Higher order response of nonlinear composite in external AC electric field

The fifth-order effective nonlinear responses at fundament frequency and higher-order harmonics are given for nonlinear composites, which obey a current-field relation of the form J = sigmaE + x\E\(2) E, if a sinusoidal alternating current (AC) external field with finite frequency omega is applied. As two examples, we have investigated the cylinder and spherical inclusion embedded in a host and, for larger volume fraction, also derived the formulae of effective nonlinear responses at higher-order harmonics by the aid of the general effective response definition. Furthermore, the relationships between effective nonlinear responses at harmonics are given. (C) 2003 Elsevier Science B.V. All rights reserved.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

Effects of nitrogen source and concentration on growth rate and fatty acid composition of Ellipsoidion sp (Eustigmatophyta)

In order to study the effects of different nitrogen source and concentration on the growth rate and fatty acid composition, a marine microalga Ellipsoidion sp. with a high content of eicosapentaenoic acid (EPA) was cultured in media with different nitrogen sources and concentrations. During the pre-logarithmic phase, the alga grew faster with ammonium as N source than with nitrate, but the reverse applied during the post-logarithmic phase. The alga grew poorly in N-free medium or medium with urea as the sole N source. In the same growth phase, ammonium medium resulted in higher yield of total lipid, but the EPA yield did not differ significantly different from that using nitrate medium. The maximum growth rate occurred in medium containing 1.28 mmol L-1 sodium nitrate, while maximum EPA and total lipid contents were reached at 1.92 mmol L-1, when EPA accounted for 27.9% total fatty acids. The growth rate kept stable when NH4Cl ranged from 0.64 to 2.56 mmol L-1, and the maximum content of total lipid and EPA occurred in the medium with 2.56 mmol L-1 NH4Cl. The EPA content was higher in the pre- than post-logarithmic phase, though the total lipid content was lower. The highest EPA content expressed as percent total fatty acid was 27.9% in nitrate medium and and 39.0% in ammonium medium.

基于显式分形插值的高保真地震数据重建方法研究

Based on the fractal theories, contractive mapping principles as well as the fixed point theory, by means of affine transform, this dissertation develops a novel Explicit Fractal Interpolation Function（EFIF）which can be used to reconstruct the seismic data with high fidelity and precision. Spatial trace interpolation is one of the important issues in seismic data processing. Under the ideal circumstances, seismic data should be sampled with a uniform spatial coverage. However, practical constraints such as the complex surface conditions indicate that the sampling density may be sparse or for other reasons some traces may be lost. The wide spacing between receivers can result in sparse sampling along traverse lines, thus result in a spatial aliasing of short-wavelength features. Hence, the method of interpolation is of very importance. It not only needs to make the amplitude information obvious but the phase information, especially that of the point that the phase changes acutely. Many people put forward several interpolation methods, yet this dissertation focuses attention on a special class of fractal interpolation function, referred to as explicit fractal interpolation function to improve the accuracy of the interpolation reconstruction and to make the local information obvious. The traditional fractal interpolation method mainly based on the randomly Fractional Brown Motion (FBM) model, furthermore, the vertical scaling factor which plays a critical role in the implementation of fractal interpolation is assigned the same value during the whole interpolating process, so it can not make the local information obvious. In addition, the maximal defect of the traditional fractal interpolation method is that it cannot obtain the function values on each interpolating nodes, thereby it cannot analyze the node error quantitatively and cannot evaluate the feasibility of this method. Detailed discussions about the applications of fractal interpolation in seismology have not been given by the pioneers, let alone the interpolating processing of the single trace seismogram. On the basis of the previous work and fractal theory this dissertation discusses the fractal interpolation thoroughly and the stability of this special kind of interpolating function is discussed, at the same time the explicit presentation of the vertical scaling factor which controls the precision of the interpolation has been proposed. This novel method develops the traditional fractal interpolation method and converts the fractal interpolation with random algorithms into the interpolation with determined algorithms. The data structure of binary tree method has been applied during the process of interpolation, and it avoids the process of iteration that is inevitable in traditional fractal interpolation and improves the computation efficiency. To illustrate the validity of the novel method, this dissertation develops several theoretical models and synthesizes the common shot gathers and seismograms and reconstructs the traces that were erased from the initial section using the explicit fractal interpolation method. In order to compare the differences between the theoretical traces that were erased in the initial section and the resulting traces after reconstruction on waveform and amplitudes quantitatively, each missing traces are reconstructed and the residuals are analyzed. The numerical experiments demonstrate that the novel fractal interpolation method is not only applicable to reconstruct the seismograms with small offset but to the seismograms with large offset. The seismograms reconstructed by explicit fractal interpolation method resemble the original ones well. The waveform of the missing traces could be estimated very well and also the amplitudes of the interpolated traces are a good approximation of the original ones. The high precision and computational efficiency of the explicit fractal interpolation make it a useful tool to reconstruct the seismic data; it can not only make the local information obvious but preserve the overall characteristics of the object investigated. To illustrate the influence of the explicit fractal interpolation method to the accuracy of the imaging of the structure in the earth’s interior, this dissertation applies the method mentioned above to the reverse-time migration. The imaging sections obtained by using the fractal interpolated reflected data resemble the original ones very well. The numerical experiments demonstrate that even with the sparse sampling we can still obtain the high accurate imaging of the earth’s interior’s structure by means of the explicit fractal interpolation method. So we can obtain the imaging results of the earth’s interior with fine quality by using relatively small number of seismic stations. With the fractal interpolation method we will improve the efficiency and the accuracy of the reverse-time migration under economic conditions. To verify the application effect to real data of the method presented in this paper, we tested the method by using the real data provided by the Broadband Seismic Array Laboratory, IGGCAS. The results demonstrate that the accuracy of explicit fractal interpolation is still very high even with the real data with large epicenter and large offset. The amplitudes and the phase of the reconstructed station data resemble the original ones that were erased in the initial section very well. Altogether, the novel fractal interpolation function provides a new and useful tool to reconstruct the seismic data with high precision and efficiency, and presents an alternative to image the deep structure of the earth accurately.

