Copula Processes

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility (GCPV), to predict the latent standard deviations of a sequence of random variables. To make predictions we use Bayesian inference, with the Laplace approximation, and with Markov chain Monte Carlo as an alternative. We find both methods comparable. We also find our model can outperform GARCH on simulated and financial data. And unlike GARCH, GCPV can easily handle missing data, incorporate covariates other than time, and model a rich class of covariance structures.

On the diffraction of acoustic waves by a quarter-plane

This paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shanin's theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Green's functions, leads to three modified Smyshlyaev formulae, which partially solve the far-field problem of scattering of an incident plane wave by a quarter-plane in the Dirichlet case. In this paper, we present similar formulae in the Neumann case, and describe a numerical method allowing a fast computation of the diffraction coefficient using Shanin's third modified Smyshlyaev formula. The method requires knowledge of the eigenvalues of the Laplace-Beltrami operator on the unit sphere with a cut, and we also describe a way of computing these eigenvalues. Numerical results are given for different directions of incident plane wave in the Dirichlet and the Neumann cases, emphasising the superiority of the third modified Smyshlyaev formula over the other two. © 2011 Elsevier B.V.

Efficient parametric uncertainty analysis within the hybrid Finite Element/Statistical Energy Analysis method

This paper is concerned with the development of efficient algorithms for propagating parametric uncertainty within the context of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) approach to the analysis of complex vibro-acoustic systems. This approach models the system as a combination of SEA subsystems and FE components; it is assumed that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. The method has been recently generalised by allowing the FE components to possess parametric uncertainty, leading to two ensembles of uncertainty: a non-parametric one (SEA subsystems) and a parametric one (FE components). The SEA subsystems ensemble is dealt with analytically, while the effect of the additional FE components ensemble can be dealt with by Monte Carlo Simulations. However, this approach can be computationally intensive when applied to complex engineering systems having many uncertain parameters. Two different strategies are proposed: (i) the combination of the hybrid FE/SEA method with the First Order Reliability Method which allows the probability of the non-parametric ensemble average of a response variable exceeding a barrier to be calculated and (ii) the combination of the hybrid FE/SEA method with Laplace's method which allows the evaluation of the probability of a response variable exceeding a limit value. The proposed approaches are illustrated using two built-up plate systems with uncertain properties and the results are validated against direct integration, Monte Carlo simulations of the FE and of the hybrid FE/SEA models. © 2013 Elsevier Ltd.

PH值、氯离子浓度和监酸浓度对于铁的腐蚀电化学行为的影响

本文研究了Armco铁在盐酸溶液中的腐蚀电化学行为，探讨了ψ~-离子和PH值对铁的阳极溶解过程的影响，并进而讨论了ψ~-离子浓度和PH值对铁的腐蚀电化学行为的影响之间是否存在交互效应。在本工作中，作者提出了两个新的研究方法：(a) 从单支弱极化曲线测定腐蚀电流和阴、阳极反应的Tafep斜率；(b)根据交流方波电流扰动的响应函数方程测定极化电阻Rp和界面电容C。设I_c、I_(2c)、I_(3c)及I_(4c)分别为对应于弱极化区内极化电位为ΔE、2ΔE、3ΔE和4ΔE的极化电流，且令a = I_(2c)/I_c, b = I_(3c)/I_c, c = I_(4c)/I_(2c), 而(4b-3a~2)~(1/2)、(3c-2b)~(1/2)、(2c-a~2)~(1/2)则以S_j表示之，则可得到：I_(corr) = I_c/S_j b_c = ΔE/lg((a+s_j)/2) b_a = -ΔE/lg((a-s_j)/2)为了方便，准确地求出动力学参数，可选用一系列的ΔE值，得出相应的极化电流I_λ，求出S_λ，应用统计方法处理数据，可得：I_(corr) = ∑ from i=1 to n I_λ/∑ from i=1 ton S_λ b_c = ∑ form λ to n ΔE_λ/∑ form i=1 to n lg ((a_λ+S_λ)/2) b_a = ∑ form i=1 ton ΔE_λ/∑ form i=1 to n lg ((a_λ-S_λ)/2)在线性极化区间内向腐蚀金属电极体系施加一交流方波电流扰动讯号时，通过Laplace变换分析，得到相应的响应函数方程为：E_1(t) = λ_o(R_s+R_p) - 2λ_oR_p (e~(-(τ-λ)/RpC))/(1+e~(λ/RpC)) (o<τ<λ) E_2(t) = -λ_o(R_s+R_p) + 2λ_oR_p (e~(-(τ-λ)/RpC))/(1+e~(λ/RpC)) (λ<τ<2λ)由此方程可知，它们在E～λ坐标系统中的轨迹为对称兴致勃勃原点的两条直线。由此方程可进一步得到:ΔE = 2λ_oR_p (e~(λ/RpC)-1)/(e~(λ/RpC)+1) = 2λ_oR_p t_(anh)(λ/(2RpC)) Δh = 2λ_o Rs式中ΔE为单支响应直线的长度，Δh则为两条直线最高点之间的距离。上述公式可进一步简化为：Rp =(ΔE)/(2λ_o) λ>>RpC (λ_o)/(ΔE) = C/λ + 1/(2Rp) λ<

