DEM提取谷地线的有效汇水量阈值范围

基于地表径流的自然特性从DEM提取谷地线,使用的一个关键参量是汇水量阈值,目前该阈值的选择具有很大的主观性和随机性,没有一个定量的确定模型。从谷地系统自身的相似性特征出发,研究了多尺度条件下汇水量阈值与谷地线平均分叉比的关系,基于自相似性和平均分叉比趋近常数的原理确定了有效的汇水量阈值区间。     

平面应变状态下土体的软化特性与本构模拟

在平面应变状态下,由于土体在应力峰值状态出现了应变局部化现象,从而变形模式失去了原有的均匀性而呈现软化特性。为此,采用常规的弹塑性本构模型模拟土体峰值前的均匀变形,对应力峰值状态则采用非共轴的分叉理论进行预测,而土样在峰值后出现不均匀变形的宏观力学特性则通过复合体理论加以描述。理论预测表明,构建这样的软化本构模型能真实反映平面应变状态下的应力-应变特性。理论分析还表明,经典的变形分叉理论中引入非共轴弹塑性模型,才能准确地预测土体的应力峰值,这是构建平面应变状态下土体软化本构模型的关键所在。     

关于固体地球系统与地质作用的三点认识

文中讨论了作为极复杂巨系统的固体地球内部运动规律的 3条推论 :(1)地球系统在偏离平衡态时 ,有选择能量耗散最小方式的“惯性” ,在系统内禀熵急增时或者回到一种准稳定的定态 ,或者通过自组织迅速减少内禀熵增加率。换言之 ,地球系统可能有种尽量保存自身内能不受大量耗散的惯性 ,使其总体内禀熵产生率对时空的积分取极小值。我们把这一认识称为总体熵产生率取极小准则 ,对于孤立与渐变的地质过程 ,它等同于热力学第二定律与普里高津最小熵产生原理 ,对于极复杂地球巨系统及远离平衡态情况加了“总体”两字 ,意思是在局部或短期突变时熵产生率可能是大的 ,但它对全球与长时间的积分而言仍然取极小。换句话说 ,作为一个巨系统 ,固体地球在其局部远离平衡状态时 ,仍然能保持总体上内能消耗取极小的惯性 ,维持对全部固体地球时空系统总体熵产生率取极小准则。 (2 )关于地质作用过程演化的定态遍历准则。地球系统的复杂性不仅表现在其非线性 ,即同时存在着多种可能的定态作为其演化的趋势 ,而且表现在其时空发展过程中将经历尽可能多的定态。非线性非平衡态动力学的一般规律符合大多数包含激变事件的地质作用过程。将来在地球系统偏离平衡态足够远时 ,它可能会具有无穷多个耗散结构 ,因而使系统进入完全?     

Numerical modelling of bifurcation and localisation in cohesive-frictional materials

Methods are reviewed for analysing highly localised failure and bifurcation modes in discretised mechanical systems as typically arise in numerical simulations of failure in soils, rocks, metals and concrete. By the example of a plane-strain biaxial test it is shown that strain softening and lack of normality in elasto-plastic constitutive equations and the ensuing loss of ellipticity of the governing field equations cause a pathological mesh dependence of numerical solutions for such problems, thus rendering the results effectively meaningless. The need for introduction of higher-order continuum models is emphasised to remedy this shortcoming of the conventional approach. For one such a continuum model, namely the unconstrained Cosserat continuum, it is demonstrated that meaningful and convergent solutions (in the sense that a finite width of the localisation zone is computed upon mesh refinement) can be obtained.     

Dziobek’s configurations in restricted problems and bifurcation

We consider some questions on central configurations of five bodies in space. In the first one, we get a general result of symmetry for the restricted problem of n+1 bodies in dimension n-1. After that, we made the calculation of all c.c. for n=4. In our second result, we extend a theorem of symmetry due to [Albouy, A. and Libre, I.: 2002, Contemporary Math. 292, 1-16] on non-convex central configurations with 4 unit masses and an infinite central mass. We obtain similar results in the case of a big, but finite central mass. Finally, we continue the study by [Schmidt, D.S.: 1988, Contemporary Math. 81 ] of the bifurcations of the configuration with four unit masses located at the vertices of a equilateral tetrahedron and a variable mass at the barycenter. Using Liapunov-Schmidt reduction and a result on bifurcation equations, which appear in [Golubitsley, M., Stewart, L. and Schaeffer, D.: 1988, Singularties and Groups in Bifurcation Theory, Vol. II, Springer-Verlag, New York], we show that there exist indeed seven families of central configurations close to a regular tetrahedron parameterized by the value of central mass.     

