Stiffness pathologies in discrete granular systems: Bifurcation,neutral equilibrium,and instability in the presence of kinematic constraints

The paper develops the stiffness relationship between the movements and forces among a system of discrete interacting grains. The approach is similar to that used in structural analysis, but the stiffness matrix of granular material is inherently nonsymmetric because of the geometrics of particle interactions and of the frictional behavior of the contacts. Internal geometric constraints are imposed by the particles' shapes, in particular, by the surface curvatures of the particles at their points of contact. Moreover, the stiffness relationship is incrementally nonlinear, and even small assemblies require the analysis of multiple stiffness branches, with each branch region being a pointed convex cone in displacement space. These aspects of the particle-level stiffness relationship give rise to three types of microscale failure: neutral equilibrium, bifurcation and path instability, and instability of equilibrium. These three pathologies are defined in the context of four types of displacement constraints, which can be readily analyzed with certain generalized inverses. That is, instability and nonuniqueness are investigated in the presence of kinematic constraints. Bifurcation paths can be either stable or unstable, as determined with the Hill–Bažant–Petryk criterion. Examples of simple granular systems of three, 16, and 64 disks are analyzed. With each system, multiple contacts were assumed to be at the friction limit. Even with these small systems, microscale failure is expressed in many different forms, with some systems having hundreds of microscale failure modes. The examples suggest that microscale failure is pervasive within granular materials, with particle arrangements being in a nearly continual state of instability.     

Shift in the bifurcation points of rotating magnetized newtonian polytropes caused by a magnetic field

Criteria are formulated for determining the critical points and bifurcation points of rotating, magnetized, newtonian polytropes, which coincide in the absence of a magnetic field. The magnitude of the shift in these points is estimated in terms of the flatness parameter e and rotation speed ε. The dependence of the total energy of a polytrope near the bifurcation and critical points is calculated as a function of the asymmetry parameters X for the distribution of mass relative to the axis of rotation and of the rotation speed ε for ε ≪ 1. The stability of the rotating polytrope with respect to the parameter X is analyzed. __________ Translated from Astrofizika, Vol. 51, No. 2, pp. 321–327 (May 2008).     

Network concepts to describe channel importance and change in multichannel systems: test results for the Jamuna River,Bangladesh

Most of the largest rivers on Earth have multiple active channels connected at bifurcations and confluences. At present a method to describe a channel network pattern and changes in the network beyond the simplistic braiding index is unavailable. Our objectives are to test a network approach to understand the character, stability and evolution of a multi‐channel river pattern under natural discharge conditions. We developed a semi‐automatic method to derive a chain‐like directional network from images that represent the multi‐channel river and to connect individual network elements through time. The Jamuna River was taken as an example with a series of Landsat TM and ETM+ images taken at irregular intervals between 1999 and 2004. We quantified the overall importance of individual channels in the entire network using a centrality property. Centrality showed that three reaches can be distinguished along the Jamuna with a different network character: the middle reach has dominantly one important channel, while upstream and downstream there are about two important channels. Temporally, relatively few channels changed dramatically in both low‐flow and high‐flow periods despite the increase of braiding index during a flood. Based on the centrality we calculated a weighted braiding index that represents the number of important channels in the network, which is about two in the Jamuna River and which is larger immediately after floods. We conclude that the network measure centrality provides a novel characterization of river channel networks, highlighting properties and tendencies that have morphological significance. Copyright © 2013 John Wiley & Sons, Ltd.     

Earthquake prediction: Is it a practicable scientific perspective or a challenge to science?

It is shown that the main problem in earthquake prediction consists not in separating a useful signal on an imminent strong earthquake from noise but in determining the character of the signal itself. The signal, due to the fractal and roughly discontinuous nature of the geological medium, is not an isolated precursor anomaly but always presents a host of varied-rank wavelets that are not distinctly recognizable and, in addition, are fluctuating in their amplitudes and duration. Bifurcation and the extreme dependence of the behavior of nonlinear geological system upon initial and continuously variable current conditions explain the inevitable unreliability of predicting the most mature earthquake sources.     

The Lagrange and Two-Center Problems in the Lobachevsky Space

The generalization of the two-center problem and the Lagrange problem (a mass point motion under the action of attracting center field and the analog of a constant homogeneous field) to the case of a constant curvature space, in the three-dimensional space of Lobachevsky (³), is investigated in this paper. The integrability of these problems is proved. The bifurcation set in the plane of integrals of motion is constructed and the classification of the domains of possible motion is carried out. An analog of a constant homogeneous field is obtained in the Lobachevsky space.     

