基于广义Lippmann-Schwinger方程的地震波场模拟算法与应用

In the last several decades, due to the fast development of computer, numerical simulation has been an indispensable tool in scientific research. Numerical simulation methods which based on partial difference operators such as Finite Difference Method (FDM) and Finite Element Method (FEM) have been widely used. However, in the realm of seismology and seismic prospecting, one usually meets with geological models which have piece-wise heterogeneous structures as well as volume heterogeneities between layers, the continuity of displacement and stress across the irregular layers and seismic wave scattering induced by the perturbation of the volume usually bring in error when using conventional methods based on difference operators. The method discussed in this paper is based on elastic theory and integral theory. Seismic wave equation in the frequency domain is transformed into a generalized Lippmann-Schwinger equation, in which the seismic wavefield contributed by the background is expressed by the boundary integral equation and the scattering by the volume heterogeneities is considered. Boundary element-volume integral method based on this equation has advantages of Boundary Element Method (BEM), such as reducing one dimension of the model, explicit use the displacement and stress continuity across irregular interfaces, high precision, satisfying the boundary at infinite, etc. Also, this method could accurately simulate the seismic scattering by the volume heterogeneities. In this paper, the concrete Lippmann-Schwinger equation is specifically given according to the real geological models. Also, the complete coefficients of the non-smooth point for the integral equation are introduced. Because Boundary Element-Volume integral equation method uses fundamental solutions which are singular when the source point and the field are very close，both in the two dimensional and the three dimensional case, the treatment of the singular kernel affects the precision of this method. The method based on integral transform and integration by parts could treat the points on the boundary and inside the domain. It could transform the singular integral into an analytical one both in two dimensional and in three dimensional cases and thus it could eliminate the singularity. In order to analyze the elastic seismic wave scattering due to regional irregular topographies, the analytical solution for problems of this type is discussed and the analytical solution of P waves by multiple canyons is given. For the boundary reflection, the method used here is infinite boundary element absorbing boundary developed by a pervious researcher. The comparison between the analytical solutions and concrete numerical examples validate the efficiency of this method. We thoroughly discussed the sampling frequency in elastic wave simulation and find that, for a general case, three elements per wavelength is sufficient, however, when the problem is too complex, more elements per wavelength are necessary. Also, the seismic response in the frequency domain of the canyons with different types of random heterogeneities is illustrated. We analyzed the model of the random media, the horizontal and vertical correlation length, the standard deviation, and the dimensionless frequency how to affect the seismic wave amplification on the ground, and thus provide a basis for the choice of the parameter of random media during numerical simulation.

The Nonlinear Phenomena Of Thin Polydimethylsiloxane (Pdms) Films In Electrowetting

Electrowetting (EW) is an effective way to manipulate small volume liquid in micro- and nano-devices, for it can improve its wettability. Since the late 1990s, electrowetting-on-dielectric (EWOD) has been used widely in bio-MEMS, lab-on-a-chip, etc. Polydimethlsiloxane (PDMS) is extensively utilized as base materials in the fabrication of biomedical micro- and nano-devices. The properties of thin PDMS films used as dielectric layer in EW are studied in this paper. The experimental results show that the thin PDMS films exhibit good properties in EWOD. As to PDMS films with different thicknesses, a threshold voltage and a hysteresis were observed in the EIWOD experiments.

An Electrowetting Model For Rough Surfaces Under Low Voltage

Electrowetting is one of the most effective methods to enhance wettability. A significant change of contact angle for the liquid droplet can result from the surface microstructures and the external electric field, without altering the chemical composition of the system. During the electrowetting process on a rough surface, the droplet exhibits a sharp transition from the Cassie-Baxter to the Wenzel regime at a low critical voltage. In this paper, a theoretical model for electrowetting is put forth to describe the dynamic electrical control of the wetting behavior at the low voltage, considering the surface topography. The theoretical results are found to be in good agreement with the existing experimental results. (c) Koninklijke Brill NV, Leiden, 2008.

中能核反应中的统计发射过程及核温度参量

在过去的几年里，利用兰州重离子加速器（HIRFL）提供的束流，以及在OUVERTURE合作研究中，利用意大利国家核物理研究院南方实验室（INFN-LNS）超导回旋提供的束流，进行了多次中能区重离子核反应实验研究工作。如，最初的46.7MeV/u ~(12)C+~(58)Ni，~(115)In，~(197)Au的实验及30MeV/u ~(40)Ar+~(58)Ni，~(64)Ni~(115)In和30MeV/u Ni轰击Ni，Au，Al在MULTICS+MEDEA：4π装置上进行的实验工作。此外，本人还从事过一些理论研究工作，包括多粒子散射形式理论和相关数学物理问题研究，量子分子动力学和量子统计模型计算。本文是从事这些核物理研究工作的积累，主要侧重于实验结果的物理内容分析，而不强调实验技术，数据处理的技巧。主要的物理内容有以下几个方面：1.对于利用双同位素产额比提取同位素核温度的方法进行研究推广，使得对于实验中碰到的仅有部分能谱可以实现很好同位素分辩的情况，即使不能得到总的同位素产额，仅仅通过一段能区的同位素产额也可提取核温度。用于具体的实验研究工作中后，对于46.7MeV/u ~(12)C+~(58)Ni，~(115)In，~(197)Au核反应过程，同一体系利用这种方法得到的同位素核温度和利用粒子非稳态布居提取的核温度一致。2.围绕核反应过程中核温度的参量的提取，对于双同位素产额比与核温度的刻度关系进行了分析研究，通过计算考虑中等质量碎片（IMF）内部激发能后的内部配分函数表明，中等质量碎片的内部激发对刻度关系有重要影响。零阶近似下区域密度近似的结果和Gemini模拟计算的结果反映了相同的情况。3.研究核反应机制，多个粒子散射的形式理论的必需的，对于两体散射，其形式理论已经比较成熟，但是对于多个粒子散射问题出现的严重的困难是多体Lippmann-Schwinger方程无唯一收敛的解。作为一种探索性的研究工作，开展了多体散射理论研究工作，发展了一些具有普遍意义的数学物理方法。在本项研究工作中，通过能基础数学中的约当引理的推广，发现一个特例：对非连接图，Lippmann-Schwingwer方程存在收敛的解，因此多体散射形式理论，有可能重新建立。由于核力和多体问题是当今核物理研究的两大难点，世界各国的科学家都在努力以图攻克它们，而且多体问题还是物理学的其它许多领域的难题，因而多体散射还是引起诸多研究学科广泛兴趣的课题。通过发展一些新的数学理论和方法，我们已得到一些有意义的结果。4.将量子分子动力学这种中高能量区域所用的理论分析方法扩展至较低能区，通过对相空间中初始位置和动量抽样增加限制条件。如结合能和实验值要求一致，平均核势，核内Pauli阻塞更强一些，在演化中能量和动量守恒等等。得到一个很稳定的初始基态。均方半径保持不弥散的时间可达1600fm/c，用于研究10.6MeV/u Ne~(20)+Al~(27)的实验分析过程中。另外，量子统计模型（QSM）主要描述中心核-核碰撞，将它和碎裂模型结合，作一些改进后，可以对核-核碰撞进行统一描述。5.在中能核反应研究中发现，核反应过程中有大量的中子，轻带电粒子以及中等质量碎片发射出来，可以将这些粒子发射机制大致分为两大类。其中一类可以归结为动力学发射过程的产物。另一类则可以归于统计发射的产物。在低能核反应中，其发射能谱的斜率的负倒数，可作为复合核的核温度。而在中能重离子核反应中，其发射能谱变得很复杂，不再具有Maxwell分布。通常的三源拟合所给出的温度参数，已不能反映物理实质。提出多阶矩分析方法用于分析中能核反应中统计发射规律及受动力学过程的影响。

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Direct numerical test of the B-G-K model equation by the DSMC method

In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.

A lattice Boltzmann method for KDV equation

We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters of this scheme can be determined by analysing the energy dissipation.

Modified Simplified Rate Equation Model of Flowing Chemical Oxygen-Iodine Laser and its Application

A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.

A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations (CDEs) is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.

A lattice Boltzmann equation for waves

We propose a lattice Boltzmann model for the wave equation. Using a lattice Boltzmann equation and the Chapman-Enskog expansion, we get 1D and 2D wave equations with truncation error of order two. The numerical tests show the method can be used to simulate the wave motions.

Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

A Variational Approach to the Burridge-Knopoff Equation

A variational principle is obtained for the Burridge-Knopoff model for earthquake faults, and this paper considers an analytic approach that does not require linearization or perturbation.

Variational Approach to the Thomas-Fermi Equation

By the semi-inverse method, a variational principle is obtained for the Thomas-Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method.