Controlling Chaos in Neuron Based on LasalleInvariance Principle

A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalle invariant principle. The control technique does not
require analytical knowledge of the system dynamics and operates without an explicit knowledge of the desired steady-state position. The well-known modified Hodgkin-Huxley (MHH) andHindmarsh-Rose (HR) model neurons are taken as examples to verify the implementation of our method. Simulation results show the proposed control law is effective. The outcome of this study is significant since it is helpful to understand the learning process
of a human brain towards the information processing, memory and abnormal discharge of the brain neurons.     

多组份流动质量分数保极值原理算法

对基于质量分数的Mie-Gruneisen状态方程多流体组份模型提出了新的数值方法.该模型保持混合流体的质量、动量、和能量守恒,保持各组份分质量守恒,在多流体组份界面处保持压力和速度一致.该模型是拟守恒型方程系统.对该模型系统的离散采用波传播算法.与直接对模型中所有守恒方程采用相同算法不同的是,在处理分介质质量守恒方程时,对波传播算法进行了修正,使之满足质量分数保极值原理.而不作修改的算法则不能保证质量分数在[0,1]范围.数值实验验证了该方法有效.     

Trilinear equations, Bell polynomials, and resonant solutions

A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative examples are made by an algorithm using weights of dependent variables.     

RESEARCH OF CONSTITUTIVE RELATION CORRECTION OF GEOTECHNICAL MATERIALS AND THEORETICAL SOLUTION DUE TO PILE-SOIL INTERACTION

地基土的变形模量值不仅和土层所受的先期固结压力大小直接相关, 还受桩土作用产生的附加体积应变的影响.首先, 针对岩土散体材料分析其本构关系的主要影响因素, 研究模量随埋藏深度和体积应变的变化规律, 并对Duncan-Chang本构模型进行抗拉模量值修正.其次, 综合考虑岩土材料拉压模量不等修正以及桩土作用位移边界特点, 应用变分理论推导桩土作用造成的位移、应变和应力场理论解答.最后, 应用已有的经典土压力理论和小孔扩张理论对理论推导结果进行对比和分析验证.研究结果对桩基础设计施工、相应环境保护措施的选择和设计有较大的指导作用.     

Fractional visco-elastic Euler–Bernoulli beam

Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some case studies.     

神经元电生理学等效电路模型及参数特性研究

从考虑神经元轴突朗飞结的电缆模型入手,根据脑磁图和电磁场理论的“场路一致性”原理,讨论了应该从著名的Hodgkin-Huxley一阶静态等效电路扩展为二阶动态电路的合理性和必要性,并通过具体的计算实例进一步研究电生理学材料参数膜电容C 和电感L的频率特性,实验结果表明,有髓神经元纤维轴向信号传递速度越快,其电容和电感值就越小.     

基于干涉原理的双图像加密系统

提出一种新的虚拟光学加密方法,该方法分3个步骤将两幅图像隐藏于3个随机相位板中。将两幅图像分别作为相位和幅度信息隐藏于一个复数场中,利用随机相位板作为参考光,并采用数字全息术将该复数场转换成平稳随机白噪声,利用干涉加密原理进一步将此白噪声储存于2个随机相位板中,从而将两幅图像信息隐藏于3个纯随机相位板中。该方法原理简单,无需进行迭代操作。计算机模拟结果显示:任何一个密钥错误,均无法得到原始图像的任何信息。同时,解密过程对系统中距离及波长等参数非常敏感,较大地提升了系统的安全性。     

Geometric formulations and variational integrators of discrete autonomous Birkhoff systems

The variational integrators of autonomous Birkhoff systems are obtained by the discrete variational principle. The geometric structure of the discrete autonomous Birkhoff system is formulated. The discretization of mathematical pendulum shows that the discrete variational method is as effective as symplectic scheme for the autonomous Birkhoff systems.     

Elliptical Gaussian solitons in synthetic nonlocal nonliear media

This paper studies analytically and numerically the dynamics of two-dimensional elliptical Gaussian solitons in a "double-self-focusing" synthetic nonlocal media featuring elliptical and circular Gaussian response with different degrees of nonlocality.Based on the variational approach,it obtains the approximately analytical solution of such Gaussian elliptical solitons.It also computes the stability of the solitons by numerical simulations.     

Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry

This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry.The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given.The conformal factor in the determining equations is found.The relationship between Birkhoff system’s conformal invariance and second-class Mei symmetry are discussed.The necessary and sufficient conditions of conformal invariance,which are simultaneously of second-class symmetry,are given.And Birkhoff system’s conformal invariance may lead to corresponding Mei conserved quantities,which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions.Lastly,an example is provided to illustrate the application of the result.