On the use and abuse of Newton's second law for variable mass problems

We clarify some misunderstandings currently found in the literature that arise from improper application of Newton's second law to variable mass problems. In the particular case of isotropic mass loss, for example, several authors introduce a force that actually does not exist.Facultad de Ciencias Astronómicas y Geofisicas de la Universidad Nacional de La PlataOn a Fellowship from the Comisión de Investigaciones Cientificas de la Provincia de Buenos Aires.Member of the Carrera del Investigador Cientifico del Consejo Nacional de Investigaciones Cientificas y Técnicas de la República Argentina.     

On a question of A. Wintner about Jacobi coordinates in the three-body problem

In his work on the elimination of the nodes in the Three-Body Problem, Jacobi considered a certain straight line (defined below, in the Introduction) which lies always within the invariable plane. Here we settle the question of Wintner on the classification of all motions for which this line fails to exist.     

Non-Integrability of the Generalized Two Fixed Centres Problem

We consider two fixed centres attracting a third body. Each centre is the source of a force field with potential V=−ar ⁻²ⁿ , where n is a real number. We prove that this generalization of the classical two fixed centres problem is non-integrable except when n= 0, 1/2, −1 and −2. This revised version was published online in July 2006 with corrections to the Cover Date.     

Smooth inversion for ground surface temperature histories: estimating the optimum regularization parameter by generalized cross-validation

The inversion of recent borehole temperatures has proved to be a successful tool to determine ancient ground surface temperature histories. To take into account heterogeneity of thermal properties and their non-linear dependence on temperature itself, a versatile 1-D inversion technique based on a finite-difference approach has been developed. Regularization of the generally ill-posed problem is obtained by an appropriate version of Tikhonov regularization of variable order. In this approach, a regularization parameter has to be determined, representing a trade-off between data fit and model smoothness. We propose to select this parameter by generalized cross-validation. The resulting technique is employed in case studies from the Kola ultradeep drilling site, and another borehole from northeastern Poland. Comparing the results from both sites corroborates the hypothesis that subglacial ground surface temperatures as met in Kola often are much higher than the ones in areas exposed to atmospheric conditions (Poland).     

三门峡市区环境水文地质问题浅析

通过对三门峡市区地下水的综合调查,发现其环境水文地质问题以区域地下水位下降为主,并导致地下水污染等次生环境水文地质问题的发生.在环境水文地质问题形成背景和形成条件综合分析的基础上,认为其产生的根本原因是人为活动,尤其是地下水的不合理开采破坏了地下水循环系统的天然均衡状态.最后,提出了减少和防止三门峡市区环境水文地质问题的具体措施.     

简述瞬变电磁法(TEM)的研究现状、进展与问题

近年来,由于电子技术的快速发展、勘查市场的旺盛需求以及瞬变电磁法(TEM)的自身优点,使得TEM方法从仪器到方法技术均获长足进展。在此,简述了TEM仪器及方法技术的研究现状与进展,总结了TEM的应用领域,分析了TEM方法目前存在的主要问题,探讨了TEM急需解决的问题及发展方向。     

地震波散射研究回顾与展望

地震波散射是地球物理学中一个非常重要的研究领域,其进展对人们正确认识和了解地球深部的细节及物性具有重大意义,对地球动力学的研究也具有不可忽视的推动作用。这里从地震波散射的理论和方法研究二个方面,对地震波散射研究的进展作评述。首先回顾了地震波散射的基本概念、研究历程及研究的各个方面,对散射理论进行了系统评述,同时对先辈们关于散射波数值模拟的情况进行了总结。     

Biot固结有限元方程组的病态规律分析

针对Biot固结有限元方程组的病态问题，采用正交试验和量纲分析法探讨病态性的变化规律及其影响因素。主要考虑单元平均尺寸、时间步长、压缩性和渗透性等4个因素的影响。分别提出2组相互独立的相似准则，在此基础上得到2个新的无量纲量，并将其用于分析Biot固结有限元方程组系数矩阵的条件数的变化规律。结合算例进行参数分析结果表明，对病态程度的敏感性由大到小依次为单元平均尺寸、时间步长、压缩性和渗透性；单元平均尺寸太小会使病态加剧；随着2个无量纲量的增大，病态程度呈现单调增加的趋势。其结果为深化对Biot固结数值分析病态问题的认识提供有益参考。