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1.
The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies. 相似文献
2.
Haje Korth Brian J. Anderson James A. Slavin Sean C. Solomon 《Planetary and Space Science》2004,52(8):733-746
The MESSENGER mission to Mercury, to be launched in 2004, will provide an opportunity to characterize Mercury's internal magnetic field during an orbital phase lasting one Earth year. To test the ability to determine the planetary dipole and higher-order moments from measurements by the spacecraft's fluxgate magnetometer, we simulate the observations along the spacecraft trajectory and recover the internal field characteristics from the simulated observations. The magnetic field inside Mercury's magnetosphere is assumed to consist of an intrinsic multipole component and an external contribution due to magnetospheric current systems described by a modified Tsyganenko 96 model. Under the axis-centered-dipole approximation without correction for the external field the moment strength is overestimated by ∼4% for a simulated dipole moment of , and the error depends strongly on the magnitude of the simulated moment, rising as the moment decreases. Correcting for the external field contributions can reduce the error in the dipole term to a lower limit of ∼1-2% without a solar wind monitor. Dipole and quadrupole terms, although highly correlated, are then distinguishable at the level equivalent to an error in the position of an offset dipole of a few tens of kilometers. Knowledge of the external magnetic field is therefore the primary limiting factor in extracting reliable knowledge of the structure of Mercury's magnetic field from the MESSENGER observations. 相似文献
3.
各向异性双相介质中多极源声波测井理论研究 总被引：4，自引：0，他引：4
将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场 相似文献
4.
When standard boundary element methods (BEM) are used in order to solve the linearized vector Molodensky problem we are confronted with
two problems: (1) the absence of O(|x|−2) terms in the decay condition is not taken into account, since the single-layer ansatz, which is commonly used as representation
of the disturbing potential, is of the order O(|x|−1) as x→∞. This implies that the standard theory of Galerkin BEM is not applicable since the injectivity of the integral operator
fails; (2) the N×N stiffness matrix is dense, with N typically of the order 105. Without fast algorithms, which provide suitable approximations to the stiffness matrix by a sparse one with O(N(logN)
s
), s≥0, non-zero elements, high-resolution global gravity field recovery is not feasible. Solutions to both problems are proposed.
(1) A proper variational formulation taking the decay condition into account is based on some closed subspace of co-dimension
3 of the space of square integrable functions on the boundary surface. Instead of imposing the constraints directly on the
boundary element trial space, they are incorporated into a variational formulation by penalization with a Lagrange multiplier.
The conforming discretization yields an augmented linear system of equations of dimension N+3×N+3. The penalty term guarantees the well-posedness of the problem, and gives precise information about the incompatibility
of the data. (2) Since the upper left submatrix of dimension N×N of the augmented system is the stiffness matrix of the standard BEM, the approach allows all techniques to be used to generate
sparse approximations to the stiffness matrix, such as wavelets, fast multipole methods, panel clustering etc., without any
modification. A combination of panel clustering and fast multipole method is used in order to solve the augmented linear system
of equations in O(N) operations. The method is based on an approximation of the kernel function of the integral operator by a degenerate kernel
in the far field, which is provided by a multipole expansion of the kernel function. Numerical experiments show that the fast
algorithm is superior to the standard BEM algorithm in terms of CPU time by about three orders of magnitude for N=65 538 unknowns. Similar holds for the storage requirements. About 30 iterations are necessary in order to solve the linear
system of equations using the generalized minimum residual method (GMRES). The number of iterations is almost independent
of the number of unknowns, which indicates good conditioning of the system matrix.
Received: 16 October 1999 / Accepted: 28 February 2001 相似文献
5.