地震波谱元法数值模拟和偏移研究

With the development of both seismic theory and computer technology, numerical modeling technology of seismic wave has achieved great advancement during the past half century. The current methods under development include finite differentiation method (FDM), finite element method (FEM), pseudospectral method (PSM), integral equation method (IEM) and spectral element method (SEM). They exert their very important roles in every corner of seismology and seismic prospecting. Large quantity of researches towards spectral element method in the end of last century bring this method to a new era, which results in perfect solution of many difficult problems. However, parts of posterior works such as seismic migration and inversion which base on spectral element method have never been studied widely at least up to the present whereas are of importance to seismic imaging and seismic wave propagation. Based on previous work, this paper uses spectral element method to investigate the characteristics and laws of the seismic wave propagation in isotropic and anisotropic media. By thoroughly studying this high-accuracy method, we implement a kind of reverse-time pre- and post-stack migration based on SEM. In order to verify the validity of the SEM method, we have simulated the propagation of seismic wave in several different models. The simulation results show that: (1) spectral element method can be used to model any complex models and the computational results are comparable with the expected results and the analytic results; (2) the optimum accuracy can be achieved when the rank is between 4 and 9. When it is below 4, the dispersion may occur; and when it is above 9, the time step-length will be changed accordingly with the reducing space step-length in order to keep the computation stability. This will exponentially increase the computation time and at the same time the memory even if simulating the same media. This paper also applies explosive reflection surface imaging technology, time constancy principle of wave-filed extrapolation and least travetime raytracing technology of surface source to SEM pre- and post-stack migration of isotropic and anisotropic media. All imaging results derived by the above methods agree well with the real geological models and the position of interface and inflexions can also return to their right location well. This indicates that the method proposed in this paper is a kind of technology with high accuracy and robust stability. It can serve as an alternative method in real seismic data processing. All these work can boost the development of high-accuracy seismic imaging, and therefore have significant inference value.