Bifurcation of central configuration in the 2N+1 body problem

The bifurcation of central configuration in the Newtonian N-body problem for any odd number N ≥ 7 is shown. We study a special case where 2n particles of mass m on the vertices of two different coplanar and concentric regular n-gons (rosette configuration) and an additional particle of mass m₀ at the center are governed by the gravitational law he 2n+1 body problem. This system is of two degrees of freedom and permits only one mass parameter μ =m ₀/m. This parameter μ controls the bifurcation. If n≥ 3, namely any odd N ≥ 7, then the number of central configurations is three when μ ≥ μ _c , and one when μ ≥ μ _c . By combining the results of the preceding studies and our main theorem, explicit examples of bifurcating central configuration are obtained for N ≤ 13, for any odd N ∈ [15,943], and for any N ≥ 945.     

Travelling wave convection in a rotating layer

Abstract

Small amplitude two-dimensional Boussinesq convection in a plane layer with stress-free boundaries rotating uniformly about the vertical is studied. A horizontally unbounded layer is modelled by periodic boundary conditions. When the centrifugal force is balanced by an appropriate pressure gradient the resulting equations are translation invariant, and overstable convection can take the form of travelling waves. In the Prandtl number regime 0.53 < [sgrave] < 0.68 such solutions are preferred over the more usual standing waves. For [sgrave] < 0.53, travelling waves are stable provided the Taylor number is sufficiently large.     

海洋生态系统非线性动力学研究

海洋生态经济系统非线性动力学模型的建立及分析,对我国海洋生态经济发展乃至社会经济的发展都具有重要意义.建立了新的海洋生态经济系统动力学模型,研究了模型的稳定性和分岔现象,揭示了该系统的非线性动力学特性.     

Post-sedimentary Transformation of Lateral Moraines——the Tributary Tongue Basins of the Kvíárjokull（Iceland）

The Kvíárjokull,a southern outlet glacier of the Vatnajokull,is confined in the mountain foreland by lateral moraines measuring a height of up to 150 m. Each of the lateral moraines shows considerable breaches with deviations of the main moraine ridges. The paper discusses the possible origins of these modifications of the lateral moraines as result of： 1） ice overlappings during glacier advances and subsequent breaches of the lateral moraine,2） bifurcations of the Kvíárjokull glacier tongue triggered by the preglacial relief conditions and the prehistorical moraine landscape leading to afflux conditions,3） drainage of ice-marginal glacier lakes and 4. volcanic activities,such as lava flows and volcanic-induced jokulhlaups. A historic-genetic model of the formation of the lateral moraines is presented considering the breaches in the lateral moraines as result from glacier bifurcations and therefore as former tributary tongue basins. Such breaches in the lateral moraines are also common landscape features at glaciers outside of Iceland and are from wider importance for the paleoreconstruction of former glacier stages. The knowledge of their development is essential for an adequate relative age classification of individual moraine ridges. In regard to the origin of the debris supply areas of the large-sized Kvíárjokull moraines,the resedimentation of prehistoric till deposits by younger glacier advances plays a role in the formation of the lateral moraines apart from englacial and supraglacial sediment transfer processes.     

地球自转日长变化(LOD)和大气角动量(AAM)所对应的动力系统

利用一个多分维的分形地应的一维映射可以用子波变换反演出来,对地自转日长（ＬＯＤ）资料和大气角动量（ＡＡＭ）资料进行子波变换说明,在２０年尺度上、周年尺度和２－３２年尺度上,ＬＯＤ和ＡＡＭ的突变时间基本一致,所反演出的不同层次上分岔时间的分段映射动力系统也极其相似。