Propagation of Rayleigh waves on cylindrical surfaces of transversely isotropic material and of varying density in a magnetic field

Summary Three dimensional magneto-elastic equations pertaining to the problem of propagation of axial Rayleigh waves on the surface of elastic cylinder of isotropic material have been solved. Two cases have been considered — first, when the density varies linearly and second, when it varies inversely as the radius vector and frequency equations for both the cases have been obtained.     

三维地震勘探数据的剩余静校正方法研究与软件实现

剩余静校正的目的是消除地震道中由近地表因素造成的静态剩余时差的影响,通常以时差的四因子分解模型为基础建立剩余静校正方程组,并采用迭代求解方法获得剩余静校正量。但实际上,由于地层的倾斜,时差中还应包含横向和纵向倾角项,因此本文首先对剩余校正的理论模型进行了改进,提出了以扩展面元为计算单元的时差分解六因子模型。又由于地层的走向具有局部线性性,因此剩余动校正项,横向及纵向倾角项系数仅在一些给定的面元上计     

Three-dimensional analysis of gravity anomalies of sedimentary basins by polygonal prismatic model with a quadratic density function

The decrease of density contrast in sedimentary strata may be approximated by a quadratic function. A sedimentary basin may be considered as a number of horizontal polygonal prisms of finite thickness placed one over the other. Equations for the gravity anomaly of ann-sided polygon prism have been derived using a quadratic density function. A method has been developed for inversion of the gravity anomalies using a polygonal prismatic model. An analytical method has been employed for evaluating the necessary derivatives as the computing time by this method is much slower than by a numerical method. Approximate equations have been derived for rapid calculation of the anomalies and derivatives. Efficient computer programs have been developed for calculation of the anomalies and derivatives by an appropriate use of the exact and approximate equations. The depths to the polygon prisms constituting the basin are iteratively adjusted by minimizing the sum of the squares of the differences between the observed and calculated anomalies. These methods have been applied to analyze the Bouguer anomaly map of the Los Angeles basin, California.     

On the propagation of magneto-elastic waves

Summary The electromagnetic equations of Maxwell, equations of elasticity have been used to solve the problem of propagation of waves for a one-dimensional magneto-elastic problem. The frequency equation has also been set forth.     

Compressibility coefficients and Moelwyn-Hughes parameters of solids under pressure

Expanding energy as a function of volume in a Taylor series and taking the Padé approximant, different equations of state have been obtained, which are first tested with Born-Mayer and logarithmic model solids. These equations of state are applied to compute pressure, compressibility and the Moelwyn-Hughes parameter as functions of volume for NaCl, AgCl and CsCl crystals. The results agree fairly well with the observed data.     

Elastic radiation from buried sources in a semi-infinite heterogeneous medium

Summary The wave equations of elasticity in the presence of body forces for a semi-infinite, isotropic, heterogeneous medium with exponentially varying material properties have been solved. Using double Fourier transform the equations are first transformed to linear second order differential equations. From the solution of these equations the displacements are obtained by the use of inversion theorem for double Fourier transform. The method followed resolves the disturbance into its constitutive parts—incident and reflectedP, SV andSH type waves. Surface displacements due to a single couple, double couple and various other sources have been calculated.     

Analytical solution of specific energy and specific force equations: Trapezoidal and triangular channels

The specific energy and specific force equations have many applications in open-channel flow problems. At present, these equations have analytical solution only for rectangular channels. Trial and error procedure also graphical solutions are the existing methods of solving these equations. No analytical solutions are available in the technical literature for these equations in trapezoidal and triangular channels because it is presumed that these equations are quintic equations. The inversion of such equations consists of finding the roots of quintic equations. In the current study for a given channel geometry and discharge, the subcritical (supercritical) depth is analytically found in terms of the other supercritical (subcritical) depth. For this purpose, by considering physically meaningful domains, a quintic equation has been reduced to a quartic equation. In the next step, this quartic equation has been converted to a resolvent cubic equation and two quadratic equations. This research shows these steps clearly to reach an acceptable physical analytic solution for water depth in trapezoidal and triangular channels.     

Modelling rocking response via equivalent viscous damping

The assessment of the out-of-plane response of masonry structures has been largely investigated in literature assuming that walls respond as rigid or semi-rigid bodies, and relevant equations of motion of single-degree-of-freedom and multi-degree of freedom systems have been proposed. Therein, energy dissipation has been usually modelled resorting to the classical hypotheses of impulsive dynamics, delivering a velocity-reduction coefficient of restitution applied at impact. In fewer works, a velocity-proportional damping force has been introduced, by means of a viscous coefficient being constant or variable. A review of such models is presented, a criterion for equivalence of dissipated energy is proposed, equations predicting equivalent viscous damping ratios are derived and compared with experimental responses. Finally, predictive equations are examined in terms of incremental dynamic analyses for large sets of natural ground motions.     