R. Bianchi A. Forni F. Cámara R. Oberti H. Ohashi 《Physics and Chemistry of Minerals》2007,34(8):519-527
The synthetic LiGaSi2O6 clinopyroxene is monoclinic C2/c at room-T. Its experimental electron density, ρ(r), has been derived starting from accurate room-T single-crystal diffraction data. Topological analysis confirms an intermediate ionic-covalent character for Si–O bonding,
as found by previous electron-density studies on other silicates such as diopside, coesite and stishovite. The non-bridging
Si–O bonds have more covalent character than the bridging ones. The Ga–O bonds have different bonding characters, the Ga–O2
bond being more covalent than the two Ga–O1 bonds. Li–O bonds are classified as pure closed-shell ionic interactions. Similar
to spodumene (LiAlSi2O6), Li has sixfold coordination, but the bond critical points associated to the two longest bonds are characterized by very
low electron density values. Similar to what previously found in spodumene and diopside, O···O interactions were detected
from the topological analysis of ρ(r), and indicate a cooperative interaction among the lone pairs of neighbouring oxygen atoms. In particular, this kind of interaction
has been obtained for the O1···O1 edge shared between two Ga octahedra. Integration over the atomic basins gives net charges
of −1.39(10), 2.82(10), 1.91(10) and 0.82(8) e for O (averaged), Si, Ga and Li atoms, respectively. Periodic Hartree–Fock
and DFT calculations confirm the results obtained by multipole refinement of the experimental data. Moreover, the theoretical
topological properties of the electron density distribution on the Si2O6 group are very similar to those calculated for spodumene.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
6.
各向异性介质地层中多极源声波测井的现状与发展 总被引：5，自引：1，他引：4
多级源声波测井最初是针对直接横波速度测井这一目的而被提出并发展起来的。然而在实际情况中,多极源声波测井的意义除主要集中在横波测量（特别是在软地层时）以上外,更为重要的意义是对井孔周围地层的各向异性作出可能的分析和判断。因此,各向异性介质地层中多极源声波侧井的研究已越来越被人们关注和重视,近年来已取得了很大的进展。本文在消化、吸收大量文献的基础上,对各向异性多极源声波侧井的发展进行了回顾和分析,对具 相似文献
7.
By extending the work of Linton (Linton, C.M., 1991. Radiation and diffraction of waver waves by a submerged sphere in finite depth. Ocean Engineering 18 (1/2), 61–74), the problem of radiation of water waves by a submerged pulsating sphere in finite depth is formulated using the multipole method. As in Linton (1991), this leads to an infinite system of linear equations, which are easily solved numerically. Simple expressions are derived for the hydrodynamic characteristics of such a body. Results showing the effect of varying both the immersion depth and the water depth on the hydrodynamic coefficients of the pulsating sphere are given. The paper resumes the work presented in Lopes (Lopes, D.B.S., 1999. On the study of the Archimedes wave swing device for wave energy utilization (in Portuguese). MSc on the Management and Modelling of the Marine Environment, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa.). 相似文献
8.
利用反射声场探测井外地质构造的声波远探测方法已逐渐成为石油测井的一门重要应用技术.在远探测测井中声源常采用单极、偶极和四极等.为了考察各种声学辐射器的辐射性能,本文从辐射声场和井孔声场的能流密度出发,提出了一种利用辐射器向井外辐射的能量与沿井筒传播的能量比的大小来评价其辐射效率的方法,考察了不同声源激发的沿井传播的导波能流、地层辐射波能流及声源辐射效率随频率的变化规律.计算结果表明:不同声源的辐射效率和优势激发频段各不相同.单极声源在低频下的辐射效率很低,因为此时声源激发的能量几乎全部被斯通利波带走,相比之下,偶极声源在低频时的辐射效率远大于单极声源.本文的结果说明了偶极声源作为低频远探测声源要优于单极声源. 相似文献
9.
各向异性双相介质中多极源声波测井理论研究 总被引：1，自引：0，他引：1
将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场 相似文献
10.
This study examines the Bragg reflection of water waves by multiple submerged semi-circular breakwaters. The multipole expansions combined with the shift of polar coordinates are used to develop full linear potential solutions of the problem. In the full solutions, the obliquely and normally incident waves are independently considered. Experimental tests are carried out to measure the reflection and transmission coefficients of the breakwaters at different wave periods and body spacings. The analytical results are in reasonable agreement with the experimental data. The peak reflection coefficient of multiple submerged semi-circular breakwaters and the bandwidth of Bragg reflection are carefully examined by numerical examples. Some significant results for practical application are discussed. 相似文献