-regression models. In the last part, we try to overcome the other well-know problem of the Vasicek model. Both the Vasicek model and SDM model fall into the family of the Gaussian copula. Although the Gaussian copula is widely used in the industry for its nice properties, the 2008 financial crisis warned researchers that tail independence can lead to some fatal results. In order to solve this problem, we change the underlying distribution from normal distribution to t-distribution

Palladium-Catalyzed Deprotonative Cross-Coupling And Carbonylative Cross-Coupling Processes

Metal-catalyzed direct C−H bond activation arylation reactions of non- or weakly acidic C−H bonds have recently received much attention. Compared to traditional catalysts that activate C−H bonds, conventional deprotonative cross-coupling processes (DCCP) undergoes an in-situ C−H deprotonation and metalation of the substrate under catalytic cross-coupling conditions. DCCP reactions are generally directing-group-free methods employing simple starting materials under mild reaction conditions. This thesis describes mechanistic study of DCCP-type triarylation of benzylic methyl groups and introduces two novel methods of deprotonative carbonylation of weakly acidic benzylic C(sp3)−H bonds. In Chapter 1, a comprehensive mechanistic study of our palladium-catalyzed deprotonative triarylation of heteroarylmethanes at the benzylic C-H bonds is reported. The reaction works with a variety of aryl halides, enabling the rapid synthesis of triaryl(heteroaryl)methanes. Mechanistic studies point to Pd(cataCXium A)2 being the resting state of the catalyst and reductive elimination being the turnover-limiting step in the ultimate catalytic cycle. In Chapter 2, a novel highly selective palladium-catalyzed deprotonative carbonylation of azaarylmethylamines with aryl bromides under 1 atm of CO gas has been achieved. The methods enable access to key components of numerous biologically active natural products and synthetic compounds. The key to success is the presence of a NIXANTPHOS-based palladium catalyst, which efficiently activates aryl bromides and facilitates the deprotonative cross-coupling process under CO. Chapter 3 presents a novel, selective and high-yielding palladium-catalyzed carbonylative arylation of a variety of weakly acidic (pKa 25–35 in DMSO) benzylic and heterobenzylic C(sp3)−H bonds with aryl bromides. The Josiphos-based catalytic system, identified by high-throughput experimentation (HTE), solved the selectivity issue in deprotonative carbonylation reactions, providing ketone products without the formation of direct coupling byproducts. Additionally, (Josiphos)Pd(CO)2 was identified as the catalyst resting state. A kinetic study suggests that the oxidative addition of aryl bromides is the turnover-limiting step. Key catalytic intermediates including (Josiphos)Pd(Ar)(Br) and (Josiphos)Pd(COAr)Br were also isolated

Minimal-time Deadbeat Consensus and Individual Disagreement Degree Prediction for High-order Linear Multi-agent Systems

In this paper, a Hankel matrix-based fully distributed algorithm is proposed to address a minimal-time deadbeat consensus prediction problem for discrete-time high-order multi-agent systems (MASs). Therein, each agent can predict the consensus value with the minimum number of observable historical outputs of its own. Accordingly, compared to most existing algorithms only yielding asymptotic convergence, the present method can attain deadbeat consensus instead. Moreover, based on the consensus value prediction, instant individual disagreement degree value of MASs can be calculated in advance as well. Sufficient conditions are derived to guarantee both the minimal-time deadbeat consensus and the instant individual disagreement degree prediction. Finally, both the effectiveness and superiority of the proposed deadbeat consensus algorithm are substantiated by numerical simulations.Comment: 12 pages, 3 figure