潮波模型的优化开边界方法研究

数值模式是潮波研究的一种有利手段，但在研究中会面临各种具体问题，包括开边界条件的确定、底摩擦系数和耗散系数的选取等。数据同化是解决这些问题的一种途径，即利用有限数量的潮汐观测资料对潮波进行最优估计，其根本目的是迫使模型预报值逼近观测值，使模式不要偏离实际情况太远。本文采用了一种优化开边界方法，沿着数值模型的开边界优化潮汐水位信息，目的是设法使数值解在动力约束的意义下接近观测值，获得研究区域的潮汐结果。边界值由指定优化问题的解来定，以提高模拟区域的潮汐精度，最优问题的解是基于通过开边界的能量通量的变化，处理开边界处的观测值与计算值之差的最小化。这里提供了辐射型边界条件，由Reid 和Bodine（本文简称为RB）推导，我们将采用的优化后的RB方法（称为ORB）是优化开边界的特殊情况。 本文对理想矩形海域（ E- E， N- N， 分辨率 ）进行了潮波模拟，有东部开边界，模式采用ECOM3D模式。对数据结果的误差分析采用，振幅平均偏差，平均绝对偏差，平均相对误差和均方根偏差四个值来衡量模拟结果的好坏程度。 需要优化入开边界的解析潮汐值本文采用的解析解由方国洪《海湾的潮汐与潮流》（1966年）方法提供，为验证本文所做的解析解和方文的一致，本文做了其第一个例子的关键值a,b,z,结果与其结果吻合的相当好。但略有差别，分析的可能原因是两法在具体迭代方案和计算机保留小数上有区别造成微小误差。另外，我们取m=20，得到更精确的数值，我们发现对前十项的各项参数值，取m=10,m=20各项参数略有改进。当然我们可以获得m更大的各项参数值。 同时为了检验解析解的正确性讨论m和l变化对边界值的影响，结果指出，增大m，m=20时，u的模最大在本身u1或u2的模的6%；m=100时，u的模最大在本身u1或u2的模的4%；m再增大，m=1000时，u的模最大在本身u1或u2的模的4%，改变不大。当l<1时， =0处u的模最大为2。当l=1时， =0处u的模最大为0.1，当l>1时，l越大，u的模越小，当l=10时，u的模最大为0.001，可以认为为0。 为检验该优化方法的应用情况，我们对理想矩形区域进行模拟，首先将本文所采用的优化开边界方法应用于30m的情况，在开边界优化入开边界得出模式解，所得模拟结果与解析解吻合得相当好，该模式解和解析解在整个区域上，振幅平均绝对偏差为9.9cm,相位平均绝对偏差只有4.0 ，均方根偏差只有13.3cm，说明该优化方法在潮波模型中有效。 为验证该优化方法在各种条件下的模拟结果情况，在下面我们做了三类敏感性试验： 第一类试验：为证明在开边界上使用优化方法相比于没有采用优化方法的模拟解更接近于解析解，我们来比较ORB条件与RB条件的优劣，我们模拟用了两个不同的摩擦系数，k分别为：0,0.00006。 结果显示，针对不同摩擦系数，显示在开边界上使用ORB条件的解比使用RB条件的解无论是振幅还是相位都有显著改善，两个试验均方根偏差优化程度分别为84.3%，83.7%。说明在开边界上使用优化方法相比于没有采用优化方法的模拟解更接近于解析解，大大提高了模拟水平。上述的两个试验得出， k=0.00006优化结果比k=0的好。 第二类试验，使用ORB条件确定优化开边界情况下，在东西边界加入出入流的情况，流考虑线性和非线性情况，结果显示，加入流的情况，潮汐模拟的效果降低不少，流为1Sv的情况要比5Sv的情况均方根偏差相差20cm,而不加流的情况只有0.2cm。线性流和非线性流情况两者模式解相差不大，振幅，相位各项指数都相近, 说明流的线性与否对结果影响不大。 第三类试验，不仅在开边界使用ORB条件，在模式内部也使用ORB条件，比较了内部优化和不优化情况与解析解的偏差。结果显示，选用不同的k,振幅都能得到很好的模拟，而相位相对较差。另外，在内部优化的情况下，考虑不同的k的模式解， 我们选用了与解析解相近的6个模式解的k,结果显示，不同的k,振幅都能得到很好的模拟，而相位较差。 总之，在开边界使用ORB条件比使用RB条件好，振幅相位都有大幅度改进，在加入出入流情况下，流的大小对模拟结果有影响，但线形流和非线性流差别不大。内部优化的结果显示，模式采用不同的k都能很好模拟解析解的振幅。

