非线性玻尔兹曼方程的傅里叶谱方法

玻尔兹曼方程作为空气动理学中最基本的方程之一,是连接微观牛顿力学和宏观连续介质力学的重要桥梁.该方程描述了一个由大量粒子组成的复杂系统的非平衡态时间演化:除了基本的输运项,其最重要的特性是粒子间的相互碰撞由一个高维,非局部且非线性的积分算子来描述,从而给玻尔兹曼方程的数值求解带来非常大的挑战.在过去的二十年间,基于傅里叶级数的谱方法成为了数值求解玻尔兹曼方程的一种很受欢迎且有效的确定性算法.这主要归功于谱方法的高精度及它可以被快速傅里叶变换加速的特质.本文将回顾玻尔兹曼方程的傅里叶谱方法,具体包括方法的导出,稳定性和收敛性分析,快速算法,以及在一大类基于碰撞的空气动理学方程中的推广.     

Kinetics Study of the Thermal Decomposition of Post-consumer Poly(Ethylene Terephthalate) in an Argon Atmosphere

The thermal decomposition of post-consumer samples of a carbonated water bottle made of poly(ethylene terephthalate), PC-PET, was examined by linear temperature programing under an argon atmosphere to determine its mass loss kinetics. A simple kinetic model, called the first order pseudo single-component model, was used. The total weight-loss of each sample assumed to be in two periods, with each period corresponding to a one step decomposition of the PC-PET to volatiles. Three methods for determining the kinetic parameters by thermal gravimetric analysis were examined: differential analysis at a constant heating rate (differential), temperatures of a given conversion at a number of heating rates (isoconversional), and the maximum rate at multiple heating rates (peak temperature). The latter two multiple heating rates methods results were comparable to each other but they were not in agreement with the results from the differential method. The results of the differential method were insensitive to the heating rate and consistent with kinetics data reported in the literature for PET.     

Modifying LnHPDO3A Chelates for Improved T1 and CEST MRI Applications

The new ligand HPDO3MA [(R,R,R,R)-10-(2-hydroxypropyl)-α,α′,α′′-trimethyl-1,4,7,10-tetraazacyclododecane-1,4,7-triacetic acid] was designed to combine and optimize the chemical properties of the macrocyclic ligands HPDO3A and DOTMA. The presence of the methyl groups on the acetic pendant arms of HPDO3A is expected to rigidify the structure of the ligand and favor an increase of the kinetic inertness of the Ln complexes. ¹H NMR spectra of Eu(HPDO3MA) displayed the presence of two pairs of diastereoisomers: SAP (square antiprismatic) and TSAP (twisted square antiprismatic) isomers (56 and 44 %, respectively). In addition, ¹H and ¹⁷O relaxometric NMR studies of Gd(HPDO3MA) showed approximately a 10 % increase in relaxivity and a faster water exchange rate with respect to Gd(HPDO3A). Moreover, a detailed chemical exchange saturation transfer (CEST) characterization of Yb(HPDO3MA) displayed a sensitivity about two times larger than that of Yb(HPDO3A) both in phantom and in cell labeling experiments. Finally, the kinetic inertness of Yb(HPDO3MA) was measured to be twice as high as that of Yb(HPDO3A), with a dissociation half-life at physiological pH of about 2500 years.     

Influence of the pH Value on the Hydrothermal Degradation of Fructose

The hydrothermal treatment of sugars features a promising technology for the production of fine and platform chemicals from renewable resources. In this work the hydrothermal decomposition of fructose was studied in a buffered medium at a pH range between 2.2 and 8.0. It is demonstrated that at lower pH values mainly 5-hydroxymethylfurfural (HMF), levulinic acid and humin are generated, while lactic acid and acetic acid are produced at higher pH values. The work shows that the use of moderate acidic conditions may have advantages for the hydrothermal HMF production over the use of strongly acidic conditions, as especially the degradation into levulinic acid is suppressed. Besides, this study deals with a rather complex reaction network, hence limitations and need for adaption of the kinetic model are discussed.     