On disturbances in a viscoelastic (three-parameter type) medium acted upon by a magnetic field

Summary In this note, the problem of disturbances has been investigated in two perfectly (electrically) conductive media-an ideal liquid and a viscoelastic solid of three-parameter type-acted upon by a magnetic field. The electromagnetic equations of Maxwell and the equations of mechanical motion together with the stress-strain relation of the viscoelastic material of three-parameter type have been used to work out the problem. The results exhibit the predominance of transient behaviour in the displacements as well as in the stresses.     

Effect of surface stress on magneto-elastic surface waves in finitely conducting media

This paper deals with the investigation of the effect of surface stress and conductivity on the propagation of surface wave in isotropic, homogeneous, elastic media under the action of a primary magnetic field. Formulation of the general surface wave propagation problem has been made, and the corresponding frequency equation has been derived. Frequency equations for Rayleigh wave, surface shear wave and Stoneley wave have been deduced from that of general surface wave as special cases. The effects of surface stress and magnetic field on the wave velocities and attenuation factors of Rayleigh wave and surface shear wave are shown by numerical calculations and graphs. Some important wave velocity equations, as obtained by other authors, have been deduced as special cases from the wave velocity equation for Stoneley wave. It is found that the combined effect of surface stress and magnetic field modulates the wave velocity ratios and attenuation factors of Rayleigh wave and surface shear wave to a considerable extent.     

Refinement of predictive reaeration equations for a typical Indian river

Dissolved oxygen mass balance has been computed for different reaches of River Kali in western Uttar Pradesh (India) to obtain the reaeration coefficient (K₂). A total of 270 field data sets have been collected during the period from March 1999 to February 2000. Eleven most popular predictive equations, used for reaeration prediction and utilizing mean stream velocity, bed slope, flow depth, friction velocity and Froude number, have been tested for their applicability in the River Kali using data generated during field survey. The K₂ values computed from these predictive equations have been compared with the K₂ values observed from dissolved oxygen balance measurements in the field. The performance of predictive equations have been evaluated using error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and correlation statistics. The equations developed by Smoot and by Cadwallader and McDonnell showed comparatively better results. Moreover, a refined predictive equation has been developed using a least‐squares algorithm for the River Kali that minimizes error estimates and improves correlation between observed and computed reaeration coefficients. Copyright © 2001 John Wiley & Sons, Ltd.     

构造热演化的数值模拟方法

对模拟构造热演化的二维和三维非稳态热传导-平流微分方程的数值求解进行了研究.在空间和时间上分别应用有限单元法和差分法进行离散化处理;推导了非稳态热传导-平流有限元方程.在求解技术上发展了“迎风”权函数方法,将有限元法、有限差分法和“迎风”权函数法结合起来,使用变网格、变结点方法对地质体的运动介质、运动边界、多热源的非线性、非稳态的构造热演化进行了模拟.并对各种热源体的处理、初始条件和边界条件的处理进行了分析.     

Thermodynamics and constitutive theory for multiphase porous-media flow considering internal geometric constraints

This paper provides the thermodynamic approach and constitutive theory for closure of the conservation equations for multiphase flow in porous media. The starting point for the analysis is the balance equations of mass, momentum, and energy for two fluid phases, a solid phase, the interfaces between the phases and the common lines where interfaces meet. These equations have been derived at the macroscale, a scale on the order of tens of pore diameters. Additionally, the entropy inequality for the multiphase system at this scale is utilized. The internal energy at the macroscale is postulated to depend thermodynamically on the extensive properties of the system. This energy is then decomposed to provide energy forms for each of the system components. To obtain constitutive information from the entropy inequality, information about the mechanical behavior of the internal geometric structure of the phase distributions must be known. This information is obtained from averaging theorems, thermodynamic analysis, and from linearization of the entropy inequality at near equilibrium conditions. The final forms of the equations developed show that capillary pressure is a function of interphase area per unit volume as well as saturation. The standard equations used to model multiphase flow are found to be very restricted forms of the general equations, and the assumptions that are needed for these equations to hold are identified.     