Optical Factors Determined by the T-matrix Method in Turbidity Measurement of Absolute Coagulation Rate Constants

Turbidity measurement for the absolute coagulation rate constant of suspensions has been extensively adopted because of its simplicity and easy implementation. A key factor to derive the rate constant from experimental data is how to theoretically evaluate the so-called optical factor involved in calculating the extinction cross section of doublets formed in the aggregation. In a previous paper, we have shown that compared with other theoretical approaches, the T-matrix method provides a robust solution to this problem and is effective in extending the applicability range of the turbidity methodology as well as increasing measurement accuracy. This paper will provide a more comprehensive discussion about the physical insight of using the T-matrix method in turbidity measurement and associated technical details. In particular, the importance of ensuring the correct value for the refractive indices for colloidal particles and the surrounding medium used in the calculation is addressed because the indices generally vary with the wavelength of the incident light. The comparison of calculated results with experiments shows that the T-matrix method can correctly calculate optical factors even for large particles, whereas other existing theories cannot. In addition, the calculated data of the optical factor by the T-matrix method for a range of particle radii and incident light wavelengths are listed.

Study on improving the turbidity measurement of the absolute coagulation rate constant

The existing theories dealing with the evaluation of the absolute coagulation rate constant by turbidity measurement were experimentally tested for different particle-sized (radius = a) suspensions at incident wavelengths (lambda) ranging from near-infrared to ultraviolet light. When the size parameter alpha = 2 pi a/lambda > 3, the rate constant data from previous theories for fixed-sized particles show significant inconsistencies at different light wavelengths. We attribute this problem to the imperfection of these theories in describing the light scattering from doublets through their evaluation of the extinction cross section. The evaluations of the rate constants by all previous theories become untenable as the size parameter increases and therefore hampers the applicable range of the turbidity measurement. By using the T-matrix method, we present a robust solution for evaluating the extinction cross section of doublets formed in the aggregation. Our experiments show that this new approach is effective in extending the applicability range of the turbidity methodology and increasing measurement accuracy.

Absolute measurement of roughness and lateral-correlation length of random surfaces by use of the simplified model of image-speckle contrast

We present a method of image-speckle contrast for the nonprecalibration measurement of the root-mean-square roughness and the lateral-correlation length of random surfaces with Gaussian correlation. We use the simplified model of the speckle fields produced by the weak scattering object in the theoretical analysis. The explicit mathematical relation shows that the saturation value of the image-speckle contrast at a large aperture radius determines the roughness, while the variation of the contrast with the aperture radius determines the lateral-correlation length. In the experimental performance, we specially fabricate the random surface samples with Gaussian correlation. The square of the image-speckle contrast is measured versus the radius of the aperture in the 4f system, and the roughness and the lateral-correlation length are extracted by fitting the theoretical result to the experimental data. Comparison of the measurement with that by an atomic force microscope shows our method has a satisfying accuracy. (C) 2002 Optical Society of America.

Accurate determination of the absolute phase and temporal-pulse phase of few-cycle laser pulses

A Fourier analysis method is used to accurately determine not only the absolute phase but also the temporal-pulse phase of an isolated few-cycle (chirped) laser pulse. This method is independent of the pulse shape and can fully characterize the light wave even though only a few samples per optical cycle are available. It paves the way for investigating the absolute phase-dependent extreme nonlinear optics, and the evolutions of the absolute phase and the temporal-pulse phase of few-cycle laser pulses.

Absolute phase control of spectra effects in a two-level medium driven by two-color ultrashort laser pulses

Using a omega-3 omega combination scenario, we investigate the absolute phase control of the spectra effects for ultrashort laser pulses propagating in a two-level medium. It is found that the higher spectral components can be controlled by the absolute phases. In particular, different absolute phase combinations can lead to the buildup or split of the even harmonics. (c) 2006 Elsevier B.V. All rights reserved.

Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map

Among different phase unwrapping approaches, the weighted least-squares minimization methods are gaining attention. In these algorithms, weighting coefficient is generated from a quality map. The intrinsic drawbacks of existing quality maps constrain the application of these algorithms. They often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. In order to deal with those intractable wrapped phase data, a new weighted least-squares phase unwrapping algorithm based on derivative variance correlation map is proposed. In the algorithm, derivative variance correlation map, a novel quality map, can truly reflect wrapped phase quality, ensuring a more reliable unwrapped result. The definition of the derivative variance correlation map and the principle of the proposed algorithm are present in detail. The performance of the new algorithm has been tested by use of a simulated spherical surface wrapped data and an experimental interferometric synthetic aperture radar (IFSAR) wrapped data. Computer simulation and experimental results have verified that the proposed algorithm can work effectively even when a wrapped phase map contains intractable error sources. (c) 2006 Elsevier GmbH. All rights reserved.

Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal

In this paper we theoretically study the left-handed behaviors in a two-dimensional triangular photonic crystal made of elliptical rods in air. An absolute left-handed region is found in the second photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Typical left-handed behaviors such as negative refraction, flat superlensing and plano-concave lensing are demonstrated by the finite-difference time-domain simulations. These behaviors are also compared with the quasi-negative refraction and the resulted focusing effects in a square-lattice two-dimensional photonic crystal. (c) 2005 Optical Society of America

Composition deviation of arrays of FePt nanoparticles starting from poly(styrene)-poly(4-vinylpyridine) micelles

Ordered arrays of FePt nanoparticles were prepared using a diblock polymer micellar method combined with plasma treatment. Rutherford backscattering spectroscopy analyses reveal that the molar ratios of Fe to Pt in metal-salt-loaded micelles deviate from those when metal precursors are added, and that the plasma treatment processes have little influence upon the compositions of the resulting FePt nanoparticles. The results from Fourier transform infrared spectroscopy show that the maximum loadings of FeCl3 and H2PtCl6 inside poly( styrene)-poly(4-vinylpyridine) micelles are different. The composition deviation of FePt nanoparticles is attributed to the fact that one FeCl3 molecule coordinates with a single 4-vinylpyridine (4VP) unit, while two neighboring and uncomplexed 4VP units are required for one H2PtCl6 molecule. Additionally, we demonstrate that the center-to-center distances of the neighboring FePt nanoparticles can also be tuned by varying the drawing velocity.

A new beam propagation method based on least-squares expansion approximating

A new finite difference wide-angle beam propagation method is developed by introducing the least-squares expansion approximant in the propagator expansion. In this new method it is not necessary to select the reference index point because of the whole region approaching the lease-square expansion. This method avoids the problems induced by error selection of the reference index in the old methods based on Taylor or Pade expansion. Several typical structures are simulated by the new method and the results prove the validity of it.

Absolute measurement of detector quantum efficiency using optical parametric down-conversion pumped by femtosecond laser pulses

Absolute measurement of detector quantum efficiency using optical parametric down-conversion has been extensively studied for the case of a continuous wave pump. In this paper, we have used the temporally and spatially correlated properties of the down-converted photon pairs generated in a nonlinear crystal pumped by a femtosecond laser pulse to perform an absolute measurement of detector quantum efficiency. The measured detector quantum efficiency is in excellent agreement with the measured value in the conventional way. A lens with a long focal length was adopted for efficiently increasing the intensity of the down-conversion entangled photon source.

Study on the Dissociation Behavior of Gas Hydrate in Porous Sediment Based on Fractal Theory

The dissociation process of gas hydrate was regarded as a gas-solid reaction without solid production layer when the temperature was above the zero centigrade. Based on the shrinking core model and the fractal theory, a fractional dimension dynamical model for gas hydrate dissociation in porous sediment was established. The new approach of evaluating the fractal dimension of the porous media was also presented. The fractional dimension dynamical model for gas hydrate dissociation was examined with the previous experimental data of methane hydrate and carbon dioxide hydrate dissociations, respectively. The calculated results indicate that the fractal dimensions of porous media acquired with this method agree well with the previous study. With the absolute average deviation (AAD) below 10%, the present model provided satisfactory predictions for the dissociation process of methane hydrate and carbon dioxide hydrate.

Deviation from the stoichiometric composition of single-crystal 'Er2Co17'

The deviation from the stoichiometric composition of single-crystal 'Er2Co17' has been determined by theoretical analysis. It is found that the composition of this single-crystal 'Er2Co17' is rich in cobalt, and its real composition is suggested to be Er2-deltaCo17+2 delta (delta = 0.14) on the basis of a comparison of calculations based on the single-ion model with a series of experiments. The values of the Er-Co exchange field H-ex and the crystalline-electric-field (CEF) parameters A(n)(m) at the rare-earth (R) site in the 'Er2Co17' compound are also evaluated at the same time. The experiments provide the following data: the temperature dependence of the spontaneous magnetization of the compounds and the normalized magnetic moment of the Er ion, the magnetization curves dong the crystallographic axes at 4.2 K and 200 K, and the temperature dependence of the magnetization along the crystallographic axes in a field of 4 T.