Two new discrete integrable systems

In this paper,we focus on the construction of new(1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new(1+1)-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.     

Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.     

一种求解三维热辐射输运方程的整体预处理迭代方法及并行计算

为三维灰体热辐射输运方程的隐式离散纵标方法发展一个整体预处理迭代方法并研制并行程序.该方法采用组装线性代数方程组策略,同时求出所有离散方向上的辐射强度.借助预处理的Krylov子空间迭代法,避免复杂网格上扫描算法可能遇到的死锁问题,能够提高健壮性和计算效率.空间离散上采用一阶迎风有限体积格式.数值实验测试变形六面体网格...     

微透镜阵列光学相控阵扫描技术研究进展

光学相控阵光束扫描技术在激光雷达、空间光通信和光开关等领域拥有巨大的应用潜力。微透镜阵列光学相控阵可以通过微透镜阵列间μm量级的相对位移同时对多个出射光束的二维倾斜相位进行调制,从而实现大角度二维光束扫描,具有出射口径大、结构简单、体积小、微惯性、多功能等优点。首先介绍了微透镜阵列光学相控阵的扫描原理,之后对微透镜阵列光学相控阵国内外的发展现状、应用和现阶段存在的问题进行了阐述,最后对微透镜阵列光学相控阵的发展趋势进行了展望。

     

离散忆阻混沌系统的Simulink建模及其动力学特性分析

为拓广离散忆阻器的研究与应用,基于差分算子,构建了具有平方非线性的离散忆阻模型,并实现了Simulink仿真.仿真结果表明,设计的忆阻器满足广义忆阻定义.将得到的离散忆阻引入三维混沌映射中,设计了一种新型四维忆阻混沌映射,并建立了该混沌映射的Simulink模型.通过平衡点、分岔图、Lyapunov指数谱、复杂度、多稳态分析了系统复杂动力学特性.本文从系统建模角度出发,构建离散忆阻与离散忆阻混沌映射,进一步验证了离散忆阻的可实现性,为离散忆阻应用研究奠定了基础.     

运用三维离散元技术模拟落锤撞击下奥克托今颗粒的点火燃烧过程

炸药颗粒的点火燃烧过程一直是人们关注的热点问题。近年来,三维离散元技术在中尺度观测颗粒材料的动力学过程中拥有显著优势。炸药燃烧属于颗粒材料的反应动力学,运用三维离散元技术(DM3)可以有效地观测炸药燃烧传播的过程。以奥克托今(HMX)颗粒为例,本文成功模拟并观测到了HMX颗粒的燃烧反应程度,确定了颗粒开始燃烧反应的时间,以及燃烧反应传播的时间。同时,结合落锤冲击颗粒的三维图像以及其表观压强和放热功率,得到了HMX颗粒燃烧反应、燃烧传播的整个反应动力学过程,包括颗粒在冲击加载下碎化塑性变形的过程,颗粒燃烧反应放热的过程,落锤回弹颗粒喷射的过程等。同时,进一步说明了尖顶颗粒更利于颗粒点火,平顶颗粒有抑制颗粒点火的能力。     

The dynamics of a memristor-based Rulkov neuron with fractional-order difference

The exploration of the memristor model in the discrete domain is a fascinating hotspot. The electromagnetic induction on neurons has also begun to be simulated by some discrete memristors. However, most of the current investigations are based on the integer-order discrete memristor, and there are relatively few studies on the form of fractional order. In this paper, a new fractional-order discrete memristor model with prominent nonlinearity is constructed based on the Caputo fractional-order difference operator. Furthermore, the dynamical behaviors of the Rulkov neuron under electromagnetic radiation are simulated by introducing the proposed discrete memristor. The integer-order and fractional-order peculiarities of the system are analyzed through the bifurcation graph, the Lyapunov exponential spectrum, and the iterative graph. The results demonstrate that the fractional-order system has more abundant dynamics than the integer one, such as hyper-chaos, multi-stable and transient chaos. In addition, the complexity of the system in the fractional form is evaluated by the means of the spectral entropy complexity algorithm and consequences show that it is affected by the order of the fractional system. The feature of fractional difference lays the foundation for further research and application of the discrete memristor and the neuron map in the future.     

大口径光学元件中频波前的检测

大口径光学元件中频波前的准确评价已成为高功率激光系统中关注的焦点,元件中频波前均方根值是重要评价指标之一。根据波前中频检测频段及波前检测设备频响特性,将波前的中频区域分为两个检测频段,分别采用干涉仪和光学轮廓仪实现了中频波前均方根值的检测。采用大口径干涉仪可实现全口径波前中频区域低频段波前的检测,通过比对大口径干涉仪和采用小口径干涉仪结合分块融合平均方法的检测结果,提出采用分块融合平均方法也可检测相应频段全口径波前均方根。采用光学轮廓仪通过离散采样的方法检测大口径元件中频区域高频段波前均方根,针对不同离散采样方式的实验结果表明：33的采样方式能满足对410 mm410 mm口径元件中频区域高频段波前均方根的检测。     

Maximum norm stability of difference schemes for parabolic equations on overset nonmatching space-time grids

In this paper, theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space-time grids. We consider parabolic equations containing a linear reaction term on a space-time domain which is decomposed into an overlapping collection of cylindrical subregions of the form , for . Each of the space-time domains are assumed to be independently grided (in parallel) according to the local geometry and space-time regularity of the solution, yielding space-time grids with mesh parameters and . In particular, the different space-time grids need not match on the regions of overlap, and the time steps can differ from one grid to the next. We discretize the parabolic equation on each local grid by employing an explicit or implicit -scheme in time and a finite difference scheme in space satisfying a discrete maximum principle. The local discretizations are coupled together, without the use of Lagrange multipliers, by requiring the boundary values on each space-time grid to match a suitable interpolation of the solution on adjacent grids. The resulting global discretization yields a large system of coupled equations which can be solved by a parallel Schwarz iterative procedure requiring some communication between adjacent subregions. Our analysis employs a contraction mapping argument.

Applications of the results are briefly indicated for reaction-diffusion equations with contractive terms and heterogeneous hyperbolic-parabolic approximations of parabolic equations.

     

Asymptotic properties of two interacting maps

In this paper we consider a system whose state x changes to (x) if a perturbation occurs at the time t, for . Moreover, the state x changes to the new state (x) at time t, for . It is assumed that the number of perturbations in an interval (0, t) is a Poisson process. Here and are measurable maps from a measure space into itself. We give conditions for the existence of a stationary distribution of the system when the maps and commute, and we prove that any stationary distribution is an invariant measure of these maps.