Bifurcation and solitary solution of a transient temperature field along axis of gun muzzle

IntwtctionThe problem of center fiame and secondary flame inthe gUn muzile has scarcely been stUdied. A review ofthis work can be found in Yu["'], in which a solitaIysoluhon has been Put forwards. However heat transfer ofthe Problem is very comPlex, where the chain chendcaireachonsl3] is always neglected, because the chendcalreaction souree tenn is a strOng noIilinear term that willmake rigorous analysis of tbe Problem to be difficult.In this pW attenhon will be paid to the chainchendcal …     

振动磨的周期运动稳定性与分岔

由于碰撞的存在,振动磨系统的响应呈现出复杂的周期运动或混沌运动。本文将振动磨的模型进行简化,建立一维、两自由度、受简谐激振力作用的振动磨碰撞振动力学模型。基于Poincare映射原理,根据映射Jacobi矩阵分析振动磨周期运动的稳定性,并通过理论分析和数值仿真,研究振动磨周期运动的稳定性与分岔,以及由倍周期分岔通向混沌的过程。     

Chen系统的动力学行为及其吸引子结构的研究

利用受控Chen系统,并基于镜像操作方法,发现Chen吸引子是由左、右两个吸引子所组成的复合结构,且左、右吸引子均可由极限环生成.采用一维时间序列相空间重构技术和系统混沌的定量判据准则,揭示出Chen系统从规则运动转化到混沌运动所具有的普适特征:Chen系统可通过Pomeau-Manneville途径走向混沌,且其间歇性与Hopf分岔和倍周期分岔有关,在这些途径上既可观察到锁相和准周期运动,也可观察到类Chen吸引子、Chen系统和Lorenz系统之间的过渡吸引子和类Lorenz吸引子.     

Embedded strong discontinuity finite elements for fractured geomaterials with variable friction

The strong discontinuity approach to modelling strain localization, combined with an enhanced strain element, has been used for more than a decade to model strain localization in materials including geomaterials. Most implementations of enhanced strain elements in the post-localization regime use very simple constitutive formulations along the discontinuity, such as linear softening or a constant friction coefficient. However, the softening relations can be much more complex for geomaterials. For rocks this softening is induced by micro-fractures coalescing into macroscopic cracks during a narrow time interval called ‘slip weakening.’ During this interval the cohesive resistance on the nucleating crack decays to zero while the frictional resistance increases. Furthermore, research has shown that the coefficient of friction for these materials is not constant, but in fact is a function both of the slip speed and the state of the material, including wear, temperature, and other factors. In this paper we augment the modelling capabilities of an enhanced strain element by incorporating a cohesive softening law and a popular rate- and state-dependent friction model commonly used for describing the constitutive properties of rocks and rock-like materials sliding along the fractured surface. Copyright © 2007 John Wiley & Sons, Ltd.     

堤坝和基础非线性动力失稳灾变的分岔突变分析

为了更深刻本质地研究堤坝系统发生动力溃坝灾害的机理，应用非保守系统拉格朗日动力学理论建立了堤坝 基础系统在地震荷载作用下3个自由度的非线性动力学模型,它描述了堤坝 基础系统在地震荷载作用下的横向振动、竖向振动和基础振动的非线性特征.在此基础上，对由振幅、作用力和激振频率所表示的相空间中动力系统在简谐激励作用下共振响应表现出的畸变、折叠、突跳和滞后等现象，以及对在范德玻尔轨迹平面上系统稳定性分岔的特征和共振峰畸变突跳现象的机理，以及分频过程的亚谐振的现象进行了研究，从不同角度对非线性动力系统给出了双（或单）尖点突变模型，描述了由堤坝 基础结构中非线性因素演化造成系统稳定性分岔所导致的系统振幅平方A21失稳突跳抖动，使堤坝系统的动能（或动量）发生突然的改变，从而在系统内产生了很大的冲击应力的灾变机理.     

一个新的平面不可压缩的Navier-Stokes方程的八模类Lorenz方程组截断

通过对平面正方形区域上不可压缩的Navier-Stokes方程进行傅立叶展开后截断得到一个新的八模类Lorenz方程组,给出了该方程组的定常解及吸引子存在性和全局稳定性的证明。同时,数值模拟了雷诺数在一定范围内变化时方程组的基本动力学行为和混沌轨线。系统通过一系列的分岔展现了复杂的随机行为。     

Skew product cycles with rich dynamics: From totally non-hyperbolic dynamics to fully prevalent hyperbolicity

We introduce a two-parameter family of ‘partially hyperbolic’ skew products (G_{a, t})_{a > 0, t ∈ [ ? ε, ε]} maps with one dimensional centre direction. In this family, the parameter a models the central dynamics and the parameter t the unfolding of cycles (that occurs for t = 0). The parameter a also measures the ‘central distortion’ of the systems: for small a, the distortion of the systems is small and it increases and goes to infinity as a → ∞. The family (G_{a, t}) displays some of the main characteristic properties of the unfolding of heterodimensional cycles as intermingled homoclinic classes of different indices and secondary bifurcations via collision of hyperbolic homoclinic classes. For a ∈ (0, log?2), the dynamics of (G_{a, t}) is always non-hyperbolic after the unfolding of the cycle. However, for a > log?4 intervals of t-parameters corresponding to hyperbolic dynamics appear and turn into totally prevalent as a → ∞ (the density of ‘hyperbolic parameters’ goes to 1 as a → ∞). The dynamics of the maps G_{a, t} is described using a family of iterated function systems modelling the dynamics in the one-dimensional central direction.     

Complicated motion of particles on vibration screen surface

lINTRODUCTIONToday,them0tiontheoryofparticlesonscreensurfaceisanimp0rtantresearchdirectionofscreeningtechn0logyandtheory['~8].Bymeansofstudyingmotionregularityofparticles,wecanobtaintheoptimumkineticparametersfortheindustrialscreeningandraiseitsefficien-cy.Thematerialbeingscreenedhasvariableshapeandsize,withdifferentsurfacemoistureandclaymineralscontents.Themotionofparti-clesisaffectedbydisplacement,velocity,accel-erationofscreensurfaceandfrictionamongpar-ticles.S0theparticles'motiononscr…     

A discrete-integral strength criterion for complicated stress states

The atomic structure behaviour at a crack tip in closely-packed layers of atoms is studied. The deformation of a three-atomic chain for the complicated stress state is analysed. This study includes the analyses of bifurcation and post-bifurcation behaviour as well as the sensitivity of the limit strength to fixing conditions. The numerically obtained values of theoretical strengths are compared with the available experimental results and the theoretical estimates. The discrete-integral strength criterion for complicated stress states is proposed. Contrary to the classical criteria, the proposed criterion allows a limiting transition of the crack length parameter and describes the strength of cracked and crack-free solids.     

Fold-Hopf bifurcation in a simplified four-neuron BAM (bidirectional associative memory) neural network with two delays

The bidirectional associative memory (BAM) neural network with four neurons and two delays is considered in the present paper.A linear stability analysis for the trivial equilibrium is firstly employed to provide a possible critical point at which a zero and a pair of pure imaginary eigenvalues occur in the corresponding characteristic equation.A fold-Hopf bifurcation is proved to happen at this critical point by the nonlinear analysis.The coupling strength and the delay are considered as bifurcation parame...