Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites

This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions.     

Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems

This paper presents a unified framework for performing local analysis of grazing bifurcations in n-dimensional piecewise-smooth systems of ODEs. These occur when a periodic orbit has a point of tangency with a smooth (n−1)-dimensional boundary dividing distinct regions in phase space where the vector field is smooth. It is shown under quite general circumstances that this leads to a normal-form map that contains to lowest order either a square-root or a (3/2)-type singularity according to whether the vector field is discontinuous or not at the grazing point. In particular, contrary to what has been reported in the literature, piecewise-linear local maps do not occur generically. First, the concept of a grazing bifurcation is carefully defined using appropriate non-degeneracy conditions. Next, complete expressions are derived for calculating the leading-order term in the normal form Poincaré map at a grazing bifurcation point in arbitrary systems, using the concept of a discontinuity mapping. Finally, the theory is compared with numerical examples including bilinear oscillators, a relay feedback controller and general third-order systems.     

模糊数四则运算的交点-间断点法

对模糊数的四则运算提出了一种交点-间断点法:将模糊数的加法、减法和除法运算,化为求两个函数在某区间上其交点处的值;当交点不存在且两函数在该区间上的间断点为有限个时,将其运算化为求一函数在这些间断点处及区间的两端点处的最大值;将模糊数的乘法运算,化为用交点法或间断点法分别在两个区间上求出相应的值,然后取它们中最大者。     

含不连续项的常微分积分方程的解

本文研究微分积分方程 u'=g(t,u)+integral from 0 to 1(k(t,s)f(s,u(s))ds),u(0)=x_0最小解、最大解的存在性.本文的特点是关于方程中函数g(t,x),f(t,x)没作任何连续性假定.     

Discontinuous fold bifurcations in mechanical systems

Summary  This paper treats discontinuous fold bifurcations of periodic solutions of discontinuous systems. It is shown how jumps in the fundamental solution matrix lead to jumps of the Floquet multipliers of periodic solutions. A Floquet multiplier of a discontinuous system can jump through the unit circle, causing a discontinuous bifurcation. Numerical examples are treated, which show discontinuous fold bifurcations. A discontinuous fold bifurcation can connect stable branches to branches with infinitely unstable solutions. Received 20 September 2000; accepted for publication 26 June 2001     

Near-grazing dynamics in tapping-mode atomic-force microscopy

In tapping-mode atomic-force microscopy, non-linear effects due to large variations in the force field on the probe tip over very small length scales and the intermittency of contact may induce strong dynamical instabilities. In this paper, a discontinuity-mapping-based analysis is employed to investigate the destabilizing effects of low-velocity contact on a lumped-mass model of an oscillating atomic-force-microscope cantilever tip interacting with a typical sample surface. As illustrated using two tip-sample force models, the analysis qualitatively captures the potential loss of stability and disappearance of a low-contact-velocity steady-state response. The quantitative agreement of the predictions of the discontinuity-mapping-based analysis with direct numerical simulations, at least for sufficiently low contact velocity, supports its use in the passive redesign or active control of the tip-sample mechanism for purposes of preventing such a loss of stability.     

侧伏规律在岩质边坡结构面编录中的应用

理论上,据边坡设计坡面来编录展示结构面的迹线分布应与其在坡面内的侧伏交线一致。把握一定的侧伏规律,处以适当的素描技法,既可吻合实际情况,又可提高绘图效率和资料质量,对边坡结构模型的准确分析不无裨益。有鉴于此,经过现场观测总结,分析了结构面与坡面的各种交切关系及其迹线的侧伏特征。在侧伏规律公式推导的基础上,根据两者产状提出其特征三角形判别法,并编制相应的算图,可校核以及在适当条件下推测某一产状要素。讨论了实践中几类难以作图的特殊情况下侧伏规律的应用。     

Optimal DB-PAYGO pension management towards a habitual contribution rate

In this paper, we propose a new objective function, which reflects the costs of unstable contribution risk and discontinuity risk in DB-PAYGO pension system. The problem is to minimize the quadratic deviation between the actual contribution rate and a habitual target and the quadratic proportional deviation of the pension accumulation. A modified non-negative constraint of the contribution rate is added, which together with a stochastic habitual target process, causes difficulty in solving the minimization problem by Lagrange dual method. The results are split into two cases which depend on the habit-adjusted adequacy of the pension budget. In the inadequate case, the optimal contribution rate reveals a hump shape curve with respect to time, which is different from the exponential growth curve of the model with a fixed target. By moderately raising the contribution rate in the initial phase, it helps to increase the accumulation and reduce the contribution burden of the follow-up policyholders. Notably, the hump shape curve is a more practical policy, because of that the exponential growth curve raises anxiety about the unlimited growth of the contribution rate and harms the confidence in the sustainability of the pension fund. We also study the impacts of the certain trend in demography, and the uncertain fluctuations in salary and investment on the optimal control policies.     

Boundary intersection crossing bifurcation in the presence of sliding

Piecewise smooth systems are known to present a richer set of bifurcations than their smooth counterparts. An interesting family of bifurcations that is present in this type of systems are the so called boundary intersection crossing bifurcations, that take place when a periodic orbit crosses the intersection between two or more discontinuity boundaries. Such bifurcations have been observed in many different models, and have been studied in a number of papers over the past few years. Nonetheless, the particular case in which sliding solutions (as defined by Filippov) are involved, has been left out in previous analyses. This paper addresses this particular case, carrying out a complete analysis and deriving the discontinuity mappings that can be used to characterise such bifurcations. Then, in the second part of the paper, the results are applied to the study of a model of a common electronic device, showing how the mappings can be used systematically to determine the dynamics around the bifurcation.     

Imaging of chemical reactivity and buckled dimers on Si(100)2×1 reconstructed surface with noncontact AFM

We have investigated the force interactions between the Si tip and the Si(100)2×1 reconstructed surface in the noncontact atomic-force microscopy (AFM) measurement. We observed two types of frequency shift curves without and with discontinuity, similar to the Si(111)7×7 surface. The image contrast changes drastically whether the frequency shift curve shows discontinuity or not. In the case of the frequency shift curves without discontinuity, the noncontact AFM images almost reflect the surface topography including dimers and adsorbates. In the case of the frequency shift curves with discontinuity, they reflect strongly the chemical reactivity of surface. Furthermore, in the case of the frequency shift curves without discontinuity, for the first time, the stabilize-buckling of dimers induced by a defect can be observed. This suggests that the force interactions during the noncontact AFM measurement hardly influence the surface dynamics.