Error estimates for the fast multipole method

Error estimates for algorithms based on truncations for evaluating electrostatic interactions in molecular dynamics applications are very important for several reasons. For example, the estimates are necessary to establish the validity of the simulations and can be used to estimate various simulation parameters. Very precise estimates have been found for the Ewald method and the related particle mesh Ewald method. However, for the very popular fast multipole method such a precise estimate is not available. In this paper, we illustrate the rather complicated error behavior of the fast multipole method and we use statistical methods to derive an estimate for the root mean square error on the forces. Furthermore, the expected maximum error on the force acting on a single particle is studied. The estimates are tested against errors obtained from simulations and are found to be very precise.     

有效的板料成形反向模拟法应力修正策略

金属在流经凹模圆角时受到强烈的弯曲作用,传统的板料成形反向模拟法没有考虑变形历史对应力预测的影响,使得反向模拟法计算的应力值与实际情况有较大偏差.针对反向模拟法无法准确预测成形零件应力分布的缺点,提出一种快速搜索流经凹模圆角区域的单元的方法,对该部分单元进行应力修正.采用一种高效的单轴连续拉伸应力应变本构关系模型,避免了增量有限元法应力应变更新算法的复杂性,同时充分考虑了凹模圆角对金属变形历史的影响.NUMISHEET'93盒形件拉深的标准考题中,通过与增量有限元模拟软件DYNAFORM计算结果的比较,验证了采用提出的多步连续拉伸本构关系模型可以有效地反映变形历史的影响,获得更加接近实际的应力分布.     

Permeate flux inflection due to concentration polarization in crossflow membrane filtration: A novel analytic approach

A convection-diffusion equation for membrane filtration is analytically solved assuming fast crossflow velocity of a simple shear flow tangential to the membrane surface. In the direction normal to the membrane surface, solute concentration varies in a partially exponential and partially power-wise manner. The permeate flux in an asymptotic limit is proportional to the inverse square root of the distance from the inlet of the membrane channel. Osmotic pressure due to retained solutes on the membrane surface controls the profile of the permeate flux, which undergoes an inflection along the tangential direction if applied pressure is more than four times the feed osmotic pressure.     

傅里叶变换红外光谱的牛乳中αs1-酪蛋白和κ-酪蛋白含量的快速检测

为了找到一种能够对牛乳中的两种主要过敏原（α_s1和κ-酪蛋白）含量快速检测的方法,以河南、湖北、宁夏和内蒙古四省区的211份中国荷斯坦牛牛乳样本为研究对象,建立了基于傅里叶变换中红外光谱技术的牛乳中α_s1和κ-酪蛋白含量的无损快速检测模型。首先对牛乳的原始光谱进行预分析,发现水对牛乳的光谱吸收具有很强的干扰,对水的两个主要吸收区域1 597~1 712和3 024~3 680 cm-1进行分析,发现水的吸收区域1 597~1 712 cm-1和蛋白的部分吸收区域1 558~1 705 cm-1（酰胺Ⅰ）基本重合,通过对比去除1 597~1 712 cm-1前后的效果,最终选择925.92~3 005.382 cm-1的光谱区域作为敏感波段用于后续分析。选取的全光谱经手动降维,利用MCCV剔除异常样本,分别采用标准正态变量变换（SNV）、多元散射校正(MSC)等8种预处理算法和竞争性自适应重加权算法（CARS）、无信息变量消除法（UVE）等3种特征选择算法联合建立支持向量机回归模型（SVR）。经检验,对于α_s1-酪蛋白,一阶导数和CARS算法结合建立的SVR模型效果最优,训练集相关系数Rc和测试集相关系数R_p分别为0.882 7和0.899 8,训练集均方根误差RMSEC和测试集均方根误差RMSEP分别为1.136 3和1.372 6;对于κ-酪蛋白,一阶差分和UVE算法结合建立的SVR模型效果最优,训练集相关系数R_c和测试集相关系数R_p分别为0.880 8和0.890 3,训练集均方根误差RMSEC和测试集均方根误差RMSEP分别为0.534 5和0.535 4。研究结果表明,基于傅里叶变换中红外光谱技术建立的SVR模型可以对牛乳中的过敏原α_s1和κ-酪蛋白含量进行无损检测,预测效果良好,此研究弥补了国内利用光谱技术对牛乳中的酪蛋白进行无损快速检测的空白。     