脊形结构LiNbO3光波导调制器的扩展点匹配法分析

将点匹配法扩展应用于脊形结构LiNbO3光波导调制器电极的准静态分析中.将调制器各区域的势函数表示为该区域中满足Laplace方程的一系列基函数的级数,匹配边界上有限个点的边界条件以确定出级数项的系数.通过势函数得到脊形结构LiNbO3光波导调制器结构中电场分布的解析表达式,利用求得的电场可以得到调制器特性阻抗及有效折射率.所得的特性阻抗和有效折射率与采用有限元法得到的结果十分吻合.这一分析方法简便快捷,精度高,能够处理电极有一定厚度的多层光波导调制器结构.

A method to calculate the surface tension of a cylindrical droplet

The history of Laplace's equations for spherical and cylindrical droplets and the concept of dividing surface in Gibbs' thermodynamic theory of capillary phenomena are briefly reviewed. The existing theories of surface tensions of cylindrical droplets are briefly reviewed too. For cylindrical droplets, a new method to calculate the radius and the surface tension of the surface of tension is given. This method is suitable to be used by molecular dynamics simulations.

关于固体表面上液体球冠的平衡条件问题——兼评“冷凝器壁面滴状冷凝的热力学机理及最佳接触角”等文章

对于第一类液滴(尺度远大于界面层的厚度),无论是远离固体壁面的液体球或附着在壁面上的球冠,其内外压力差(简称"附加压力")均适用经典Laplace公式,并且特别对球冠情况给出了一种新的整体性证明.还澄清有关争论:指出[曹治党、郭愚1999物理学报481823]一文对附壁面第一类液体球冠所推导出的附加压力与接触角有关的公式是错误的,而[闵敬春2002物理学报512730]是正确的。

兰州重离子加速器冷却储存环主环加速过程的束流反馈

正在建设中的兰州重离子加速器冷却储存环(HIRFL-CSR)主环用于束流的加速。在加速过程中,为了保证束流的谐振加速,须准备2个束流反馈环(相位反馈环和束流径向位置反馈环)来保证主导磁场与高频频率的同步。本文基于Laplace变换及数值计算结果,分析了束流反馈环对同步加速器中束流动力学行为的影响。