MHD evolutionary processes in the Earth’s model magnetic resonator

Specific features of the spatial-temporal dynamics of LF disturbances of the Earth’s magnetosphere have been analyzed by the method of numerical simulation of magnetic hydrodynamic equations taking into account plasma temperature variations. The effects related to the appearance of long-living magnetospheric jumps of density and temperature, MHD wave scattering on such inhomogeneities, Alfvén wave reflection from the near-Earth region, and magnetospheric plasma heating as a result of dissipative processes at a repeated propagation of MHD waves between magnetically conjugate regions have been considered. The problems of conformity of the discrete mathematical model with continuous equations of magnetic hydrodynamics are discussed.     

A supplementary approach for estimating reaeration rate coefficients

Different commonly used predictive equations for the reaeration rate coefficient (K₂) have been evaluated using 231 data sets obtained from the literature and 576 data sets measured at different reaches of the River Kali in western Uttar Pradesh, India. The data sets include stream/channel velocity, bed slope, flow depth, cross‐sectional area and reaeration rate coefficient (K₂), obtained from the literature and generated during the field survey of River Kali, and were used to test the applicability of the predictive equations. The K₂ values computed from the predictive equations have been compared with the corresponding K₂ values measured in streams/channels. The performance of the predictive equations has been evaluated using different error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and coefficient of determination (r²). The results show that the reaeration rate equation developed by Parkhurst and Pomeroy yielded the best agreement, with the values of SE, NME, MME and r² as 33·387, 4·62, 3·58 and 0·95, respectively, for literature data sets (case 1) and 37·567, 3·57, 2·6 and 0·95, respectively, for all the data sets (literature data sets and River Kali data sets) (case 2). Further, to minimize error estimates and improve correlation between measured and computed reaeration rate coefficients, supplementary predictive equations have been developed based on Froude number criteria and a least‐squares algorithm. The supplementary predictive equations have been verified using different error estimates and by comparing measured and computed reaeration rate coefficients for data sets not used in the development of the equations. Copyright © 2003 John Wiley & Sons, Ltd.     

RESERVOIR CAPACITY DEPLETION ON ACCOUNT OF SEDIMENTATION

l 1NTRODUCTIONAs the sediment cAned by the river gets dePositOd in the reservoir, there is a pro gressive reduction in itscaPacity to hold water. For examPle the Zuni reservoir on river Zuni, a tributary of the little ColoradO atBlack rock, New Mexico, U.S.A., lost aboat 75% caPacity in just 20 years. Sindlary, just in l0 years theIchari reservoir on river Tons, a tribUtary of river Yamuna (Inda), reduced to about l5% of its originalcaPacity. Thus, at the planning stage, one must …     

利用三维非均匀不稳定渗流场的数值解求解垂直井与水平井的联合开采

用差分的方法给出了三维非均匀不稳定渗流方程的离散方程组，将配斯曼（Peaceman）方程拓展成能够被用于同时求解垂直井与水平井联合开采问题的形式，利用迭代解法求解差分方程和配斯曼方程所组成的方程组，并以实际层状不均匀介质为例计算了其压强的空间分布。     

地震活动盛衰呼应关系及其逻辑组合集成预报

本文研究包括:1)以中国陆壳 Ms7强震为例,引用二值逻辑变量,讨论了地震活动盛衰呼应关系.结果表明,这类呼应关系历史拟合率不高,不是理想呼应关系;2)为了综合利用不理想呼应关系,把它改造成为理想呼应关系,使之适用于预报,作者提出应用逻辑代数函数方法,进行逻辑组合集成预报,并使用25个预报因子,具体组建一个预报中国陆壳 Ms7强震年度危险性的逻辑代数函数方程.该方程历史拟合率高,外推检验效果良好.本文最后还就逻辑代数函数方法对地震学应用的前景作了必要的讨论.      

Propagation of a spherical magnetogasdynamic shock in a self gravitating system

Summary This paper considers a spherical shock, in a conducting gas, produced on account of explosion into an inhomogeneous self gravitating system. Similarity principles have been used to reduce the equations governing the flow to ordinary differential equations under the assumption that the density varies as an inverse-power of distance from the explosion centre.     

Magneto-elastic plane waves in a cosserat medium

Summary The propagation of plane waves in an electrically conducting cosserat medium placed in a magnetic field is investigated. The constitutive equations of cosserat elasticity developed recently byParia have been combined with the field equations of electromagnetism to obtain the basic equations for the problem. The results obtained in this investigation are in agreement with the corresponding results on magneto-elastic plane waves in Hookean solids when the cosserat constants are supposed to be absent.