Hammerstein型非线性积分方程解的存在性

该文采用化为积分方程组的方法 ,利用锥上不动点指数计算 ,在不要求非线性项 f (x,u)非负的情况下 ,证明 Hammerstein型非线性积分方程 φ(x) =∫Gκ(x,y) f (y,φ(y) ) dy非平凡解和多解存在性的一些新的结果。此结果可用来证明非线性常微分方程两点边值问题解的存在性。     

Comparison of methods to model the gravitational gradients from topographic data bases

A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1" elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical–vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods.     

Global height datum unification: a new approach in gravity potential space

The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential. The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector (from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of the offset of the zero point of the Iranian height datum from the geoid’s potential value W ₀=62636855.8 m²/s². According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid.     

SH Wave Propagation in Viscoelastic Media

When comparing solutions for the propagation of SH waves in plane parallel layered elastic and viscoelastic (anelastic) media, one of the first things that becomes apparent is that in the elastic case the location of the saddle points required to obtain a high frequency approximation are located on the real p axis. This is true of the branch points also. In a viscoelastic medium this is not typical. The saddle point corresponding to an arrival lies in the first quadrant of the complex p-plane as do the branch points. Additionally, in the elastic case the saddle point and branch points lie on a straight line drawn through the origin (the positive real axis in the complex p-plane), while in the viscoelastic case this is generally not the case and the saddle point and branch points lie in such a manner as to indicate the degree of their complex values.In this paper simple SH reflected and transmitted particle displacement arrivals due to a point torque source at the surface in a viscoelastic medium composed of a layer over a half space will be considered. The path of steepest descent defining the saddle point in the first quadrant will be parameterized in terms of a real variable and the high frequency solutions and intermediate analytic results obtained will be used to formulate more specific constraints and observations regarding saddle point location relative to branch point locations in the complex p-plane.As saddle point determination for an arrival is, in general, the solution of a non-linear equation in two unknowns (the real and imaginary parts of the complex saddle point p ₀), which must be solved numerically, the use of analytical methods for investigating this problem type is somewhat limited.Numerical experimentation using well documented solution methods, such as Newton's method, was undertaken and some observations were made. Although fairly basic, they did provide for the design of algorithms for the computation of synthetic traces that displayed more efficient convergence and accuracy than those previously employed. This was the primary motivation for this work and the results from the SH problem may be used with minimal modifications to address the more complicated subject of coupled P-SV wave propagation in viscoelastic media.Another reason for revisiting a problem that has received some attention in the literature was to approach it in a fairly comprehensive manner so that a number of specific observations may be made regarding the location of the saddle point in the complex p-plane and to incorporate these into computer software. These have been found to result in more efficient algorithms for the SH wave propagation and a significant enhancement of the comparable software in the P-SV problem.     

盾构隧道抗震分析的整体强制反应位移法适用性研究

整体强制反应位移法采用土-结构相互作用模型,将地震作用下的土层位移以强制位移的方式施加到整个土层上,从而计算结构在地震作用下的响应。本文以天津某地铁盾构隧道为例,采用整体强制反应位移法进行地铁盾构隧道结构的抗震分析计算。为了验证该方法在复杂软土场地下盾构隧道结构抗震分析中的适用性,以时程分析法为基准,对比分析整体强制反应位移法、反应位移法和时程分析法3种方法计算出的盾构隧道结构内力图和内力峰值。研究表明,整体强制反应位移法具有较好的适用性及易操作性,具有较高的计算精度,是一种方便有效的抗震设计拟静力方法。     

基于GTP的地下工程与围岩一体化真三维空间构模

针对地下工程开挖体的基本特征及其真三维建模要求，在广义三棱柱(GTP)模型的基础上进行扩展，提出采用E—GTP模型来构建地下工程开挖体的真三维模型。通过与其围岩地质体的G—GTP模型的耦合，实现了基于GTP的工程开挖体与围岩地质体的一体化建模。该模型将地下三维空间实体抽象为点、线、面、体四类对象，通过结点、TIN边、侧边、TIN面、侧面和GTP体元共6个基本几何元素进行统一表达。该文重点讨论了E—GTP的建模原理与方法，并介绍了基于面向对象思想的一体化空间数据结构。     

Design of controlled elastic and inelastic structures

One of the founders of structural control theory and its application in civil engineering,Professor Emeritus Tsu T.Soong,envisioned the development of the integral design of structures protected by active control devices.Most of his disciples and colleagues continuously attempted to develop procedures to achieve such integral control.In his recent papers published jointly with some of the authors of this paper,Professor Soong developed design procedures for the entire structure using a design-redesign proce...     

