High-order asymptotic field of tensile plane-strain nonlinear crack problems

In this paper, the governing equations and the analytical method of the secondorder asymptotic field for the plane-straln crack problems of mode I have been presented. The numerical calculation has been carried out. The amplitude coefficients k2 of the second term of the asymptotic field have been determined after comparing the present results with some fine results of the finite element calculation. The variation of coefficients k2 with changes of specimen geometry and developments of plastic zone have been analysed. It is shown that the second term of the asymptotic field has significant influence on the near-crack-tip field. Therefore, we may reasonably argue that both the J-integral and the coefficient k2 can beeome two characterizing parameters for crack initiation.

solving global unconstrained optimization problems by symmetry-breaking

IEEE Computer Society; International Association for; Computer and Information Science, ACIS

基于量子蒙特卡罗的地震波反演方法

The primary approaches for people to understand the inner properties of the earth and the distribution of the mineral resources are mainly coming from surface geology survey and geophysical/geochemical data inversion and interpretation. The purpose of seismic inversion is to extract information of the subsurface stratum geometrical structures and the distribution of material properties from seismic wave which is used for resource prospecting, exploitation and the study for inner structure of the earth and its dynamic process. Although the study of seismic parameter inversion has achieved a lot since 1950s, some problems are still persisting when applying in real data due to their nonlinearity and ill-posedness. Most inversion methods we use to invert geophysical parameters are based on iterative inversion which depends largely on the initial model and constraint conditions. It would be difficult to obtain a believable result when taking into consideration different factors such as environmental and equipment noise that exist in seismic wave excitation, propagation and acquisition. The seismic inversion based on real data is a typical nonlinear problem, which means most of their objective functions are multi-minimum. It makes them formidable to be solved using commonly used methods such as general-linearization and quasi-linearization inversion because of local convergence. Global nonlinear search methods which do not rely heavily on the initial model seem more promising, but the amount of computation required for real data process is unacceptable. In order to solve those problems mentioned above, this paper addresses a kind of global nonlinear inversion method which brings Quantum Monte Carlo (QMC) method into geophysical inverse problems. QMC has been used as an effective numerical method to study quantum many-body system which is often governed by Schrödinger equation. This method can be categorized into zero temperature method and finite temperature method. This paper is subdivided into four parts. In the first one, we briefly review the theory of QMC method and find out the connections with geophysical nonlinear inversion, and then give the flow chart of the algorithm. In the second part, we apply four QMC inverse methods in 1D wave equation impedance inversion and generally compare their results with convergence rate and accuracy. The feasibility, stability, and anti-noise capacity of the algorithms are also discussed within this chapter. Numerical results demonstrate that it is possible to solve geophysical nonlinear inversion and other nonlinear optimization problems by means of QMC method. They are also showing that Green’s function Monte Carlo (GFMC) and diffusion Monte Carlo (DMC) are more applicable than Path Integral Monte Carlo (PIMC) and Variational Monte Carlo (VMC) in real data. The third part provides the parallel version of serial QMC algorithms which are applied in a 2D acoustic velocity inversion and real seismic data processing and further discusses these algorithms’ globality and anti-noise capacity. The inverted results show the robustness of these algorithms which make them feasible to be used in 2D inversion and real data processing. The parallel inversion algorithms in this chapter are also applicable in other optimization. Finally, some useful conclusions are obtained in the last section. The analysis and comparison of the results indicate that it is successful to bring QMC into geophysical inversion. QMC is a kind of nonlinear inversion method which guarantees stability, efficiency and anti-noise. The most appealing property is that it does not rely heavily on the initial model and can be suited to nonlinear and multi-minimum geophysical inverse problems. This method can also be used in other filed regarding nonlinear optimization.

Triangle Evolution-A Hybrid Heuristic for Global Optimization

Abstract This paper presents a hybrid heuristic{triangle evolution (TE) for global optimization. It is a real coded evolutionary algorithm. As in di®erential evolution (DE), TE targets each individual in current population and attempts to replace it by a new better individual. However, the way of generating new individuals is di®erent. TE generates new individuals in a Nelder- Mead way, while the simplices used in TE is 1 or 2 dimensional. The proposed algorithm is very easy to use and e±cient for global optimization problems with continuous variables. Moreover, it requires only one (explicit) control parameter. Numerical results show that the new algorithm is comparable with DE for low dimensional problems but it outperforms DE for high dimensional problems.

