Diffusion–convection reaction equations with sign-changing diffusivity and bistable reaction term

We consider a reaction–diffusion equation with a convection term in one space variable, where the diffusion changes sign from the positive to the negative and the reaction term is bistable. We study the existence of wavefront solutions, their uniqueness and regularity. The presence of convection reveals several new features of wavefronts: according to the mutual positions of the diffusivity and reaction, profiles can occur either for a single value of the speed or for a bounded interval of such values; uniqueness (up to shifts) is lost; moreover, plateaus of arbitrary length can appear; profiles can be singular where the diffusion vanishes.     

微流控双稳振荡器光开关

针对光开关集成化、微型化、低能耗的要求,设计了一种微流控双稳振荡器1×2型光开关,其两个输出端口的插入损耗分别为1.03dB和0.18dB.微流控双稳振荡器由对称级联的两个常闭阀构成,光开关由三段嵌入在振荡器输出端的光纤波导构成,通过改变注射泵驱动微器件中液体流动的速率可以控制光开关的开关周期.利用有限元分析软件对影响开关周期的因素进行了仿真研究.结果表明,当液体的注入流速从0.2mm/s增大到1.0mm/s时,开关周期从1.25s减小到0.26s,周期占空比约为0.5,阀的阈值与开关时间常量呈线性关系.随着常闭阀阀座的增宽,开关周期变长;阀的宽长比增大,开关周期减小;振荡器的不对称设计可以调节周期的占空比.通过调节入口流速和阀的阈值特性,可以设计特定频率的光开关,这为单入多出、多入多出光开关的后续研究提供了依据.     

A parametrically excited pendulum with irrational nonlinearity

In this paper, we propose a parametrically excited pendulum with irrational nonlinearity which comprises a simple pendulum linked by a linear spring under base excitation. This parametric vibration system exhibits bistable state and discontinuous characteristics due to the geometry configuration. For small oscillations, this system can be described by Mathieu equation coupled with SD (Smooth and Discontinuous) oscillator whose dynamic response is examined analytically by using the averaging method in both smooth and discontinuous case. Numerical simulations are carried out to demonstrate the complicated dynamic behavior of multiple periodic motions and different types of chaotic motions.     

非线性光子晶体的单向透射性

利用非线性时域有限差分方法(FDTD)对光从某些一维缺陷层掺杂克尔非线性介质的四分之一波长光子晶体的正反两个不同方向入射时对应的一般透射特性进行了数值分析.计算表明：一定频率范围及一定光强范围的光从非线性光子晶体的正向入射时,透射率是其从非线性光子晶体相反方向入射时的数倍,具有单向透射性,表现为全光二极管的行为.进一步对交替介质层由空气和金红石(TiO2)组成而非线性缺陷层由聚合物(polydiacetykene 9-BCMU)组成的光子晶体模型的透射特性进行了数值分析.在某一频率和强度附近,该模型的正向透射率是反向的6倍左右,表明其可作为一种全光二极管使用.     

Reconstructing the transient,dissipative dynamics of a bistable Duffing oscillator with an enhanced averaging method and Jacobian elliptic functions

Systems characterized by the governing equation of the bistable, double-well Duffing oscillator are ever-present throughout the fields of science and engineering. While the prediction of the transient dynamics of these strongly nonlinear oscillators has been a particular research interest, the sufficiently accurate reconstruction of the dissipative behaviors continues to be an unrealized goal. In this study, an enhanced averaging method using Jacobian elliptic functions is presented to faithfully predict the transient, dissipative dynamics of a bistable Duffing oscillator. The analytical approach is uniquely applied to reconstruct the intrawell and interwell dynamic regimes. By relaxing the requirement for small variation of the transient, averaged parameters in the proposed solution formulation, the resulting analytical predictions are in excellent agreement with exact trajectories of displacement and velocity determined via numerical integration of the governing equation. A wide range of system parameters and initial conditions are utilized to assess the accuracy and computational efficiency of the analytical method, and the consistent agreement between numerical and analytical results verifies the robustness of the proposed method. Although the analytical formulations are distinct for the two dynamic regimes, it is found that directly splicing the inter- and intrawell predictions facilitates good agreement with the exact dynamics of the full reconstructed, transient trajectory.     

Bursting oscillations in electromechanical systems

This paper analyzes the bursting oscillations in a system consisting of a double-well electrical oscillator coupled magnetically to a mobile rigid beam attached to a fixed support through a spring. It is found that the shape, period and amplitude of the bursting depend on various control parameters.     

Dynamical behavior of Lotka–Volterra competition systems: non-autonomous bistable case and the effect of telegraph noise

This article is concerned with the study of trajectory behavior of Lotka–Volterra competition bistable systems and systems with telegraph noises. We proved that for bistable systems, there exists a unique solution, bounded above and below by positive constants. The oscillatory situation of systems with telegraph noises is pointed out.     

The rate dependent response of a bistable chain at finite temperature

We study the rate dependent response of a bistable chain subjected to thermal fluctuations. The study is motivated by the fact that the behavior of this model system is prototypical to a wide range of nonlinear processes in materials physics, biology and chemistry. To account for the stochastic nature of the system response, we formulate a set of governing equations for the evolution of the probability density of meta-stable configurations. Based on this approach, we calculate the behavior for a wide range of parametric values, such as rate, temperature, overall stiffness, and number of elements in the chain. Our results suggest that fundamental characteristics of the response, such as average transition stress and hysteresis, can be captured by a simple law which folds the influence of all these factors into a single non-dimensional quantity. We also show that the applicability of analytical results previously obtained for single-well systems can be extended to systems having multiple wells by proper definition of rate and of the transition stress.     

微胶囊电泳显示技术

微胶囊电泳显示是一种可逆、双稳态、柔性的电子纸显示技术。本文描述了微胶囊电泳显示技术的“单粒子”和“双粒子”两种基本显示原理,并分别针对其制备技术中的电泳颗粒的表面处理、显示液的配制以及微胶囊化三个关键步骤作了详细的介绍。还介绍了微胶囊电泳显示技术的研究现状和发展趋势。     

A bistable rolling joint for multistable structures

In this paper, a concept of using rolling joints for a multistable structure, which deforms elastically into a variety of cylindrical shapes, is presented. A bistable joint is obtained by modifying the geometry of a rolling hinge. The proposed concept can hold the stable state without any continued actuation. Then detailed mathematical derivations are carried out to obtain the wire tensions and joint resultant moment during the motion, which are used to compute the external action that should be applied to move the joint. The effects of some geometric parameters on the mechanical behavior are also investigated. The results show that higher values of the wire tension and joint resultant moments can be obtained by increasing the side included angle φ or the radius of wire wrapped circles R. Moreover, the pretension of wires in the stable configuration also increases the wire tension and the joint resultant moment.