COMPUTATIONAL FLUID DYNAMICS FOR DENSE GAS-SOLID FLUIDIZED BEDS: A MULTI-SCALE MODELING STRATEGY

Dense gas-particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic and is related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas-particle flows both (effective) fluid-particle and (dissipative) particle-particle interactions need to be accounted for because these phenomena to a large extent govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas-solid contact and as a direct consequence thereof strongly affect the performance of the process. Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid-particle and particle-particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid-particle (lattice Boltzmann model) and particle-particle (discrete particle model) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1 ) involves the lattice Boltzmann model, the discrete particle model, the continuum model based on the kinetic theory of granular flow,and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.     

FAE云雾爆轰冲击波压力测试技术研究

对数年来FAE外场试验中冲击波压力测量方法和测量技术进行了分析总结 ,着重分析了爆轰理论模型的具体应用和不规则反射对冲击波测量的影响 ,提出了传感器装置安装的有效改进方法并在试验中得到了验证 ,提高了系统测量精度。     

致密磁流体中的非线性离子声波

磁化致密等离子体系统中具有丰富的非线性波动现象. 针对非均匀系统, 采用量子流体动力模型并考虑非线性效应、碰撞效应和某些高阶偏导项等因素, 构建了离子和中子间的碰撞频率与场量的变化率不同大小情况下的非线性控制方程. 利用不同的函数变换关系得到了一系列非线性离子声波的解析解, 其结果为阐明现实中所观察到的有关物理现象提供了有益的理论参考.     

Completions of ‐Dense Partial Latin Squares

A classical question in combinatorics is the following: given a partial Latin square P, when can we complete P to a Latin square L? In this paper, we investigate the class of ε‐dense partial Latin squares: partial Latin squares in which each symbol, row, and column contains no more than ‐many nonblank cells. Based on a conjecture of Nash‐Williams, Daykin and Häggkvist conjectured that all ‐dense partial Latin squares are completable. In this paper, we will discuss the proof methods and results used in previous attempts to resolve this conjecture, introduce a novel technique derived from a paper by Jacobson and Matthews on generating random Latin squares, and use this technique to study ε‐dense partial Latin squares that contain no more than filled cells in total. In this paper, we construct completions for all ε‐dense partial Latin squares containing no more than filled cells in total, given that . In particular, we show that all ‐dense partial Latin squares are completable. These results improve prior work by Gustavsson, which required , as well as Chetwynd and Häggkvist, which required , n even and greater than 10⁷.     

浙江省大雾的气候特征及其与气象要素的关系

利用1971年以来浙江省68个测站的气候资料,统计分析了大雾日数的空间、时间分布特征及其与气象要素的关系．结果表明：浙江省大雾主要出现在东部沿海、浙北的中部和西部、浙中的西部和浙南的西南地区．浙中的南部和浙南的北部是相对少雾区;全省大部分地区年雾日呈下降趋势,特别是20世纪80年代之后下降趋势明显;各地大雾有明显的季节和地区差异．大雾以冬季最多,春、秋季次之,夏季最少．浙北多大雾日主要出现在春季、深秋至冬季两个阶段,浙中南多大雾日主要出现在深秋到冬季,东部沿海多大雾日主要出现在春季到初夏．月最多雾日东部沿海出现在春季,以平流雾为主,其他地区出现在冬季,以辐射雾为主;大雾主要发生在清晨,持续时间大多数在3h以内．统计表明：相对湿度、风速、气温和地面气压场与大雾形成关系密切．     

Matrix stretching for sparse least squares problems

For linear least squares problems min _x ‖Ax − b‖₂, where A is sparse except for a few dense rows, a straightforward application of Cholesky or QR factorization will lead to catastrophic fill in the factor R. We consider handling such problems by a matrix stretching technique, where the dense rows are split into several more sparse rows. We develop both a recursive binary splitting algorithm and a more general splitting method. We show that for both schemes the stretched problem has the same set of solutions as the original least squares problem. Further, the condition number of the stretched problem differs from that of the original by only a modest factor, and hence the approach is numerically stable. Experimental results from applying the recursive binary scheme to a set of modified matrices from the Harwell‐Boeing collection are given. We conclude that when A has a small number of dense rows relative to its dimension, there is a significant gain in sparsity of the factor R. A crude estimate of the optimal number of splits is obtained by analysing a simple model problem. Copyright © 2000 John Wiley & Sons, Ltd.     

自反算子代数的模和交换子以及一阶上同调空间

设L是赋范线性空间上的子空间格,一个子空间是自反AlgL-模的充分必要条件被得到,当L是完全分配子空间格时,自反AlgL-模的二次交换子被描述,进而,本文引入V-生成子稠格,这是一种严格地包含了完全分配格和五角格的格类。当L是可换的V-生成子稠格时,模模交换子C(AlgL;M)和代数AlgLatM都被分解成直和,并且满足条件H~1(AlgL,B(H))=0的一阶上同调空间H~1(AlgL,M)被刻划。     

Properties of the <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript>-smooth functions with nowhere dense gradient range

One of the main results of the present article is as follows Theorem. Let v: Ω → ? be a C¹-smooth function on a domain Ω ? ?². Suppose that Int?v(Ω) = ?. Then, for every point z ∈ Ω, there is a straight line L ? z such that ?v ≡ const on the connected component of the set L ? Ω containing z.Also, we prove that, under the conditions of the theorem, the range of the gradient ?v(Ω) is locally a curve and this curve has tangents in the weak sense and the direction of these tangents is a function of bounded variation.     

Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon

We give asymptotics for the cumulative distribution function (CDF) for degrees of large dense random graphs sampled from a graphon. The proof is based on precise asymptotics for binomial random variables. This result is a first step for giving a nonparametric test for identifying the degree function of a large random graph. Replacing the indicator function in the empirical CDF by a smoother function, we get general asymptotic results for functionals of homomorphism densities for partially labeled graphs. This general setting allows to recover recent results on asymptotics for homomorphism densities of sampled graphon.     

五台机器自由作业的稠密时间表

对于五台机器自由作业的稠密时间表,我们证明了一个比值不等式．