大尺寸电阻加热式碳化硅晶体生长热场设计与优化

大尺寸低缺陷碳化硅(SiC)单晶体是功率器件和射频(RF)器件的重要基础材料,物理气相传输(physical vapor transport, PVT)法是目前生长大尺寸SiC单晶体的主要方法。获得大尺寸高品质晶体的核心是通过调节组分、温度、压力实现气相组分在晶体生长界面均匀定向结晶,同时尽可能减小晶体的热应力。本文对电阻加热式8英寸(1英寸=2.54 cm)碳化硅大尺寸晶体生长系统展开热场设计研究。首先建立描述碳化硅原料受热分解热质输运及其多孔结构演变、系统热输运的物理和数学模型,进而使用数值模拟方法研究加热器位置、加热器功率和辐射孔径对温度分布的影响及其规律,并优化热场结构。数值模拟结果显示,通过优化散热孔形状、保温棉的结构等设计参数,电阻加热式大尺寸晶体生长系统在晶锭厚度变化、多孔介质原料消耗的情况下均能达到较低的晶体横向温度梯度和较高的纵向温度梯度。     

On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Mass distribution and skewness for passive scalar transport in pipes with polygonal and smooth cross sections

We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross‐sectional shapes, including regular polygons and smoothed corner ducts originating from deformations of ellipses. For the case of the triangle and localized, cross‐wise uniform initial distributions, short‐time skewness is calculated exactly to be positive, while long‐time asymptotics shows it to be negative. Monte Carlo simulations confirm these predictions, and document the timescale for sign change. The equilateral triangle appears to be the only regular polygon with this property—all others possess positive skewness at all times. Alternatively, closed‐form flow solutions can be constructed for smooth deformations of ellipses, and illustrate how both nonzero short‐time skewness and the possibility of multiple sign switching in time is unrelated to domain corners. Exact conditions relating the median and the skewness to the mean are developed which guarantee when the sign for the skewness implies front (more mass to the right of the mean) or back (more mass to the left of the mean) “loading” properties of the evolving tracer distribution along the pipe. Short‐ and long‐time asymptotics confirm this condition, and Monte Carlo simulations verify this at all times. The simulations are also used to examine the role of corners and boundaries on the distribution for short‐time evolution of point source , as opposed to cross‐wise uniform, initial data.     

Synthesis of Au nanorods via autocatalytic growth of Au seeds formed by sonochemical reduction of Au(I): Relation between formation rate and characteristic of Au nanorods

The sonochemical formation of Au seeds and their autocatalytic growth to Au nanorods were investigated in a one-pot as a function of concentration of HAuCl₄, AgNO₃, and ascorbic acid (AA). The effects of ultrasonic power and irradiation time were also investigated. In addition, the formation rate of Au nanorods was analyzed by monitoring the extinction at 400 nm by UV–Vis spectroscopy and compared with the growth behavior of Au seeds to nanorods. Most of the reaction conditions affected the yield, size, and shape of Au nanorods formed. It was confirmed that the concentration balance between HAuCl₄ and AA was important to proceed the formation of Au seeds and nanorods effectively. The formation rate became faster with increasing AA concentration and dog-bone shaped nanorods were formed at high AA concentration. It was also confirmed a unique phenomenon that the shape of Au nanorods changed even after the completion of the reduction of Au(I) in the case of short-time ultrasonic irradiation for Au seed formation.     

Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .     

高雷诺数下非混相Rayleigh-Taylor不稳定性的格子Boltzmann方法模拟

本文采用相场格子Boltzmann方法研究了竖直微通道内中等Atwoods数流体的单模Rayleigh-Taylor不稳定性问题,系统分析了雷诺数对相界面动力学行为以及扰动在各发展阶段演化规律的影响.数值结果表明高雷诺数条件下,不稳定性界面扰动的增长经历了四个不同的发展阶段,包括线性增长阶段、饱和速度阶段、重加速阶段及混沌混合阶段.在线性增长阶段,我们计算获得的气泡与尖钉振幅符合线性稳定性理论,并且线性增长率随着雷诺数的增加而增大.在第二个阶段,我们观察到气泡与尖钉将以恒定的速度增长,获得的尖钉饱和速度略高于Goncharov经典势能模型的解析解[Phys.Rev.Lett.200288134502],这归因于系统中产生了多个尺度的旋涡,而涡之间的相互作用促进了尖钉的增长.随着横向速度和纵向速度的差异扩大,气泡和尖钉界面演化诱导产生的Kelvin–Helmholtz不稳定性逐渐增强,从而流体混合区域出现许多不同层次的涡结构,加速了气泡与尖钉振幅的演化速度,并在演化后期阶段,导致界面发生多层次卷起、剧烈变形、混沌破裂等行为,最终形成了非常复杂的拓扑结构.此外,我们还统计了演化后期气泡与尖钉的无量纲加速度,发现气泡和尖钉的振幅在后期呈现二次增长规律,其增长率系数分别为0.045与0.233.而在低雷诺条件下,重流体在不稳定性后期以尖钉的形式向下运动而轻流体以气泡的形式向上升起.在整个演化过程中,界面变得足够光滑,气泡与尖钉在后期的演化速度接近于常数,未观察到后期的重加速与混沌混合阶段.     

Thermally Crosslinkable and Chemically Modifiable Aromatic Polyesters Possessing Pendant Propargyloxy Groups

New aromatic (co)polyesters containing pendant propargyloxy groups were synthesized by phase transfer‐catalyzed interfacial polycondensation of 5‐(propargyloxy)isophthaloyl chloride (P‐IPC) and various compositions of P‐IPC and isophthaloyl chloride with bisphenol A. FTIR and NMR spectroscopic data, respectively, revealed successful incorporation of pendant propargyloxy groups into (co)polyesters and formation of (co)polyesters with desired compositions. (Co)polyesters exhibited good solubility in common organic solvents such as chloroform, dichloromethane, and tetrahydrofuran and could be cast into transparent, flexible, and tough films from chloroform solution. Inherent viscosities and number average molecular weights of (co)polyesters were in the range 0.77–1.33 dL/g and 43,600–118,000 g/mol, respectively, indicating the achievement of reasonably high‐molecular weights. The 10% weight loss temperatures of (co)polyesters were in the range 390–420 °C, demonstrating their good thermal stability. (Co)polyesters exhibited T_g in the range 146–170 °C and T_g values decreased with increase in mol % incorporation of P‐IPC. The study of non‐isothermal curing by DSC indicated thermal crosslinking of (co)polyesters via propargyloxy groups. The utility of pendant propargyloxy group was demonstrated by post‐modification of the selected copolyester with 1‐(4‐azidobutyl)pyrene, 9‐(azidomethyl)anthracene, and azido‐terminated poly(ethyleneglycol) monomethyl ether via copper(I)‐catalyzed Huisgen 1,3‐dipolar cycloaddition reaction. FTIR and ¹H NMR spectra confirmed that click reaction was quantitative. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 588–597