Optimization and comparison of single- and dual-pump fiber-optical parametric amplifiers with dispersion fluctuations

Solutions for fiber-optical parametric amplifiers (FOPAs) with dispersion fluctuations are derived using matrix operators. On the basis of the propagation matrix product and the hybrid genetic algorithm, we have optimized and compared single- and dual-pump FOPAs with zero-dispersion-wavelength variations. The simulations prove that the design of FOPAs involves multimodal function optimization problems. The numerical results show that dual-pump FOPAs are highly sensitive to dispersion fluctuations whereas dispersion variations have less impact on the gain of single-pump FOPAs. To increase signal gain and reduce ripple, dual-pump FOPAs, instead of single-pump FOPAs, have to be carefully optimized with a suitable multisegment fiber structure rather than a one-segment fiber structure. The different combinations of multisegment fibers can provide highly different gain properties. The increase in gain is at the cost of the ripple.

粘弹性介质中的地震波传播与波形反演研究

The real earth is far away from an ideal elastic ball. The movement of structures or fluid and scattering of thin-layer would inevitably affect seismic wave propagation, which is demonstrated mainly as energy nongeometrical attenuation. Today, most of theoretical researches and applications take the assumption that all media studied are fully elastic. Ignoring the viscoelastic property would, in some circumstances, lead to amplitude and phase distortion, which will indirectly affect extraction of traveltime and waveform we use in imaging and inversion. In order to investigate the response of seismic wave propagation and improve the imaging and inversion quality in complex media, we need not only consider into attenuation of the real media but also implement it by means of efficient numerical methods and imaging techniques. As for numerical modeling, most widely used methods, such as finite difference, finite element and pseudospectral algorithms, have difficulty in dealing with problem of simultaneously improving accuracy and efficiency in computation. To partially overcome this difficulty, this paper devises a matrix differentiator method and an optimal convolutional differentiator method based on staggered-grid Fourier pseudospectral differentiation, and a staggered-grid optimal Shannon singular kernel convolutional differentiator by function distribution theory, which then are used to study seismic wave propagation in viscoelastic media. Results through comparisons and accuracy analysis demonstrate that optimal convolutional differentiator methods can solve well the incompatibility between accuracy and efficiency, and are almost twice more accurate than the same-length finite difference. They can efficiently reduce dispersion and provide high-precision waveform data. On the basis of frequency-domain wavefield modeling, we discuss how to directly solve linear equations and point out that when compared to the time-domain methods, frequency-domain methods would be more convenient to handle the multi-source problem and be much easier to incorporate medium attenuation. We also prove the equivalence of the time- and frequency-domain methods by using numerical tests when assumptions with non-relaxation modulus and quality factor are made, and analyze the reason that causes waveform difference. In frequency-domain waveform inversion, experiments have been conducted with transmission, crosshole and reflection data. By using the relation between media scales and characteristic frequencies, we analyze the capacity of the frequency-domain sequential inversion method in anti-noising and dealing with non-uniqueness of nonlinear optimization. In crosshole experiments, we find the main sources of inversion error and figure out how incorrect quality factor would affect inverted results. When dealing with surface reflection data, several frequencies have been chosen with optimal frequency selection strategy, with which we use to carry out sequential and simultaneous inversions to verify how important low frequency data are to the inverted results and the functionality of simultaneous inversion in anti-noising. Finally, I come with some conclusions about the whole work I have done in this dissertation and discuss detailly the existing and would-be problems in it. I also point out the possible directions and theories we should go and deepen, which, to some extent, would provide a helpful reference to researchers who are interested in seismic wave propagation and imaging in complex media.

求解非线性反问题的大范围收敛梯度正则化算法

基于同伦映射的思想,改进了求解非线性反问题的梯度正则化算法.通过路径跟踪有效地拓宽了梯度正则化算法求解的收敛范围.对于正则化参数的修正,通过引入拟Sigmoid函数,提出了一种下降速率可调的连续化参数修正方法,在保证迭代稳定的条件下,得到较好的计算效率,同时保证该算法具有很好的抵抗观测噪声能力.实际算例表明,该方法收敛范围宽,计算效率高,在存在较强观测噪声的条件下也能得到很好的反演结果.