Local histogram based geometric invariant image watermarking

Compared with other existing methods, the feature point-based image watermarking schemes can resist to global geometric attacks and local geometric attacks, especially cropping and random bending attacks (RBAs), by binding watermark synchronization with salient image characteristics. However, the watermark detection rate remains low in the current feature point-based watermarking schemes. The main reason is that both of feature point extraction and watermark embedding are more or less related to the pixel position, which is seriously distorted by the interpolation error and the shift problem during geometric attacks. In view of these facts, this paper proposes a geometrically robust image watermarking scheme based on local histogram. Our scheme mainly consists of three components: (1) feature points extraction and local circular regions (LCRs) construction are conducted by using Harris-Laplace detector; (2) a mechanism of grapy theoretical clustering-based feature selection is used to choose a set of non-overlapped LCRs, then geometrically invariant LCRs are completely formed through dominant orientation normalization; and (3) the histogram and mean statistically independent of the pixel position are calculated over the selected LCRs and utilized to embed watermarks. Experimental results demonstrate that the proposed scheme can provide sufficient robustness against geometric attacks as well as common image processing operations. (C) 2010 Elsevier B.V. All rights reserved.

Synergistic effect of supported nickel catalyst with intumescent flame-retardants on flame retardancy and thermal stability of polypropylene

Supported nickel catalyst (Ni-Cat) was used as a catalyst to improve the flame retarclancy of intumescent flame-retardants (IFR) systems based on ammonium polyphosphate and pentaerythritol (PETOL) in polypropylene (PP) matrix. Limited oxygen index (LOI), UL-94 rating, and thermogravimetric analysis were used to characterize the flame retardancy and thermal stability of the PP systems, and field emission scanning electron microscopy (FE-SEM) and Fourier transformed infrared spectroscopy (FTIR) were used to analyze the microstructure and composition of the chars formed during measuring LOI value and after combustion at 800 degrees C. The catalytic effect of NiCat was shown in an increase of LOI, a change in the char microstructure, and improvement of the thermal stability in the PP systems, which result from the synergistic effect of Ni-Cat and IFR. The results from FE-SEM and FTIR spectra of the char can explain how this synergistic effect happened.

Laser light scattering of the molecular weight distribution of unfractionated phenolphthalein poly(aryl ether sulfone)

Two unfractionated samples of phenolphthalein poly( aryl ether sulfone) (PES-C) were characterized in CHCl3 at 25 degrees C by applying a recently developed laser light-scattering (LLS) procedure. The Laplace inversion of precisely measured intensity-intensity time correlation function lead us first to an estimate of the characteristic line-width distribution G(Gamma) and then to the translational diffusion coefficient distribution G(D). A combination of static and dynamic LLS results enabled us to determine D = (2.69 x 10(-4))M(-0.553), which agrees with the calibration of D = (2.45 x 10(-4))M(-0.55) previously established by a set of narrowly distributed PES-C samples. Using this newly obtained scaling between D and M, we were able to convert G(D) into a differential weight distribution f(w)(M) for the two PES-C samples. The weight-average molecular weights calculated from f(w)(M) are comparable to that obtained directly from static LLS. Our results showed that using two broadly distributed samples instead of a set of narrowly distributed samples have provided not only similar final results, but also a more practical method for the PES-C characterization. (C) 1997 John Wiley & Sons, Inc.

Dynamic light-scattering characterization of the molecular weight distribution of a broadly distributed phenolphthalein poly(aryl ether ketone)

Using a recently developed laser light-scattering (LLS) procedure, we accomplished the characterization of a broadly distributed unfractionated phenolphthalein poly(aryl ether ketone) (PEK-C) in CHCl3 at 25 degrees C. The laplace inversion of precisely measured intensity-intensity time correlation function from dynamic LLS leads us first to an estimate of the characteristic line-width distribution G(Gamma) and then to the translational diffusion coefficient distribution G(D). By using a previously established calibration of D (cm(2)/s) = 2.37 X 10(-4)M(-0.57), were able to convert G(D) into a differential weight distribution f(w)(M). The weight-average molecular weight M(w) calculated from f(w)(M) agrees well with that directly measured in static LLS. Our results indicate that both the calibration and LLS procedure used in this study are ready to be applied as a routine method for the characterization of the molecular weight distribution of PEK-C. (C) 1996 John Wiley & Sons, Inc.