基于IERT的非线性全光谱复杂水体定量分析算法研究

水是一种有限的资源,对农业、工业乃至人类的生存都是必不可少的,良好的水环境是可持续发展的重要保障。对水质信息的科学监测,是实现水资源优化配置与高效利用的基础。联合国环境署（UNEP）与世界卫生组织（WHO）指出,应当加强发展中国家的水质监测网络,包括数据质量的保证和分析能力的提高。光谱法作为一种新兴的水质分析方法,相比传统的化学水质监测方法,具有“响应速度快、多参数同步、绿色无污染”的特点。传统单波长、多波长的线性模型依赖于水体对特定波长的吸收特征,不适用于多组分混合溶液且普适性较差。因此,提出了一种基于IERT的非线性全光谱定量分析算法,建立适用于多组分混合溶液浓度预测模型,达到利用全光谱信息来预测浓度信息的目的。利用实验室配置的COD,BOD₅和TOC多组分混合溶液与NO₃-N、浊度、色度多组分混合溶液作为实验样本,使用光谱仪采集样本的光谱曲线,通过全光谱数据进行浓度预测实验,结果显示,对于COD,BOD₅和TOC多组分混合溶液,本算法对于三种组分的决定系数（R2）分别为0.999 3,0.991 4和0.999 3,均方根误差（RMSE）分别为0.024 4,0.057 7和0.000 4;对于NO₃-N、浊度、色度多组分混合溶液,决定系数（R2）分别为0.983 4,0.868 4和0.981 0,均方根误差（RMSE）分别为0.100 5,0.326 4和0.120 2。通过对比本算法与偏最小二乘（PLS）、支持向量机回归（SVR）、决策树（DT）、极端随机树（ERT）对于同一组数据的实验结果,表明：在两组多组分混合溶液的实验中,本算法对于其中各组分的决定系数（R2）均为最优,相比于其他对比算法均方根误差（RMSE）均有大幅减少。本算法可利用光谱信息对多组分混合溶液进行定量分析,在计算时间相当的情况下,可有效的提高浓度预测精度,减少定量分析的均方根误差,可为光谱法水质监测提供一种新的有效途径。     

Non-Fermi liquid behavior in the stripe phase of the extended Hubbard model

Within a strong-coupling perturbative approach, based on a Cumulant Expansion of the extended single-band Hubbard model, we show that the on-shell inverse scattering time deviates from the normal Fermi-liquid behavior near the points of the Fermi surface connected by the characteristic wave-vector of an incommensurate charge density wave. The violation of the Fermi liquid behavior is associated with a square root behavior of the inverse quasiparticle lifetime in proximity of a stripe phase. Some relevant features observed in ARPES experiments on Bi2212 are qualitatively reproduced. Received 28 February 2002 / Received in final form 7 May 2002 Published online 9 July 2002     

三维荧光光谱结合小波压缩与交替惩罚四线性分解算法测定多环芳烃

基于三维荧光光谱结合交替惩罚四线性分解(APQLD)对痕量多环芳烃(PAHs)进行检测,实验以苊(ANA)和萘(NAP)为研究对象。首先利用小波变换对得到的三维荧光光谱数据进行压缩,以消除数据的冗余信息。分别在乙醇溶剂、甲醇溶剂以及超纯水条件下测定不同浓度的PAHs的激发-发射荧光光谱,并将其组合构建四维数据,利用APQLD对构建的四维光谱数据进行分析,并对比了PAHs在三种溶剂条件下各自的回收率。实验结果表明,用不同溶剂构建的四维数据能更准确地测定PAHs的浓度,其回收率更高;对比二阶校正以及其他四维校正算法,APQLD更能体现四维算法所具有的优越性;当因子数N=3时,ANA的回收率为96.5%~103.3%,预测均方根误差为0.04 μg·L-1;NAP的回收率为93.3%~110.0%,预测均方根误差为0.08 μg·L-1。     

Resistance inequalities for KMS states of the isotropic Heisenberg model

Inequalities which show that the spin correlations between spins at two lattice sites is bounded by a constant times the inverse square root of the electrical resistance between the lattice sites is proved for KMS states of the isotropic Heisenberg model. The resistance is calculated using the inverse of the coefficients occuring in the Heisenberg Hamiltionian as the resistances between neighboring lattice sites.Work supported in part by a National Science Foundation GrantOn leave from the University of Pennsylvania, Philadelphia, Pa. 19174, USA     

Asymptotic Characteristics of the Evolution of Polarization of Nonmonochromatic Radiation in Single-Mode Optical Fibers with Random Twisting of Axes of Linear Birefringence. II. The Asymptotic Behavior of the Degree of Polarization at Large Fiber Lengths

In this paper, we determine the asymptotic behavior for the squared degree of polarization of nonmonochromatic radiation propagating in a large-length fiber with random irregularities. It is found that the average squared degree of polarization tends to zero with the fiber length as the inverse square root of the fiber length.     