Optimal design of a 7 T highly homogeneous superconducting magnet for a Penning trap

A Penning trap system called Lanzhou Penning Trap (LPT) is now being developed for precise mass measurements at the Institute of Modern Physics (IMP). One of the key components is a 7 T actively shielded superconducting magnet with a clear warm bore of 156 mm. The required field homogeneity is 3 x 10(-7) over two 1 cubic centimeter volumes lying 220 mm apart along the magnet axis. We introduce a two-step method which combines linear programming and a nonlinear optimization algorithm for designing the multi-section superconducting magnet. This method is fast and flexible for handling arbitrary shaped homogeneous volumes and coils. With the help of this method an optimal design for the LPT superconducting magnet has been obtained.

贪心遗传算法求解组合优化问题

许多问题最终可以归结为求解一个组合优化问题,GA是求解组合优化问题的一个强有力的工具,但遗传算法在应用中常出现收敛过慢和封闭竞争问题,本文提出贪心遗传算法。该算法的初始种群建立、交叉和变异等过程,都引入贪心选择策略指导搜索;移民操作向种群引进新的遗传物质,克服了封闭竞争缺点。贪心遗传算法可以避免早熟收敛并改进算法的性能,算法搜索起步阶段的效率是非常高的,本文通过TSP问题仿真试验证明了算法的有效性,在较少的计算量下,得到令人满意的结果。

Design and optimization of highly nonlinear low-dispersion crystal fiber with high birefringence for four-wave mixing

We have proposed a novel type of photonic crystal fiber (PCF) with low dispersion and high nonlinearity for four-wave mixing. This type of fiber is composed of a solid silica core and a cladding with a squeezed hexagonal lattice elliptical airhole along the fiber length. Its dispersion and nonlinearity coefficient are investigated simultaneously by using the full vectorial finite element method. Numerical results show that the proposed highly nonlinear low-dispersion fiber has a total dispersion as low as +/- 2.5 ps nm(-1) km(-1) over an ultrabroad wavelength range from 1.43 to 1.8 mu m, and the corresponding nonlinearity coefficient and birefringence are about 150 W-1 km(-1) and 2.5 x 10(-3) at 1.55 mu m, respectively. The proposed PCF with low ultraflattened dispersion, high nonlinearity, and high birefringence can have important application in four-wave mixing. (C) 2010 Optical Society of America

Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.

Some advances in study of crack identification problems

In the present paper, the crack identification problems are investigated. This kind of problems belong to the scope of inverse problems and are usually ill-posed on their solutions. The paper includes two parts: (1) Based on the dynamic BIEM and the optimization method and using the measured dynamic information on outer boundary, the identification of crack in a finite domain is investigated and a method for choosing the high sensitive frequency region is proposed successfully to improve the precision. (2) Based on 3-D static BIEM and hypersingular integral equation theory, the penny crack identification in a finite body is reduced to an optimization problem. The investigation gives us some initial understanding on the 3-D inverse problems.

Optimization Of Off-Null Ellipsometry For Air/Solid Interfaces

The optimization of off-null ellipsometry is described with emphasis on the improvement of sample thickness sensitivity. Optimal conditions are dependent on azimuth angle settings of the polarizer, compensator, and analyzer in a polarizer-compensator-sample-analyzer ellipsometer arrangement. Numerical simulation utilized offers an approach to present the dependence of the sensitivity on the azimuth angle settings, from which optimal settings corresponding to the best sensitivity are derived. For a series of samples of SiO2 layer (thickness in the range of 1.8-6.5 nm) on silicon substrate, the theory analysis proves that sensitivity at the optimal settings is increased 20 times compared to that at null settings used in most works, and the relationship between intensity and thickness is simplified as a linear type instead of the original nonlinear type, with the relative error reduced to similar to 1/100 at the optimal settings. Furthermore the discussion has been extended toward other factors affecting the sensitivity of the practical system, such as the linear dynamic range of the detector, the signal-to-noise ratio and the intensity from the light source, etc. Experimental results from the investigation Of SiO2 layer on silicon substrate are chosen to verify the optimization. (c) 2007 Optical Society of America.