Second order Runge–Kutta methods for Stratonovich stochastic differential equations

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly. AMS subject classification (2000)  65C30, 65L06, 60H35, 60H10     

Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

Designing a majorization scheme for the recourse function in two-stage stochastic linear programming

We discuss issues pertaining to the domination from above of the second-stage recourse function of a stochastic linear program and we present a scheme to majorize this function using a simpler sublinear function. This majorization is constructed using special geometrical attributes of the recourse function. The result is a proper, simplicial function with a simple characterization which is well-suited for calculations of its expectation as required in the computation of stochastic programs. Experiments indicate that the majorizing function is well-behaved and stable.     

一种高可用异构容错系统的混合可用性模型

为解决高可用异构容错系统的可用性评价问题,提出了一种针对高可用异构容错系统的混合可用性评价模型。设计实现异构容错原型系统,包括硬件体系结构框架及软件系统。采用Markov过程与随机Petri网相结合的方式,从可用性量化和系统状态转换两方面构建系统的可用性模型。根据该可用性模型估算系统的高可用指标,并与同构及非容错单机系统进行比较分析。结果表明,该可用性模型能够对异构容错系统进行准确的可用性评价,验证了系统5个9的高可用指标要求。最后总结了影响系统高可用性的主要因素及提升系统可用性的有效方法。     

Approximation bounds for quadratic maximization and max-cut problems with semidefinite programming relaxation

In this paper,we consider a class of quadratic maximization problems.For a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the ratio is dependent on the data of the problem with α being a uniform lower bound.In light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α δd if every weight is strictly positive,where δd ＞ 0 is a constant depending on the problem dimension and data.     

Ratchet transport of self-propelled chimeras in an asymmetric periodic structure

We studied the rectified transport of underdamped particles subject to phase lag in an asymmetric periodic structure. When the inertia effect is considered, it is possible to observe reversals of the average velocity with small self-propelled force, whereas particles always move in the positive direction with large self-propelled force. The introduction of phase lag leads particles to follow circular orbits and suppress the polar motion. In addition, this can adjust the direction of particle motion. There exists an optimal value of polar interaction strength at which the rectification is maximal. These results open the way for many application processes, such as spatial sorting of particles mixture and separation based on their physical properties.     

河流相储层随机建模的几种方法

河流相储层在我国石油工业中占有重要的地位 ,由于其具有很强非均质性的特点 ,使得难以对其进行定量描述 .随机建模技术是近十几年发展起来并逐渐完善的一项先进的储层表征技术 ,它能够较好地表征储层的非均质性 .介绍了包括布尔模拟、顺序指示模拟、截断高斯模拟、目标法及层次目标法 ,并分析了各自的优缺点 .可表征储层非均质性及对储层不确定性进行定量评价 ,适合我国以陆源碎屑岩储层 ,尤其以河流相储层为主的情况     

Molecular dynamics of an epoxy resin modified with an epoxidized poly(styrene-butadiene) linear block copolymer during cure and microphase separation processes

Molecular dynamics of diglycidyl ether of bisphenol A (DGEBA) epoxy resin modified with an epoxidized poly(styrene-b-butadiene) (SepB) linear block copolymer has been monitored during cure and microphase separation process by dielectric relaxation spectroscopy (DRS) for wide frequency and temperature ranges. Different primary and secondary relaxation processes have been analyzed for neat components and ternary mixture. Relaxational behaviour has been modelled with Havriliak-Negami, Vogel-Fulcher-Tammann and Arrhenius equations and fitting parameters and their evolution have been obtained. The retention of the epoxidized poly(butadiene) (PepB) block in the epoxy-rich phase during all the polymerization process, previously detected by our group with atomic force and transmission electron microscopies, has been confirmed by dielectric relaxation spectroscopy. The evolution of molecular dynamics during the polymerization process of the epoxy resin in the ternary system indicates a change in the trend of the main relaxation at times that agree with phase separation detected by rheology.     

A calorimetric study of the glass transition kinetics in polyisoprene

The connection between the dielectric and calorimetric relaxation behaviours of synthetic polyisoprene Cariflex IR 305 is studied. A similar comparison of dielectric and dilatometric results was described in [1]. The heat capacity was measured during heating of samples prepared with different thermal history. Experimental results were compared with the heat capacity curves calculated for a model based on the multiparameter theory of Kovacs et al. [4]. The model considers the relaxation system as being composed of a set of subsystems characterized by different relaxation times. The distribution of relaxation times and their temperature dependence were taken from the diclectric measurement. The relaxation time of a subsystem from posed to depend, not only on the actual, temperature of the sample, but also on the deviation of this subsystem from equilibrium, or alternatively, on the deviation of the system as a whole. The comparison between the measured and modeled curves shows that both influences must be taken into account in order to explain the experimental results.Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday.     

结构可靠性仿真方法研究简

可靠性仿真是对复杂结构系统进行可靠性分析计算最为有效的方法,引起了研究者越来越广泛的关注. 综合目前结构可靠性仿真方法研究现状,介绍了蒙特卡罗（Monte-Carlo,MC）法、极限状态方程重构法、随机有限元法（stochastic finite element method,SFEM）进行结构可靠性仿真计算的特点及发展现状,归纳了固体火箭发动机（solid rocket motor,SRM）结构可靠性的特点及当前进行仿真的方法;并在此基础上分析了目前结构可靠性仿真方法及对SRM 结构可靠性进行仿真分析计算时存在的不足及需要进一步研究的内容.