Stability,morphology and surface grain size patterns of channel bifurcation in gravel–cobble bedded anabranching rivers

This study presents the first detailed field‐based analysis of the morphology of bifurcations within anabranching cobble–gravel rivers. Bifurcations divide the flow of water and sediment into downstream anabranches, thereby influencing the characteristics of the anabranches and the longevity of river islands. The history, morphology, bed grain size, and flow vectors at five bifurcations on the Renous River, New Brunswick, Canada, were studied in detail. The angles of bifurcations within five anabranching rivers in the Miramichi basin were investigated. The average bifurcation angle was 47°, within the range of values cited for braided river bifurcations. Bifurcation angle decreased when anabranches were of similar length. Shields stresses in channels upstream of bifurcations were lower than reported values for braided rivers. Stable bifurcations displayed lower Shields stresses than unstable bifurcations, contrary to experimental results from braided river bifurcations. Bifurcations in anabranching rivers are stabilized by vegetation that slows channel migration and helps to maintain a uniform upstream flow field. The morphology of stable bifurcations enhances their stability. A large bar, shaped like a shallow ramp that increases in elevation to floodplain level, forms at stable bifurcations. Floodplains at stable bifurcations accrete upstream at rates between 0·9 and 2·5 m a^?1. Bars may also form within the entrance of an anabranch downstream of the bifurcation node. These bars are associated with bifurcation instability, forming after a period of stability or an avulsion. Channel abandonment occurs when a bar completely blocks the entrance to one anabranch. The stability of channels upstream of bifurcations and the location of bars at bifurcations influence bifurcation stability and the maintenance of river anabranching in the long term. Copyright © 2006 John Wiley & Sons, Ltd.     

长江口南北槽分流口洪季水沙变化过程研究

河口分流口的水沙变化过程是影响河口三角洲发育的核心环节,对下游河势的稳定起着关键性的作用。本文通过对北槽二、三期工程前后的南北槽分流口河段洪季大潮期间的同步水沙观测数据进行分析,以探讨长江口深水航道工程整治对分流口水沙过程的影响。结果表明:(1)北槽二期工程到三期工程后,分流口洪季以落潮优势流、优势沙为主的格局基本没有发生改变,但南槽优势流、优势沙出现略有变大,而北槽略有变小现象;(2)分流口洪季的水体输移主要受控于欧拉余流的变化,除北槽入口段水体净输移量一直较小外,其他河段在二、三期工程实施期间均有大幅提升,其中斯托克斯余流变化不大,拉格朗日余流与欧拉余流变化相一致,南槽呈波动状上升,北槽先增后减;(3)在二期到三期工程期间,北槽分流比明显减小,入口段落潮流速减小,含沙量较高,水体输移量降低,输沙强度减弱,由此导致二期工程以来北槽入口河段淤积强度加重。     

太平洋北赤道流表层流速及分叉点位置

确定太平洋北赤道流表层流速及分叉点位置的变化是海洋环境研究中的1个重要问题。使用1987～1998年的WOCE浮标资料,通过估算得到了季节平均和年平均意义下北赤道流表层流速(1989～1998)。计算结果显示:北赤道流表层流的流速冬季最大,夏季最小,春秋两季相仿。在厄尔尼诺发生年的第2年,夏季平均流速往往较大。对浮标轨迹的逐年分析表明表层北赤道流分叉点的位置在11°N～14 .7°N之间,从轨迹较为密集的4年的分析可以看出,表层流分叉点的位置具有年际变化,其中,2个ElNino年分叉点偏北。     

Bifurcation of Pacific North Equatorial Current at the surface

The grid altimetry data between 1993 and 2006 near the Philippines were analyzed by the method of Empirical Orthogonal Function (EOF) to study the variation of bifurcation of the North Equatorial Current at the surface of the Pacific. The relatively short-term signals with periods of about 6 months, 4 months, 3 months and 2 months are found besides seasonal and interannual variations mentioned in previous studies. Local wind stress curl plays an important role in controlling variation of bifurcation latitude except in the interannual timescale. The bifurcation latitude is about 13.3°N in annual mean state and it lies at the northernmost position (14.0°N) in January, at the southernmost position (12.5°N) in July. The amplitude of variation of bifurcation latitude in a year is 1.5°, which can mainly be explained as the contributions of the signals with periods of about 1 year (1.2°) and 0.5 year (0.3°). Supported by National Basic Research Program of China (Grant No. 2007CB411802), National Natural Science Foundation of China (Grant Nos. 40806012, 40876013), Open Fund of the Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences (Grant No. KLOCAW0803) and Scientific Research Foundation for Talent, Guangdong Ocean University (Grant No. E06118)     

剪应力作用下Ⅱ型平行节理扩展模式的分叉研究

利用伪力法考虑了剪应力作用下Ⅱ型平行节理之间的相互作用,提出利用节理的长度和间距之比, ,来确定平行裂纹发生分叉的条件。从理论上研究了2条,3条和任意多条平行节理在剪应力作用下的分叉。对于2条平行节理,当节理的长度和间距之比 大于0.816 497 5时,节理的扩展模式要发生分叉;对于3条平行节理,当节理的长度和间距之比 大于0.717 572 8时,节理的扩展模式要发生分叉;对于无穷多条平行节理,当节理的长度和间距之比 大于0.636 638 5时,节理的扩展模式要发生分叉。计算了2条到150条平行节理的分叉问题,结果表明节理数越大,节理发生分叉时节理的长度和间距之比越小。