Scale dependent dynamic capillary pressure effect for two-phase flow in porous media

Causes and effects of non-uniqueness in capillary pressure and saturation (P^c–S) relationship in porous media are of considerable concern to researchers of two-phase flow. In particular, a significant amounts of discussion have been generated regarding a parameter termed as dynamic coefficient (τ) which has been proposed for inclusion in the functional dependence of P^c–S relationship to quantify dynamic P^c and its relation with time derivative of saturation. While the dependence of the coefficient on fluid and porous media properties is less controversial, its relation to domain scale appears to be dependent on artefacts of experiments, mathematical models and the intra-domain averaging techniques. In an attempt to establish the reality of the scale dependency of the τ–S relationships, we carry out a series of well-defined laboratory experiments to determine τ–S relationships using three different sizes of cylindrical porous domains of silica sand. In this paper, we present our findings on the scale dependence of τ and its relation to high viscosity ratio (μ_r) silicone oil–water system, where μ_r is defined as the viscosity of non-wetting phase over that of the wetting phase. An order of magnitude increase in the value of τ was observed across various μ_r and domain scales. Also, an order of magnitude increase in τ is observed when τ at the top and the bottom sections in a domain are compared. Viscosity ratio and domain scales are found to have similar effects on the trend in τ–S relationship. We carry out a dimensional analysis of τ which shows how different variables, e.g., dimensionless τ and dimensionless domain volume (scale), may be correlated and provides a means to determine the influences of relevant variables on τ. A scaling relationship for τ was derived from the dimensionless analysis which was then validated against independent literature data. This showed that the τ–S relationships obtained from the literature and the scaling relationship match reasonably well.     

一类偶数阶Sturm-Liouvile四点边值问题多个正解的存在性

讨论了一类偶数阶四点边值问题正解的存在性,借助Leggett-Williams不动点定理和不等式技巧,得到了该边值问题至少存在三个和任意奇数个正解的充分条件.     

一种改进的客户端平衡的密钥交换算法研究

目前安全套接层协议在性能上存在不足,大量的加密解密操作消耗了太多的系统资源,对服务器的性能影响非常大。为此提出利用客户机协助安全套接层服务器进行RSA私钥解密的握手,以充分利用客户机等待服务器消息的空闲时间,提高服务器处理该连接的速度。为进一步提高安全套接层服务器的计算速度,采用中国余数定理对指数进行降幂。利用开源软件包实现改进的基于中国余数定理客户端平衡的握手实验,实验表明,在密钥长度为1024位的情况下,改进后算法的解密速度提高了8倍,在一定程度上改善了系统资源利用率。     

基于下限定理的路面结构安定分析

传统的以弹性理论和经验方法为基础的路面结构设计方法,对路面结构的安全性评价存在着不合理性。安定理论可为复杂荷载作用下的路面结构承载力分析提供理论依据,基于该定理发展了一种应用于路面结构的安定分析方法,并应用于2层路面结构的安定分析,计算给出了荷载作用方式、路面结构形式、材料性质变化对路面安定极限影响的定量分析结果,通过对比表明了安定分析应用于路面结构的可行性。安定极限可为路面结构的分析与设计提供一定的参考价值。     

Practically Applicable Central Limit Theorem for Spatial Statistics

Let {Z(s):s∈D⊆ℝ ^d } be a zero mean stationary random field observed at a finite number of locations. Lahiri (Sankhya Ser. A 65:356–388, 2003) proved spatial central limit theorems (CLT) for ∑ _i=1 ⁿ Z(s _i ) assuming a ‘nearly infill domain sampling’. Applications of his results depended on the underlying spatial sampling region and the design in a complicated fashion. The main objective of this paper is to provide CLTs that could be applied easily in practice. We present two main results assuming a ‘nearly infill domain sampling’ defined mainly in terms of dependence. Theorem 1 establishes a CLT for ∑ _i=1 ⁿ Z(s _i ) and Theorem 2 is obtained mainly for applications to density estimates. We report on a simulation study for illustrating a way of applying our results in practice.     

NWP模式中纬向平均环流系统误差的动力诊断

证明了模式在预报时段的纬向平均环流误差，是由于在预报时段内模式大气和真实大气中西风加速过程的不同造成的。又由于原始方程的无加速定理中各强迫因子具有良好的线性迭加性，因此能够清楚地将造成模式系统误差的动力因子分解开来。通过对Ｔ４２Ｌ９模式的分析，说明原始方程的无加速定理可以作为分析模式系统误差的良好手段。动力诊断分析结果表明，模式对纬向平均环流分布具有较好的预报能力，但在各缔带也存在明显的误差。通过无加速定理的分解分析，本文研究了这些误差的成因及改善模式的可能途径。     

辅助纬度与大地纬度间的无穷展开

利用无穷级数理论和拉格朗日反演定理,详细推导了大地测量和制图学中常用的辅助纬度与大地纬度间的无穷展开,主要表现为参考椭球第一偏心率的幂级数形式。通过建立一系列严格的系数递推公式,得到了等量纬度反解展开式和等角纬度反解展开式;同时,推导了古德曼函数的泰勒展开式,进而得到了等角纬度正解展开式;利用级数除法公式,得到了等距离纬度正解展开式系数的行列式表示。通过比较本文方法与计算机代数系统Mathematica直接推导求得的辅助纬度正反解展开式e^0～e⁴⁰阶系数和相应的程序用时,表明本文算法是正确的、快速的。以CGCS2000参考椭球为例,对辅助纬度正反解进行了算例分析,也进一步验证了本文公式的正确性。     

奇异非线性二阶诺伊曼边值问题恰有5个正解的条件

主要研究奇异非线性二阶诺伊曼边值问题的正解个数.应用比较原理、最大值原理和上界方法得出了在一定条件下,该问题恰好有5个正解的结果.     

Mesoscale Barotropic Instability of Vortex Rossby Waves in Tropical Cyclones

In this study, the barotropic stability of vortex Rossby waves (VRWs) in 2D inviscid tropical cyclone (TC)-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered: (a) there must be at least one zero point of basic vorticity gradient in the radial scope; and (b) the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum ...