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Elastic wave propagation in inhomogeneous anisotropic media

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Acta Seismologica Sinica(English Edition) 1998年第6期11卷 3-15页

作者： XIU CHENG WEI 1) MIN YU DONG 1) YUN YAI CHEN 2) 1) geoscience department, university of petroleum, beijing 102200, china 2) Institute of Geophysics, china Seismological Bureau, beijing 100081, china 1. geoscience department University of Petroleum 102200 Beijing China 2. Institute of Geophysics China Seismological Bureau 100081 Beijing China

Plane wave decomposition is a convenient and effective method in the study of wave field. Various complex wave fields can be obtained by using plane wave composition. In this paper, the method of plane wave is used to study elastic wave propagation in inhomogeneous and anisotropic media. The f k transformation is applied to time space domain wave equation in inhomogeneous anisotropic media. As a result, the frequency wave number domain wave equation (Christoffel equation) can be obtained. Using the relation between elastic parameters or its spatial derivatives and Christoffel matrix elements, a method for solving the Christoffel matrix in inhomogeneous anisotropic media is formulated and applied to inhomogeneous TIV as well as inhomogeneous EDA media. The results obtained show that directional derivative of wave amplitude in continuum is negative, so amplitude is reduced, when propagating direction directs to velocity increasing direction; and directional derivative of wave amplitude is positive that means amplitude enhanced when propagating direction directs to velocity decreasing direction. Thus, wave amplitude depends on propagation direction (even in isotropic medium), but does not always attenuate. The conclusion that in continuum wave amplitude attenuates does not apply to all propagation direction.

关键词： inhomogeneous anisotropy continuum Christoffel equation

Neuroimaging studies of self-reflection

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Progress in Natural Science:Materials International 2004年第4期14卷 10-16页

作者： ZHU Ying(department of Psychology, Peking university, beijing 100871, china) Dept. of Psychology Peking Univ. Beijing 100871 China

This paper reviews some basic findings and methodological issues in neuroimaging studies of self-referential processing. As a general rule, making judgments about one’s self, inclusive of personality trait adjectives or current mental states (person’ s preferences, norms, aesthetic values and feeling) uniformly generates medial prefrontal activations, regardless of stimulus materials (words or pictures) and modality (visual or auditory). Cingulate activations are also observed in association with most self-referential processing. Methodological issues include treating self-referential processing as either representing one’s own personality traits or representing one’s own current mental states. Finally, self-referential processing could be considered as implement of "I think therefore I am" approach to neuroimaging the self.

关键词： self self-referential processing medial prefrontal cortex cingulate brain image.

The Laplacian spectral radii of unicyclic and bicyclic graphs with n vertices and k pendant vertices

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Science china Mathematics 2010年第8期53卷 2135-2142页

作者： GUO JiMing department of Applied Mathematics,china university of petroleum,Dongying 257061,china department of Applied Mathematics China University of Petroleum Dongying China

In this paper,we determine graphs with the largest Laplacian spectral radius among the unicyclic and the bicyclic graphs on n vertices with k pendant vertices,respectively.

关键词： Laplacian matrix Laplacian spectral radius unicyclic graph bicyclic graph

An equality on Hochschild homology groups

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Chinese Science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. department of Mathematics, university of Science and Technology of china, Hefei 230026, china 2. department of Mathematics, beijing Normal university, beijing 100875, china department of Mathematics University of Science and Technology of China Hefei China department of Mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

Estimates for eigenvalues of Laplacian operator with any order

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Science china Mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2 1 department of Mathematics,beijing Jiaotong university,beijing 100044,china 2 department of Mathematics,Henan Normal university,Xinxiang 453007,china department of Mathematics Beijing Jiaotong University Beijing China department of Mathematics Henan Normal University Xinxiang China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G25

Equivalent construction of the infinitesimal time translation operator in algebraic dynamics algorithm for partial differential evolution equation

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Science china(Physics,Mechanics & Astronomy) 2010年第8期53卷 1475-1480页

作者： LIU ChengShi department of Mathematics, Northeast petroleum university, Daqing 163318, china department of Mathematics Northeast Petroleum University Daqing China

We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.

关键词： algebraic dynamics infinitesimal time translation operator partial differential evolution equation

The refined theory of deep rectangular beams for symmetrical deformation

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Science china(Physics,Mechanics & Astronomy) 2009年第6期52卷 919-925页

作者： GAO Yang1 & WANG MinZhong2 1 College of Science, china Agricultural university, beijing 100083, china 2 State Key Laboratory for Turbulence and Complex Systems and department of Mechanics and Aerospace Engineering, Peking university, beijing 100871, china College of Science China Agricultural University Beijing China State Key Laboratory for Turbulence and Complex Systems and department of Mechanics and Aerospace Engineering Peking University Beijing China

Based on elasticity theory, various one-dimensional equations for symmetrical deformation have been deduced systematically and directly from the two-dimensional theory of deep rectangular beams by using the Papkovich-Neuber solution and the Lur'e method without ad hoc assumptions, and they construct the refined theory of beams for symmetrical deformation. It is shown that the displacements and stresses of the beam can be represented by the transverse normal strain and displacement of the mid-plane. In the case of homogeneous boundary conditions, the exact solutions for the beam are derived, and the exact equations consist of two governing differential equations: the second-order equation and the transcendental equation. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the beam under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively, and the correctness of the stress assumptions in classic extension or compression problems is revised. Meanwhile, as an example, explicit expressions of analytical solutions are obtained for beams subjected to an exponentially distributed load along the length of beams.

关键词： deep rectangular beams the refined theory symmetrical deformation the Papkovich-Neuber solution the Lur’e method

Study on the two and three-parameter working stability regions of 3Y-TZP suspension

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Science china(Technological Sciences) 2006年第5期49卷 547-568页

作者： CHEN Youqiang1, 2, ZHANG Xinni3, CHEN Sha’ou3 & QI Ping3 1. department of Chemistry, Qingdao university, Qingdao 266071, china 2. department of Chemistry, Tsinghua university, beijing 100084, china 3. department of Physics, Qingdao university, Qingdao 266071, china department of Chemistry Qingdao University Qingdao China department of Chemistry Tsinghua University Beijing China department of Physics Qingdao University Qingdao China

We determined the variation tendency of viscosity (η) at various solids load- ing (α) for 3Y-TZP suspension as a function of dispersant concentration (Cw) using vis- cosity measurement, measured the diameter of particles as a function of Cw in very dilute suspension using light scattering method, and obtained the surface features of the sedi- ment of suspension with different Cw using SEM. We also discussed the influence of the microstructure of adsorbed polymer layers on particles and their interactions in the dis- persing medium on the stability of suspension. Then two different stable states and two different unstable states for 3Y-TZP suspension were given. Accordingly, the (Cw, η), (Cw, α), and (α, η) two-parameter, and (Cw, α, η) three-parameter stability maps were con- structed. Based on the DLVO theory calculations, the dispersant concentration, particle distance (r), and interparticle potential energy (VT) maps with various solids loading for 3Y-TZP aqueous suspension were also constructed. In (Cw, r) two-parameter coordinate system, the stable motion region map for particles was established. The Cw, α, and VT,max (the highest potential energy) surface of the potential barrier map was obtained through calculation and simulation on the basis of the surfaces of Cw, r, VT maps introduced above. The (Cw, α) two-parameter stability map was then obtained from the Cw, α, VT,max map. The results showed that this theoretical map can qualitatively prove the experimentally obtained results—the existence of different dispersed states of particles in suspension system and the variation tendency of suspension stability with changing each parame- ter—were reasonable.

关键词： 3Y-TZP, suspension, stability, DLVO theory, interparticle potential energy.

Physical simulation of fluid flow and production performance in extra-low permeability porous media

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petroleum Science 2009年第4期6卷 415-420页

作者： You Yuan Yue Xiang’an Li Mingyi Zhao Chunpeng Zhang Tao Key Laboratory of petroleum Engineering Ministry of EducationChina University of PetroleumBeijing 102249China Enhanced Oil Recovery Research Center China University of PetroleumBeijing 102249China Jilin Oil Field PetroChinaSongyuanJilin 138000China Exploration&Production Research Institute SinopecBeijing 100083China Exploration department Changqing Oil FieldPetroChinaXi’anShaanxi 710018China

For extra-low permeability reservoirs, with a permeability of about 0.3×10?3 μm2, fluid flow and production performance in cores were studied. A long core holder with a multi-location piezometric measurement was specially designed. An artificial long core, about 700 mm long and with a cross section of 45mm×45mm, was used. In the experiment, pressure distribution along the core can be measured in real time. Single phase flow in the core was investigated. Different modes of production in long cores were also simulated including natural depletion, water flooding, and advanced water flooding. Through physical simulation, flow parameters were collected and production characteristics in extra-low permeability cores were studied. From experimental results, it can be seen that fluid flow in extra-low permeability cores is different from that in high permeability cores. Transmission of pressure in extra-low permeability cores is very slow, and it needs a long time for the pressure to become stable. The distribution curve of pressure along the core is nonlinear and the production rate in extra-low permeability reservoirs decreases sharply. The development effects of different production modes in extra-low permeability cores were compared with one another. Among the production modes, advanced water flooding has much potential for effective development of extra-low permeability reservoirs. Natural depletion and conventional water flooding can also be used in early production periods. In addition, the countermeasures and some ideas especially for the potential development of extra-low permeability reservoirs are suggested.

关键词： Extra-low permeability reservoirs physical simulation fluid flow production performance