奇异摄动在层流预混火焰理论研究中的应用

奇异摄动被广泛应用于求取力学问题的近似解.一个典型问题就是流体力学中的边界层.郭永怀先生曾发展了适用于平板黏性流动边界层问题的奇异摄动理论.类似于流体力学中的边界层,燃烧研究中的层流预混火焰也可以通过奇异摄动理论进行分析,在燃烧研究中通常称其为大活化能渐近分析.本文介绍了大活化能渐近分析在一维平面预混火焰和球形传播火焰中的应用及相关研究进展.首先介绍了预混火焰结构及其涉及的不同特征尺度,分析了大活化能条件下出现的特征尺度分离,并给出了关于平面预混火焰大活化能渐近分析的详细推导,讨论了热辐射对火焰传播的影响;然后介绍了大活化能渐近分析在点火与球形传播火焰方面的应用,指出了只有能够同时描述点火与球形火焰传播的理论才能准确地预测临界点火条件,并讨论了考虑链式反应的点火与火焰传播理论,分析了热辐射对球形火焰传播的影响,给了关于火焰稳定性理论研究的发展趋势.最后,基于当前研究进展对未来的研究方向进行了展望,其中涉及多步化学反应、低温冷火焰、复杂流动、辐射重吸收等.      

水下超声速气体射流诱导尾空泡实验研究

两相射流与空化问题对采用喷气推进的水下高速运载器而言不可避免.本文通过水洞实验,探究了回转体在水流场中由亚声速及超声速气体射流诱导形成尾空泡的形态特征,发现了四种不同类型的诱导尾空泡,并探讨了相应的形成机理和控制条件.通过高速图像采集及数字处理技术,得到了不同弗劳德数和通气流量系数下诱导尾空泡的瞬时及时间平均形态.通过气体射流数值解及射流耦合空泡闭合理论模型与实验图像的对比分析,得到如下结论:根据形态特征,将观察到的射流诱导尾空泡划分为泡沫状、完整、部分破碎和脉动泡沫状四类,其中诱导产生的部分破碎尾空泡在形态上与超空泡存在明显差异,脉动泡沫状则为诱导空泡所特有;气体射流受到空泡阻挡发生回射后对应的实际通气流量系数是控制空泡形态的关键;诱导空泡类型转变可以通过Paryshev提出的射流空泡耦合模型预测,但必须在考虑射流空间结构和流动损失的前提下;进行上述修正后,诱导尾空泡形态变化规律与理论模型估算得到的实际流量系数相符合.     

Counterflow diffusion flames: effects of thermal expansion and non-unity Lewis numbers

In this work we re-examine the counterflow diffusion flame problem focusing in particular on the flame–flow interactions due to thermal expansion and its influence on various flame properties such as flame location, flame temperature, reactant leakage and extinction conditions. The analysis follows two different procedures: an asymptotic approximation for large activation energy chemical reactions, and a direct numerical approach. The asymptotic treatment follows the general theory of Cheatham and Matalon, which consists of a free-boundary problem with jump conditions across the surface representing the reaction sheet, and is well suited for variable-density flows and for mixtures with non-unity and distinct Lewis numbers for the fuel and oxidiser. Due to density variations, the species and energy transport equations are coupled to the Navier–Stokes equations and the problem does not possess an analytical solution. We thus propose and implement a methodology for solving the free-boundary problem numerically. Results based on the asymptotic approximation are then verified against those obtained from the ‘exact’ numerical integration of the governing equations, comparing predictions of the various flame properties.     

On the Asymptotic Behavior of the Harmonic Renewal Measure

We study the tail behavior of the harmonic renewal measure U= _n=1 (1/n)F ^n* where F is a probability distribution with finite negative mean and F ⁿ * is the n-fold convolution of F. As an application of the obtained result on U, we give alternative proofs of some known results concerning the tail behavior of the supremum and the first positive sum of a random walk with negative drift.     

Optimal trajectory to overflow in a queue fed by a large number of sources

We analyse the deviant behavior of a queue fed by a large number of traffic streams. In particular, we explicitly give the most likely trajectory (or optimal path) to buffer overflow, by applying large deviations techniques. This is done for a broad class of sources, consisting of Markov fluid sources and periodic sources. Apart from a number of ramifications of this result, we present guidelines for the numerical evaluation of the optimal path.     

On Extreme Regression Quantiles

Smith (1994) introduced the idea of extreme regression quantiles and he developed some asymptotic results for algebraically tailed error distributions. The results provided a close analogy to standard extreme value theory for one-sample extremes. Here we obtain the following generalizations. First, an extreme value distribution theory is developed in the exponentially tailed case, where the extreme slope estimates need not diverge to infinity and may actually be consistent. The design conditions of Smith (1994) are also generalized. Second, the tail behavior measure of Jureckova´ (1981) and He et al. (1990) is considered for extreme quantiles. For algebraically tailed error distributions, the average right extreme regression fit acts like a one-sample right extreme; while in the exponentially tailed case, the tail behavior is more like that of a slightly more central order statistic.     

Ruin probabilities with insurance and financial risks having an FGM dependence structure

We consider a discrete-time risk model,in which insurance risks and financial risks jointly follow a multivariate Farlie-Gumbel-Morgenstern distribution,and the insurance risks are regularly varying tailed.Explicit asymptotic formulae are obtained for finite-time and infinite-time ruin probabilities.Some numerical results are also presented to illustrate the accuracy of our asymptotic formulae.     

Second order risk aggregation with the Bernstein copula

We analyze the tail of the sum of two random variables when the dependence structure is driven by the Bernstein family of copulas. We consider exponential and Pareto distributions as marginals. We show that the first term in the asymptotic behavior of the sum is not driven by the dependence structure when a Pareto random variable is involved. Consequences on the Value-at-Risk are derived and examples are discussed.     

Non-Weyl resonance asymptotics for quantum graphs in a magnetic field

We study asymptotical behaviour of resonances for a quantum graph consisting of a finite internal part and external leads placed into a magnetic field, in particular, the question whether their number follows the Weyl law. We prove that the presence of a magnetic field cannot change a non-Weyl asymptotics into a Weyl one and vice versa. On the other hand, we present examples demonstrating that for some non-Weyl graphs the “effective size” of the graph, and therefore the resonance asymptotics, can be affected by the magnetic field.     

我国大额实时支付系统支付流统计特征分析

本文基于我国大额支付系统支付流自2005年7月到2008年7月的数据进行统计特征的研究。通过对中央银行历次准备金率调整对支付流影响的研究,发现在大多数调整时段内准备金率的调整会引起支付流数值的均值与波动的增加,右尾厚尾指数降低。而支付流是相关序列的数据检验结果是我国可以借鉴国外经典风险管理模型对支付流进行风险管理的依据。