Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR     

Random walk in an inhomogeneous medium with local impurities

In spite of Sinai's result that the decay of the velocity autocorrelation function for a random walk on ^d (d=2) can drastically change if local impurities are present, it is shown that local impurities can not abolish weak convergence to the Brownian motion if d2.     

Properties of the random search in global optimization

From theorems which we prove about the behavior of gaps in a set ofN uniformly random points on the interval [0, 1], we determine properties of the random search procedure in one-dimensional global optimization. In particular, we show that the uniform grid search is better than the random search when the optimum is chosen using the deterministic strategy, that a significant proportion of large gaps are contained in the uniformly random search, and that the error in the determination of the point at which the optimum occurs, assuming that it is unique, will on the average be twice as large using the uniformly random search compared with the uniform grid. In addition, some of the properties of the largest gap are verified numerically, and some extensions to higher dimensions are discussed. The latter show that not all of the conclusions derived concerning the inadequacies of the one-dimensional random search extend to higher dimensions, and thaton average the random search is better than the uniform grid for dimensions greater than 6.This paper is based on work started in the Statistics Department of Princeton University when the first author was visiting as a Research Associate. Part of this research was supported by the Office of Naval Research, Contract No. 0014-67-A-0151-0017, and by the US Army Research Office—Durham, Contract No. DA-31-124-ARO-D-215.2 The authors wish to thank B. Omodei for his careful work in preparing the programs for the results of Figs. 1–2 and Table 1. The computations were performed on the IBM 360/50 of the Australian National University's Computer Centre. Thanks are also due to R. Miles for suggestions regarding the extension of the results to multidimensional regions, and to P. A. P. Moran and R. Brent for suggestions regarding the evaluation of the integral ₀ ¹ ... ^0/1 (x ₁ ² + ... +x _n ^/2 )^1/2 dx ₁ ...dx _n.     

同分布NA列Jamison型加权和强稳定的充要条件

本文将Ｊａｍｉｓｏｎ等（１９６５）关于ｉｉｄ列加权和强稳定的充分性结果推广到ＮＡ列的场合并且得到了ＮＡ列Ｊａｍｉｓｏｎ型加权和强稳定的必要性结果。     

垂直水声通信中的伪随机序列精确定时算法*

针对垂直水声通信中时变多普勒引起的定时偏差问题,研究一种基于伪随机序列的迭代定时估计及补偿算法。该方法利用伪随机序列作为同步信号,分三步估计时变多普勒：采用低复杂度的模糊函数法粗补偿接收信号内的平均多普勒;通过迭代插值法实现残留时变多普勒的精确估计及补偿;利用基于信道相关函数的相位信息,纠正均衡后信号的偏转相位。为实现高阶海试数据的有效解调,采用基于伪随机序列均方误差的多通道加权合并方式,获得空间分集增益。仿真及海试数据处理结果证明所提方法具有良好的时变多普勒估计及补偿性能,同时对30个通道内的1024QAM数据进行合并处理,在500 m的通信距离下,误码率为0.04,信道容量达到7.6 bits/symbol。与传统数据帧结构相比,无需使用线性调频信号,可以提高有效数据传输率。     

随机振动数值仿真中基础激励的自动反馈识别

利用ANSYS的APDL(ANSYS Parametric Design Language)语言的强大功能,结合工程实际问题,实现了随机振动试验数值仿真计算中基础输入功率谱的自动反馈识别．反馈过程中使用多个表格来存储基础输入谱,突破了基础输入谱只能用50个以内的数据点来描述的限制,故可以一次性完成基础输入谱的反馈识别,大大提高计算效率与精度．     

Comparison of Physical Adsorption and Covalent Coupling Methods for Surface Density-Dependent Orientation of Antibody on Silicon

The orientation of antibodies, employed as capture molecules on biosensors, determines biorecognition efficiency and bioassay performance. In a previous publication we demonstrated for antibodies attached covalently to silicon that an increase in their surface amount Γ, evaluated with ellipsometry, induces changes in their orientation, which is traced directly using Time-of-Flight Secondary Ion Mass Spectroscopy combined with Principal Component Analysis. Here, we extend the above studies to antibodies adsorbed physically on a 3-aminopropyltriethoxysilane (APTES) monolayer. Antibodies physisorbed on APTES (0 ≤ Γ ≤ 3.5 mg/m²) reveal the Γ ranges for flat-on, side-on, and vertical orientation consistent with random molecular packing. The relation between orientation and Γ is juxtaposed for silicon functionalized with APTES, APTES modified with glutaraldehyde (APTES/GA) and N-hydroxysuccinimide-silane (NHS-silane). Antibody reorientation occurs at lower Γ values when physisorption (APTES) is involved rather than chemisorption (APTES/GA, NHS-silane). At high Γ values, comparable proportions of molecules adapting head-on and tail-on vertical alignment are concluded for APTES and the NHS-silane monolayer, and they are related to intermolecular dipole–dipole interactions. Intermolecular forces seem to be less decisive than covalent binding for antibodies on the APTES/GA surface, with dominant head-on orientation. Independently, the impact of glutaraldehyde activation of APTES on vertical orientation is confirmed by separate TOF-SIMS measurements.     

From Chaos to Ordering: New Studies in the Shannon Entropy of 2D Patterns

Properties of the Voronoi tessellations arising from random 2D distribution points are reported. We applied an iterative procedure to the Voronoi diagrams generated by a set of points randomly placed on the plane. The procedure implied dividing the edges of Voronoi cells into equal or random parts. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of the positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude that by applying even a simple set of rules to a random set of seeds, we can introduce order into an initially disordered system. At the same time, the Shannon (Voronoi) entropy showed a tendency to attain values that are typical for completely random patterns; thus, the Shannon (Voronoi) entropy does not distinguish the short-range ordering. The Shannon entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase in the number of iteration steps. The Shannon entropy grew with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Shannon (Voronoi) entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Shannon entropy.     

NOD随机变量序列加权乘积和的强大数律

利用乘积和的一表示定理和NOD（negatively orthant dependent）随机变量的性质,在较一般的条件下,得到了不同分布的NOD随机变量序列加权乘积和的强大数律,推广和改进了已知的一些文献中相应的结论.     

行NA随机变量三角阵列的完全收敛性

令{Xm;1≤i≤n,n≥1}是行NA的随机变量三角阵列．利用NA随机变量序列的一个矩不等式,讨论了行NA的随机变量三角阵列在被随机变量X弱平均控制的条件下的完全收敛性．所得到的结果推广了行独立的随机变量三角阵列相应的结果．