基于波动方程的层间多次波预测方法研究

In exploration geophysics，velocity analysis and migration methods except reverse time migration are based on ray theory or one-way wave-equation. So multiples are regarded as noise and required to be attenuated. It is very important to attenuate multiples for structure imaging, amplitude preserving migration. So it is an interesting research in theory and application about how to predict and attenuate internal multiples effectively. There are two methods based on wave-equation to predict internal multiples for pre-stack data. One is common focus point method. Another is inverse scattering series method. After comparison of the two methods, we found that there are four problems in common focus point method: 1. dependence of velocity model; 2. only internal multiples related to a layer can be predicted every time; 3. computing procedure is complex; 4. it is difficult to apply it in complex media. In order to overcome these problems, we adopt inverse scattering series method. However, inverse scattering series method also has some problems: 1. computing cost is high; 2. it is difficult to predict internal multiples in the far offset; 3. it is not able to predict internal multiples in complex media. Among those problems, high computing cost is the biggest barrier in field seismic processing. So I present 1D and 1.5D improved algorithms for reducing computing time. In addition, I proposed a new algorithm to solve the problem which exists in subtraction, especially for surface related to multiples. The creative results of my research are following: 1. derived an improved inverse scattering series prediction algorithm for 1D. The algorithm has very high computing efficiency. It is faster than old algorithm about twelve times in theory and faster about eighty times for lower spatial complexity in practice; 2. derived an improved inverse scattering series prediction algorithm for 1.5D. The new algorithm changes the computing domain from pseudo-depth wavenumber domain to TX domain for predicting multiples. The improved algorithm demonstrated that the approach has some merits such as higher computing efficiency, feasibility to many kinds of geometries, lower predictive noise and independence to wavelet； 3. proposed a new subtraction algorithm. The new subtraction algorithm is not used to overcome nonorthogonality, but utilize the nonorthogonality's distribution in TX domain to estimate the true wavelet with filtering method. The method has excellent effectiveness in model testing. Improved 1D and 1.5D inverse scattering series algorithms can predict internal multiples. After filtering and subtracting among seismic traces in a window time, internal multiples can be attenuated in some degree. The proposed 1D and 1.5D algorithms have demonstrated that they are effective to the numerical and field data. In addition, the new subtraction algorithm is effective to the complex theoretic models.

地震波模拟：非规则网格离散的数值解法、吸收边界及其实际应用

This dissertation presents a series of irregular-grid based numerical technique for modeling seismic wave propagation in heterogeneous media. The study involves the generation of the irregular numerical mesh corresponding to the irregular grid scheme, the discretized version of motion equations under the unstructured mesh, and irregular-grid absorbing boundary conditions. The resulting numerical technique has been used in generating the synthetic data sets on the realistic complex geologic models that can examine the migration schemes. The motion equation discretization and modeling are based on Grid Method. The key idea is to use the integral equilibrium principle to replace the operator at each grid in Finite Difference scheme and variational formulation in Finite Element Method. The irregular grids of complex geologic model is generated by the Paving Method, which allow varying grid spacing according to meshing constraints. The grids have great quality at domain boundaries and contain equal quantities of nodes at interfaces, which avoids the interpolation of parameters and variables. The irregular grid absorbing boundary conditions is developed by extending the Perfectly Matched Layer method to the rotated local coordinates. The splitted PML equations of the first-order system is derived by using integral equilibrium principle. The proposed scheme can build PML boundary of arbitrary geometry in the computational domain, avoiding the special treatment at corners in a standard PML method and saving considerable memory and computation cost. The numerical implementation demonstrates the desired qualities of irregular grid based modeling technique. In particular, (1) smaller memory requirements and computational time are needed by changing the grid spacing according to local velocity; (2) Arbitrary surfaces and interface topographies are described accurately, thus removing the artificial reflection resulting from the stair approximation of the curved or dipping interfaces; (3) computational domain is significantly reduced by flexibly building the curved artificial boundaries using the irregular-grid absorbing boundary conditions. The proposed irregular grid approach is apply to reverse time migration as the extrapolation algorithm. It can discretize the smoothed velocity model by irregular grid of variable scale, which contributes to reduce the computation cost. The topography. It can also handle data set of arbitrary topography and no field correction is needed.

