风海流方程低谱模式多态解问题（二）

本文用四系数的低阶谱模式研究了一个可移动风应力强迫作用下的海流方程多态解的问题。定常解的分布特征及其稳定性对风应力强迫的移动速度有很强的依赖性并且在ε较小时有同时存在三组解的情况。对方程各项大小的计算表明，当风应力强迫主要用来平衡摩擦项或β项时，解是稳定的；其他情况下解一般不稳定。另外，本文还从能量关系讨论了解的稳定性，表明当海洋响应的能量主要集中在低阶谱上时，解一般是稳定的，这时能量平衡关系主要表现为风应力强迫项与摩擦项的平衡。     

声波方程逆散射反演的近似方法

我们在文献[1]里研究了介质参考波速沿某个方向线性变化时的三维声散射理论,导出了声波方程逆散射反演问题解的解析表达式.考虑到应用时的实际条件,本文根据上述反演方法导出2.5维模型的声波方程逆散射反演的波速扰动计算公式,给出该方法在“高频”近似条件下的波速扰动反演计算公式,从而使我们提出的“参考波速线性变化时的声波方程逆散射反演”理论更接近实际应用条件.本文给出的这些反演公式仍然具有原方法的优点,即不但可以使Born近似的假定在大多数情况下能得以满足,而且可以利用快速Fourier变换来快速实现介质波速扰动的反演成象.     

Heat capacities of aqueous solutions of sodium hydroxide and water ionization up to 300 °C at 10 MPa

A commercial (Setaram C80) calorimeter has been modified to measure the heat capacities of highly caustic solutions at temperatures up to 300 °C and pressures up to 20 MPa. The improvements have allowed more accurate determination of the isobaric volumetric heat capacities of chemically aggressive liquids at high temperatures. Test measurements with aqueous solutions of sodium chloride showed a reproducibility of about ±0.1%, with an accuracy of ∼0.3% or better, over the whole temperature range. Heat capacities of aqueous solutions of sodium hydroxide at concentrations from 0.5 to 8 mol/kg were measured at temperatures from 50 to 300 °C and a pressure of 10 MPa. Apparent molar isobaric heat capacities of NaOH(aq) were calculated using densities determined previously for the same solutions by vibrating-tube densimetry. Standard state (infinite dilution) partial molar isobaric heat capacities of NaOH(aq) were obtained by extrapolation using an extended Redlich-Meyer equation. Values of the standard heat capacity change for the ionization of water up to 300 °C were derived by combining the present results with the literature data for HCl(aq) and NaCl(aq).     

How far have management practices come in ‘working with the river’?

The philosophy of ‘working with nature’ and ‘working with the river’ is increasingly embedded in global management practice. However, what does this mean? Has real progress been made in operationalizing what is known, how scientists and practitioners work and how rivers are conceptualized as integral parts of landscapes, culture and society? The first sections of this commentary outline what this philosophy means to us (the authors) and briefly summarize the evolution of associated concepts and principles in recent decades. In the final section, we comment on what we believe needs to be done to ‘work with the river’ in practice. We are communicating to both river scientists and practitioners as a collective when we ask: Will we be brave enough to hold the course in the face of many global challenges, be ready to respond when called upon, and commit to creation of diverse, inclusive and open access communities of practice in geoethical programmes that ‘work with the river’?     

New Periodic Solution for Planar 8-body Problems

For planar Newtonian 8-body problems with equal masses, we prove the existence of the new non-collision periodic solution such that two pair bodies move clockwise and the other two pairs counter-clockwise. This revised version was published online in July 2006 with corrections to the Cover Date.     

Transient solution for a plane‐strain fracture driven by a shear‐thinning,power‐law fluid

This paper analyses the problem of a fluid‐driven fracture propagating in an impermeable, linear elastic rock with finite toughness. The fracture is driven by injection of an incompressible viscous fluid with power‐law rheology. The relation between the fracture opening and the internal fluid pressure and the fracture propagation in mobile equilibrium are described by equations of linear elastic fracture mechanics (LEFM), and the flow of fluid inside the fracture is governed by the lubrication theory. It is shown that for shear‐thinning fracturing fluids, the fracture propagation regime evolves in time from the toughness‐ to the viscosity‐dominated regime. In the former, dissipation in the viscous fluid flow is negligible compared to the dissipation in extending the fracture in the rock, and in the later, the opposite holds. Corresponding self‐similar asymptotic solutions are given by the zero‐viscosity and zero‐toughness (J. Numer. Anal. Meth. Geomech. 2002; 26 :579–604) solutions, respectively. A transient solution in terms of the crack length, the fracture opening, and the net fluid pressure, which describes the fracture evolution from the early‐time (toughness‐dominated) to the large‐time (viscosity‐dominated) asymptote is presented and some of the implications for the practical range of parameters are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Lateral stress caused by horizontal and vertical surcharge strip loads on a cross‐anisotropic backfill

This study derives analytical solutions for estimating the lateral stress caused by horizontal and vertical surcharge strip loads resting on a cross‐anisotropic backfill. The following loading types are employed in this work: point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load and downward nonlinear‐varying strip load. The cross‐anisotropic planes are assumed to be parallel to the horizontal surface of the backfill. The solutions proposed herein have never been mentioned in previous literature, but can be derived by integrating the point load solution in a Cartesian co‐ordinate system for a cross‐anisotropic medium. The calculations by the presented solutions are quick and accurate since they are concise and systematized. Additionally, the proposed calculations demonstrate that the type and degree of material anisotropy and the horizontal/vertical loading types decisively influence the lateral stress. This investigation presents examples of the proposed horizontal and vertical strip loads acting on the surface of the isotropic and cross‐anisotropic backfills to elucidate their effects on the stress. The analytical results reveal that the stress distributions accounting for soil anisotropy and loading types are quite different from those computed from the available isotropic solutions. Restated, the derived solutions, as well as realistically simulating the actual surcharge loading circumstances, provide a good reference for the design of retaining structures for the backfill materials are cross‐anisotropic. Copyright © 2005 John Wiley & Sons, Ltd.     

New Periodic Solutions for 3-Body Problems

For Newtonian 3-body problems in ℝ², we prove the existence of new symmetric noncollision periodic solutions with some fixed winding numbers and masses.     

LCR-G型重力仪仪器参数的时变特征

采用区域适定法对LCR－G型重力仪的仪器参数进行适时标定。对标定结果的分析表明：（1）区域适定法标定结果与基线标定结果精度相当；（2）重力仪的线性项参数呈现随时间的趋势性下降和非线性。采用区域适定解校正后的线性项参数处理区域重力网的观测资料，不仅能有效地削弱系统误差，而且可提高重力仪检测地震信息的能力。     

区间系统与区间优化模型——理论与应用

区间系统与区间优化模型是一种应用广泛的描述不确定性问题的数学模型.本文综述区间系统与区间优化模型在理论与应用方面的研究进展.特别地,本文将介绍区间线性系统的解和可解性问题、区间线性优化模型的最优解和最优性问题以及区间二次优化模型的最优解和最优性问题,最后简单概述它们的各种应用实例.