Statistical structure of the velocity field in cavitating flow around a 2D hydrofoil

Transformation of flow turbulence structure with cavitation occurrence, determination of the flow conditions favorable for nucleation of cavitation bubbles, influence of the statistical structure of turbulence on this process and the inverse effect of cavitation on the flow dynamics are challenging problems in modern fluid mechanics. The paper reports on the results of statistical processing of the velocity fields measured by a PIV technique in cavitating flow over a 2D symmetric hydrofoil for four flow conditions, starting from a cavitation-free regime and finishing by unsteady cloud cavitation. We analyze basic information on the statistical structure of velocity fluctuations in the form of histograms and Q-Q diagrams along with profiles of the mean velocity and turbulent kinetic energy. The research reveals that the flow turbulence pattern and distributions of turbulent fluctuations change significantly with the cavitation development. Under unsteady cloud cavitation conditions, the probability density function of the fluctuating velocity has a two-mode distribution, which indicates switching of two alternating flow conditions in a region above the hydrofoil aft part due to periodic passing of cavitation clouds. Behaviors of the mean and most probable velocities unexpectedly appear to be different with a monotonous increase of the incoming flow velocity. This finding must be caused by modification of the skewness coefficient of the fluctuating velocity.     

Acoustic scattering in a rarefied gas: Solving the R13 equations in spherical polar coordinates

In some circumstances, sound waves in a rarefied gas can be studied using a linearised form of the regularised 13-moment equations of Struchtrup and Torrilhon. We build solutions of those equations in spherical polar coordinates using vector spherical harmonics. We first solve a reduced system of equations (with 11 unknowns) after introduction of a force vector (divergence of the stress). We then show that the stresses themselves can be recovered by solving five additional equations. The results obtained are expected to be useful for problems such as acoustic scattering of a plane wave by a sphere in a rarefied gas.     

野外砾石统计方法的应用与对比

砾石对于研究构造活动和气候变化具有重要意义，而砾石粒径是其中的重要参数，如何准确地获取粒径数据则是砾石统计分析中的基础性工作。为了能更全面地了解和使用砾石统计方法，对地表砾石统计和地层砾石统计这2种方法从操作流程、抽样过程、样本容量、误差分析和适用条件等方面进行了分析和总结。地表砾石统计，主要有沃尔曼法和面积样本法，前者强调抽样的随机性，多适用于对粒径>2 mm砾石的统计，常用于研究砾质河床的砾石粒径顺流变化趋势；后者适用的粒径范围更广，可达细砂级沉积物，多用于探索河床砾-砂转换带和生物栖息环境划分等领域。地层砾石统计，大多使用体积样本法，强调砾石的成层性，可根据研究目的确定相应的网格筛，粒径范围也可达细砂级别，多用于沉积地层粒度对气候与构造的响应、河床监测和泥沙运移等方面。砾石统计方法的选择很大程度上取决于研究目的及野外工作条件，可根据实际情况灵活选择。     

Kinetic Resolution of Racemic Allylic Alcohols by Catalytic Asymmetric Substitution of the OH Group with Monosubstituted Hydrazines

A new strategy has been established for the kinetic resolution of racemic allylic alcohols through a palladium/sulfonyl‐hydrazide‐catalyzed asymmetric OH‐substitution under mild conditions. In the presence of 1 mol % [Pd(allyl)Cl]₂, 4 mol % (S)‐SegPhos, and 10 mol % 2,5‐dichlorobenzenesulfonyl hydrazide, a range of racemic allylic alcohols were smoothly resolved with selectivity factors of more than 400 through an asymmetric allylic alkylation of monosubstituted hydrazines under air at room temperature. Importantly, this kinetic resolution process provided various allylic alcohols and allylic hydrazine derivatives with high enantiopurity.     

Modeling and testing of snow penetration

Penetration by a cone into snow is commonly used to characterize snow properties. However, the effects of the diameter and half-angle of the cone on the mechanical properties of snow have not been systematically studied. In addition, no estimation of material parameters in a physically-based model has been made such that the results from penetration provide only an index of snow properties. In this paper, modeling and experimental methods are used to examine the effects of cone geometry on the maximum penetration force and associated hardness, with penetrometers ranging from 2.5 to 4 mm in diameter, 15° to 45° in cone half-angle, and testing both fine-grained and coarse-grained snows. The material point method, in conjunction with the Drucker–Prager cap plasticity model, was used to obtain the theoretical penetration force-distance relationship. Global sensitivity studies were conducted that indicate that the cohesion accounts for 86% of the penetration force, followed distantly by friction angle which accounts for 27%. A general trend, for the simulation results was established: for a given half-angle, the penetration force increases with the increase of diameter which holds for most of the test data as well; for a given diameter, the penetration force decreases with the increase of half-angle, which holds for some of the test data. In addition, for a given half-angle, the hardness decreases with the increase of diameter; for a given diameter, the hardness decreases with the increase of half-angle. To take into consideration the uncertainty of test data, a simple interval-based metric was used to compare test data with simulation results; the comparison was satisfactory. The material parameters from the simulations can thus be considered as calibrated ones for the snow studied.