The second order characteristic condition for plastic flow

In this paper the second order characteristic (discontinuous bifurcation) condition is derived for the granular flow (fully plastic) equations. This second order bifurcation equation is shown to be formally identical to the first order localization requirement during steady elastoplastic deformation provided the elastic compliance tensor is substituted for the product of the plastic multiplier with the flow Hessian. For isotropic yield and flow functions the invariant form of the characteristic condition is given in detail, as well as an alternative expression in adapted co‐ordinates. The characteristic condition can be regarded as defining a hardening function which is maximized to identify the critical angles. When the method is applied to 3D Coulomb flow, Mohr's 3D fracture plane conditions are obtained uniquely. Copyright © 2003 John Wiley & Sons, Ltd.     

正弦锁相环路方程的调和解、浑沌与分支

讨论调频输入正弦锁相环路方程的调和解、浑饨与分支。利用Melnikov方法确定了产生浑沌与次谐波分支及其稳定性的条件，同时我们证明了当方程的参数适当小时，它必存在调和解。     

Nonlinear chemical couplings in the tropospheric NO x -HO x gas phase chemistry

A bifurcation phenomenon with relevance to atmospheric chemistry is discussed. The gasphase reactions in the troposphere exhibit two types of temporal evolution which are controlled by the strength of the source,Q, of nitric oxide, NO, via the nonlinear chemical coupling between the hydrogen oxides and nitrogen oxides chemistry. IfQ remains below a threshold value, all short-lived species, including NO, approach steady-state concentrations, while above the threshold bifurcation to another state with increasing (nonstationary) NO concentrations accompanied by a depletion of the OH and HO₂ abundances takes place.     

Transient bifurcation condition of partially saturated porous media at finite strain

Bifurcation of unsaturated soils into a localized shear band is a ubiquitous failure mode of partially saturated soils. The density and degree of saturation have major impacts on the inception of localized deformations in unsaturated soils. Unsaturated fluid flow may dramatically change the density and degree of fluid saturation of unsaturated soils. Therefore, the unsaturated fluid flow is a potential trigger for shear banding in such materials. In this paper, we derive a simplified bifurcation condition of localized deformation in unsaturated soils under the local transient condition at finite strain. This transient bifurcation condition is implemented into a nonlinear finite element code to study the inception of localized deformation in unsaturated soil specimens. Numerical simulations are conducted to study the impact of soil fabrics of density, a ‘bonding’ variable, and intrinsic permeability on the inception of localized failures via the transient bifurcation criterion. Mesh sensitivity analysis is performed to demonstrate the viscosity effect of unsaturated fluid flow on the localized deformation. Numerical simulations demonstrate that the transient bifurcation condition can detect the localized deformation triggered by the internal unsaturated fluid flow process in unsaturated soils. Copyright © 2016 John Wiley & Sons, Ltd.     

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton–Rogers–Lapwood problem in a fluid-saturated porous medium. The Horton–Rogers–Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton–Rogers–Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton–Rogers–Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton–Rogers–Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. © 1997 by John Wiley & Sons, Ltd.     

An experimental investigation into topographic resonance in a baroclinic rotating annulus

This paper documents an experimental investigation in which a differentially-heated rotating annulus experiment was used to investigate the effects of topography on fluid flow under conditions similar to the atmospheric and oceanic circulation on Earth and other planets. In particular, the relationship between the effects of topographic resonance and the existence and mechanism for generation of low-frequency variability (LFV) were studied, motivated by outstanding questions in works such as Jin and Ghil (J. Atmos. Sci., 1990, 47) and Read and Risch (Geophys. Astrophys. Fluid Dyn., 2011, 105). Whilst employing sinusoidal wavenumber-3 topography a new regime was encountered within a region of stationary wavenumber-3 structural vacillation. Denoted as the “stationary-transition” regime, it featured periodic oscillations between a dominant stationary wavenumber-3 flow and axisymmetric or chaotic flow. Further investigation found that the “stationary-transition” regime appeared to be a near-resonant region where nonlinear topographic resonant instability led to a 23–42 “day” oscillatory behaviour. Within the regime, a Hopf bifurcation sequence was discovered, and the nonlinear instabilities were found to have terms in both wave-zonal flow and wave–wave interactions, including a notable resonant wave-triad. This report summarises the nature of the “stationary-transition” regime, and also makes comparisons with similar regimes of LFV found in other experimental studies, as well as intraseasonal oscillations in the atmosphere.     

北赤道流分叉点及南海北部环流的研究进展

介绍了北赤道流分叉点、南海北部环流的一些研究成果,并就黑潮对南海的影响所作的研究进行了回顾.北赤道流分叉点的位置对于北赤道流系水体疏运变化及在黑潮和MC之间水体、热量、盐度输运的分配中起着重要的作用.北赤道流分叉点位置约在14.6°N上,分叉点位置随深度增加而北移.分叉点有明显的季节变化和年际变化,在春、夏季向南移动,而在秋、冬季则向北移动.年际变化与ENSO现象相关紧密,在El Nio事件NEC分叉纬度处于最北端,在La Nio事件处于最南端.对于分叉点位置的定量化研究,仍然需要更多的观测结果进行研究.季风和黑潮是影响南海北部环流的两种主要因素.南海北部上层流场主要由广东沿岸流、黑潮入侵流套、东沙海流、南海暖流和吕宋海流组成.除海盆、次海盆尺度环流外,受季风、黑潮和地形等因素的影响,南海表现出多涡结构.通过近些年的卫星观测和数值模拟的结果,人们对南海中尺度涡的认识大大加深,但要想模拟出风应力形成涡的机制,还需要提高风场和模式的分辨率.由于观测资料的限制,对南海流场的垂直结构、以及春-秋季季风转相时期的流场结构等还研究得较少.吕宋海峡水交换是西太平洋对南海影响的主要途径.黑潮在吕宋海峡附近的形变一直是有争议的热点问题,目前对于黑潮入侵有3种观点:(1) 认为黑潮经过吕宋海峡形成流套结构,并分离出中尺度涡影响南海流场、水团结构;(2) 认为黑潮有一直接分支分离出来进入南海形成黑潮分支;(3) 认为吕宋海峡水交换不属于以上两种情况,西太平洋对南海的水团输送另有机制.北赤道流分叉点在对黑潮的水体、热量、盐度输运的分配中起着重要的作用,黑潮对南海北部环流的影响可能与NEC的分叉点位置有关,但目前对NEC的分叉点位置与南海北部环流相关性的研究甚少.最后提出了对未来加强该方面研究的一些展望.     

The Collision Manifold of the Collinear One-Bumper Two-Body Problem

We present a special model which is a caricature of the collinear three-body problem. Near triple-collision behavior for the model is governed by the collision manifold. We study the bifurcations of the dynamics on this manifold as we vary the ratio of masses. Both analytic and numerical results are presented.This revised version was published online in October 2005 with corrections to the Cover Date.