扬声器锥形振膜环反谐振频率的计算

本文在求解扬声器锥形振膜低频振动的基础上,得到了计算扬声器锥壳环反谐振频率的精确公式,并借助特征频率反比于质量平方根的物理概念,推出了适于工程应用的近似公式,其偏差在３％以内。     

核能谱单能峰快速高精度高斯函数拟合算法研究

在核能谱分析中,高斯函数最小二乘拟合法是计算单能峰净峰面积常用的方法,该方法精度较高,但噪声敏感性较强,导致拟合出的高斯函数在峰位附近的残差向量较大。针对该问题,对高斯函数最小二乘拟合法进行了详细推导,分析了峰位附近残差向量较大的原因,提出了一种基于高斯函数最小二乘拟合法的高斯函数加权最小二乘拟合法,即在高斯函数最小二乘拟合法的基础上,引入了权重因子。该权重因子与取对数后数据权重削弱趋势相反或与数据本身趋势相符,以减小噪声敏感性。由于在求解高斯函数参数的过程中涉及到求逆矩阵运算,计算量较大,耗时较长,为了提高实时性,将求逆矩阵的运算过程转换为了简单的方程组运算,并给出了高斯函数的幅值、中心及方差参数的快速求解公式。将这两种方法用于55Fe的特征X射线单能峰的实际拟合中,结果表明,高斯函数加权最小二乘拟合法效果均较好,这说明该方法降低了噪声敏感性,减小了高斯函数在峰位附近的残差向量,进一步提高了拟合精度。另外,使用快速求解公式,也减小了运算量,增强了实时性,为在便携式设备中的有效使用提供了可能。     

向列相液晶中强非局域空间光孤子的相互作用

在数值和实验上研究了向列相液晶中空间光孤子的相互作用.向列相液晶中的响应函数为指数衰减函数,这不同于Snyder-Mitchell模型.数值模拟发现向列相液晶中的孤子相互作用仍然满足交叉点位置与输入功率的平方根成反比,强非局域下的Snyder-Mitchell模型交叉点位置与两束光的间距无关,而在向列相液晶中交叉点位置与两束光的间距有关;在实验上发现,向列相液晶中两束光交叉点的位置与输入功率平方根成反比,还和形成孤子的临界功率以及两束光之间的间距有关. 关键词： 强非局域非线性 向列相液晶 孤子相互作用 交叉点     

向列相液晶中强非局域空间光孤子的相互作用

在数值和实验上研究了向列相液晶中空间光孤子的相互作用.向列相液晶中的响应函数为指数衰减函数，这不同于Snyder-Mitchell模型.数值模拟发现向列相液晶中的孤子相互作用仍然满足交叉点位置与输入功率的平方根成反比，强非局域下的Snyder-Mitchell模型交叉点位置与两束光的间距无关，而在向列相液晶中交叉点位置与两束光的间距有关；在实验上发现，向列相液晶中两束光交叉点的位置与输入功率平方根成反比，还和形成孤子的临界功率以及两束光之间的间距有关.     

一种快速稀疏贝叶斯学习的水声目标方位估计方法研究

针对以具有时序结构的稀疏贝叶斯学习(Temporally multiple sparse Bayesian learning,TMSBL)为重构算法的水声目标DOA (Direction-of-arrival)估计方法存在运算速度慢的问题,结合块稀疏贝叶斯学习(Block-spare Bayesian learning,BSBL)理论框架下DOA估计模型与特点,采用MacKay提出的定点方法(Fixed-point method)对TMSBL算法中的核心超参量进行求解,提出一种快速的水声目标方位估计稀疏贝叶斯学习的方法,该方法具有运算速度快,重构概率高的特点,并通过实验仿真从运算时间、失败率和均方根误差等方面与TMSBL算法进行比较,验证了该方法的可行性与有效性。      

Chiral optical Tamm states at the boundary of the medium with helical symmetry of the dielectric tensor

We report the observation of photovoltage oscillations in back-gated two-dimensional electron systems when tuning the density under incident microwaves and in the absence of a magnetic field. The oscillations are periodic in the inverse of the square root of the density. They originate from the interference of screened bulk plasmons with a linear dispersion. This phenomenon can be exploited to devise a spectrometer-on-a-chip for millimeter waves. The influence of a perpendicular magnetic field is investigated and reveals a transformation of screened bulk plasmons waves into screened edge magnetoplasmons.     