A DYNAMIC LASER LIGHT-SCATTERING STUDY OF CHITOSAN IN AQUEOUS-SOLUTION

The solution behavior of four chitosans (91% deacetylated chitin) with different molecular weights in 0.2M CH3COOH/0.1M CH3COONa aqueous solution was investigated at 25 degrees C by dynamic laser light scattering (LLS). The Laplace inversion of the precisely measured intensity-intensity time correlation function leads us to an estimate of the line-width distribution G(Gamma), which could be further reduced to a translational diffusion coefficient distribution G(D). By using a combination of static and dynamic LLS results, i.e. Mw and G(D), we were able to establish a calibration of D = k(D)M(-alpha D) with k(D) = (3.14 +/- 0.20) X 10(-4) and alpha(D) = 0.655 +/- 0.015. By using this calibration, we successfully converted G(D) into a molecular weight distribution f(w)(M). The larger alpha(D) value confirms that the chitosan chain is slightly extended in aqueous solution even in the presence of salts. This is mainly due to its backbone and polyelectrolytes nature. As a very sensitive technique, our dynamic LLS results also revealed that even in dilute solution chitosan still forms a small amount of larger sized aggregates that have ben overlooked in previous studies. The calibration obtained in this study will provide another way to characterize the molecular weight distribution of chitosan in aqueous solution at room temperature. (C) 1995 John Wiley & Sons, Inc.

A preliminary study on thermoluminescence characteristics of sediments from the North Pacific

Thirty-eight surficial deposit samples were collected from the equatorial North Pacific, and the natural thermoluminescence (TL) characteristics of both bulk and clay fraction samples ( < 2 mu m fractions) were studied by the FJ427 - Al automatic TL Dosimeter for the first time. With the measurements of clay mineral composition, element composition by XRD and ICP, the correlations between TL intensity and sedimentary environment proxies were analyzed, such as water depth, ratio of FeO to Fe2O3 contents, LOI, and major clay mineral concentration, and it was found the bulk sample's TL signal was stronger than the clay ones. Usually, increase in the clay components may result in the decrease of TL intensity. From the shape of TL curves, the pelagic sediments can be divided into two groups: the majority group has two glow peaks, in general, the first peak is broad and flat, but the second narrow and sharp; the minority group only has a single peak because the first is absent. The peak centers of TL curves are almost fixed, falling in the temperature sections 230 similar to 260 and 390 similar to 405 degrees C respectively. Lorentz model packed in the Origin 7.5 was chosen to deal with the TL curves. From the processing results, three parameters ( H, C and A), corresponding to the height, center, and kurtosis of TL curve, were obtained to describe the curve characteristics. The correlations between TL curve parameters and sedimentary environment proxies were also calculated. On the basis of the above work, the relationship between TL characteristics and sediment type, mineral composition, sedimentary environment of surface sediments was discussed in the study area, and a conclusion is: sediments from the environment of shallower water, higher organic contents and weaker reductivity have stronger TL signals.

Generation of internal and surface waves by seafloor movement in a two layer fluid system

Internal and surface waves generated by the deformations of the solid bed in a two layer fluid system of infinite lateral extent and uniform depth are investigated. An integral solution is developed for an arbitrary bed displacement on the basis of a linear approximation of the complete description of wave motion using a transform method (Laplace in time and Fourier in space) analogous to that used to study the generation of tsunamis by many researchers. The theoretical solutions are presented for three interesting specific deformations of the seafloor; the spatial variation of each seafloor displacement consists of a block section of the seafloor moving vertically either up or down while the time-displacement history of the block section is varied. The generation process and the profiles of the internal and surface waves for the case of the exponential bed movement are numerically illustrated, and the effects of the deformation parameters, densities and depths of the two layers on the solutions are discussed. As expected, the solutions derived from the present work include as special cases that obtained by Kervella et al. [Theor Comput Fluid Dyn 21:245-269, 2007] for tsunamis cased by an instantaneous seabed deformation and those presented by Hammack [J Fluid Mech 60:769-799, 1973] for the exponential and the half-sine bed displacements when the density of the upper fluid is taken as zero.