白水剖面黄土-红粘土化学风化的粒度效应

The loess-red clay deposit in the Loess Plateau, as large regions mixed in the dust depositional areas, may recorded the chemical weathering features and recycling of the detritus material of the earth’s surface from the wide range upwind of the Loess Plateau. And the loess-red clay sequence is rare information for recovering the continent's weathering history of Late Cenozoic, as it’s clear sense of age. The concentrations of elements in loess-red clay are largely affected by grain size. Therefore, we divided samples of a long loess-red clay section and six spacial sections into three fractions in order to counteracting the effect of particle size on the values of weathering proxies. First, the loess unit L1 and S1 of six sections located at Guyuan, Baishui, Changwu, Yongshou, Yangling and Lantian, Chinese Loess Plateau were sampled. These samples were divided into three fractions: <5μm, 5-20μm, 20-63μm, which were then analyzed for the primary elements using an X-ray fluorescence analyser. Results show that the effect of particle is much smaller on the fraction <5μm than other fractions. Therefore, the fraction <5μm can reflect the change of chemical weathering intensity much better. In addition, we divided Baishui section samples into three fractions, and analyzed them with X-ray fluorescence for primary elements. Results show that the value of CIA vary in different size fractions, indicating different weathering progress. Elements K, Na, Ca and Mg in the <5μm fraction have a sequence which is the reverse of Bowen Sequence. This may be a important sense for the change of source regions.

中学生的性别—理科刻板印象及其影响因素

Gender stereotype has a great effect on an individual’s cognition and behavior. Notably, stereotyped cognition about gender and science exerts an influence on an individual’s academic or career choice. In order to weaken the negative effect of gender-science stereotype and facilitate girls’ participation in science, this study examined the development of implicit gender-science stereotype and influence factors with implicit association test and questionnaires in a sample of secondary school students. The present work showed that: Firstly, there were no gender differences and gender predominance in performance of math and physics during secondary school years. However, girls tended to attribute success in math and physics to unstable factors, or the failure to stable factors. The reverse was true for boys’ attribution. This gender difference in attribution was especially evident in their study of physics. Secondly, 7th to 11th grade students implicitly regarded science as male domain, with the exception of 7th grade boys, who thought both boys and girls can study science well. On the whole, this gender-science stereotype was more and more evident as the specialization of science subjects’ progresses through secondary school, and this inclination decreased with increasing grade. Thirdly, the negative correlation between explicit and implicit stereotype which appeared in girls from 8th grade grew stronger with increasing grade and became significant in 10th grade. On the contrary, the significantly positive correlation existed in 7th -11th boys. Fourthly, the experience including attitude toward science, science interests and self –efficacy in math and physics had significantly negative effect on girls’ implicit gender-science stereotype, and significantly positive effect on boys’. It was showed that gender moderated the effect of experience in the study of science and implicit gender-science stereotype, and the attitude toward science mediated the relationship between science interests, self-efficacy and implicit gender-science stereotype. Fifthly, the perceived teacher’s class behaviours by students and the perceived parents’ gender stereotype by children had strong predictive power on students’ implicit gender-science stereotype. And the perceived teachers’ and parents’ performance expectancies can influence gender-science stereotype indirectly through self-efficacy in related subjects and attitude toward science. In conclusion, the present study showed that cognitive bias about gender and science existed in Chinese secondary school students. The information conveyed from teachers and parents interacting with students’ experience in the study of science affect the formation of stereotyped cognition.

Taxonomic Syntax for First-Order Inference

Most knowledge representation languages are based on classes and taxonomic relationships between classes. Taxonomic hierarchies without defaults or exceptions are semantically equivalent to a collection of formulas in first order predicate calculus. Although designers of knowledge representation languages often express an intuitive feeling that there must be some advantage to representing facts as taxonomic relationships rather than first order formulas, there are few, if any, technical results supporting this intuition. We attempt to remedy this situation by presenting a taxonomic syntax for first order predicate calculus and a series of theorems that support the claim that taxonomic syntax is superior to classical syntax.

Natural Language Syntax and First Order Preference

We have argued elsewhere that first order inference can be made more efficient by using non-standard syntax for first order logic. In this paper we show how a fragment of English syntax under Montague semantics provides the foundation of a new inference procedure. This procedure seems more effective than corresponding procedures based on either classical syntax of our previously proposed taxonomic syntax. This observation may provide a functional explanation for some of the syntactic structure of English.