Random to deterministic transform

A method of transforming an ergodic random signal to its deterministic equivalent is presented. The transform requires that the spectral density of the random signal should be known. It also depends on the ability to obtain the inverse Fourier transform of a function. A specific relationship is developed to evaluate the root mean square of a random signal based on its deterministic equivalent. A sample application is presented to demonstrate that a step input can be equivalent to a hyperbolic spectral density. A linear system is subjected to the hyperbolic spectral density and the equivalent step. The calculated root mean square outputs are found to be identical. Deterministic equivalents for other random signals are also indicated.     

特征提取算法在福美双表面增强拉曼光谱定量分析中的应用

表面增强拉曼散射(SERS)技术具有快速、指纹效应与极低的检测限等优点,被越来越多地应用到有害污染物、有毒物质、危险物质的检测与分析中。在SERS光谱的测量过程中,易受基底、仪器、宇宙射线与测量环境等因素影响,出现波动现象,对后续的分析与检测造成较大的干扰。基于农药福美双SERS光谱数据,尝试利用多种特征提取算法,如主成分分析(PCA)、离散余弦变换(DCT)、非负因式分解(NMF) ,对光谱的主分量进行提取,以减弱光谱数据波动对其后续的定量分析结果的影响。然后将提取后的分量分别结合线性回归算法——偏最小二乘法回归(PLSR),非线性回归算法——支持向量机回归(SVR)建立定量模型。最后,利用5-折交叉验证方法对比不同特征提取算法在不同类型的回归算法下的效果。通过实验验证可知,SVR对福美双溶液的分析精度要明显高于PLSR,这主要是由于SERS光谱强度与被分析物浓度之间为非线性关系。同时针对两种类型回归算法,特征提取算法都能明显地提升了分析结果,主要是由于其提取了源数据的主体信息,去除干扰信息。其中在线性回归中使用PCA效果最佳,在非线性拟合中使用NMF结果最佳,分析误差最好时可降低近3倍。最优回归模型(NMF+SVR)的交叉验证均方误差(RMSECV)为0.0455 μmol·L-1(10-6 mol·L-1),达到国家对福美双的检测标准,为农药快速检测提供一种新的方法。     

Practical pulse synthesis via the discrete inverse scattering transform

This paper provides the practical details required to use the inverse scattering (IST) approach to design selective RF-pulses. As in the Shinnar-Le Roux (SLR) approach, we use a hard pulse approximation to actually design the pulse. Unlike SLR, the pulse is designed using the full inverse scattering data (the reflection coefficient and the bound states) rather than the flip angle profile. We explain how to approximate the reflection coefficient to obtain a pulse with a prescribed rephasing time. In contrast to the SLR approach, we retain direct control on the phase of the magnetization profile throughout the design process. We give explicit recursive algorithms for computing the hard pulse from the inverse scattering data. These algorithms are quite different from the SLR recursion, being essentially discretizations of the Marchenko equations. We call our approach the discrete inverse scattering transform or DIST. Overall, it is as fast as the SLR approach. When bound states are present, we use both the left and right Marchenko equations to improve the numerical stability of the algorithm. We compute a variety of examples and consider the effect of amplitude errors on the magnetization profile.     

Expansion of the kinetic hierarchy for a massive particle: The repeated ring and Fokker-Planck equations

The tagged particle BBGKY hierarchy is systematically expanded in inverse powers of the square root of the particle mass. In the Brownian limit, for fixed Knudsen number, the hierarchy reduces to the Brownian limit of the repeated ring equation which itself reduces to the Fokker-Planck equation. The friction coefficient of the Fokker-Planck equation is found to be a functional of the solution of Dorfman, van Beijeren, and McClure's extended Boltzmann equation for a fixed object in a flowing gas. As a consequence, the tagged particle diffusion coefficient calculated in the Brownian limit of the repeated ring equation is valid for all particle sizes.