Tensionless–frictionless interaction of flexible annular foundation with a transversely isotropic multi‐layered half‐space

A transversely isotropic multi‐layered half‐space, with axis of material symmetry perpendicular to the free surface, supports a flexible either annular or solid circle foundation. The contact area of the foundation and the half‐space is considered to be both frictionless and tensionless. The foundation is assumed to be affected by a vertical static axisymmetric load. Detailed analysis of the interaction of these two systems with different thickness of layers is the target of this paper. With the use of ring load Green's functions for both the foundation and the continuum half‐space, an integral equation accompanied with some inequalities is introduced to model the complex BVP. With the incorporation of ring‐shape FEM, we are capable of capturing both regular and singular solution smoothly. The validity of the combination of the analytical and numerical method is proved with comparing the results of this paper with a number of benchmark cases of both linear and nonlinear interaction of circular and annular foundation with half‐space. Some new illustrations are presented to portray the aspect of the anisotropy and layering of the half‐space. Copyright © 2014 John Wiley & Sons, Ltd.     

一种裸露土壤湿度反演方法

针对目前土壤湿度反演方法研究较少且缺少实时性的现状,该文提出一种土壤湿度反演方法——最小二乘支持向量机技术。以积分方程模型为正向算法,数值模拟不同雷达参数(频率、入射角及极化)下后向散射系数随土壤含水量和地表粗糙度的变化情况。经过数据敏感性分析,选取C-波段和X-波段、小入射角下的同极化后向散射系数作为支持向量回归的训练样本信息;经过适当的训练,利用支持向量回归技术对土壤含水量进行了反演研究;并考虑通过多频率、多极化、多入射角数据的组合,消除地表粗糙度的影响,提高反演精度。模拟结果表明,该方法反演土壤湿度具有较高的精度和较好的实时性;同时,与人工神经网络方法的结果比较,证明了该方法的有效性,为土壤湿度的反演研究提供了一种方法。     

河套盆地北缘色尔滕山河流地貌参数特征及其成因分析

地貌形态是构造和地表过程相互作用的复杂产物,主要通过构造活动和岩石的抗侵蚀能力等来调节。构造活动相对较弱的古老造山带往往可以忽略构造驱动的岩石抬升,使得研究岩石抗侵蚀能力对其地貌雕刻的贡献成为可能。但是目前大多数活动造山带地貌研究的结果显示地貌主要受控于活动构造,关于岩性对地貌演化影响的报道较少。色尔滕山山前断裂为河套盆地北缘的一条重要控盆断裂,全新世以来该断裂的活动性较强,曾发生过两次较大震级地震（M6. 4和M5. 9）。前人活动构造研究表明该断裂的活动性具有空间差异,中部乌加河镇活动性最强,两端逐渐减弱。但相对河套盆地北缘其他大型断裂（如狼山山前断裂、乌拉山北缘断裂和大青山山前断裂）,该断裂的地貌参数研究较少。同时其地貌演化特征及发育机理仍然不清楚,这些均制约了对该断裂的变形动力学理解。本文基于30 m分辨率的DEM数据对该断裂进行详细的河流地貌学参数研究,包括使用Arcgis和Matlab脚本提取色尔滕山山前33条河流的子流域盆地面积 高程积分（HI）和相应河道陡峭指数（Ksn）、河道纵剖面及其裂点等地貌学参数。结果表明研究区河流HI值大部分处于0. 40~0. 66之间,其中乌加河镇附近具有高值,流域盆地处于发育的壮年期。瞬态河道和稳态河道均沿着色尔滕山山前断裂走向分布,可能表明色尔滕山山前大部分河道目前处于瞬时地貌向均衡地貌演化阶段,并且通过对比发现瞬态河道裂点成因存在岩性和构造共同控制的现象。河道陡峭指数空间分布差异性较大,乌加河镇附近（S13~S20）陡峭指数较大,向两边陡峭指数逐渐减小,在S8河流以西又有增大的趋势。通过结合岩性和降雨情况分析发现,河道陡峭指数除了受岩性抗侵蚀能力影响外,其分布还与色尔滕山山前断裂垂直滑移速率分布和垂直位错分布基本一致。综合来看,地貌参数的空间分布是岩性差异和色尔滕山山前断裂活动分段差异性共同控制的结果,表明该地区岩性和构造对地貌的协同塑造作用。