Peculiarities of wave dynamics in media with oscillating inclusions

The article is concerned with mathematical models for media with oscillating inclusions. These models consist of mutually connected equations, one of which is the wave equation for carrying medium and others are equations of motion for partial oscillators. To close these models, we use cubic and nonlocal equations of state for the carrying medium. Travelling wave solutions to these models are studied in detail. Using qualitative analysis methods, the phase space is shown to contain periodic, homo- and heteroclinic trajectories. Moreover, in the case of nonlocal models we observe the creation of quasiperiodic and chaotic regimes. Bifurcations of localized regimes are studied via the Poincaré section technique.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.     

Long‐time behavior of a nonlinear viscoelastic beam equation with past history

This paper is concerned with the existence of a global attractor for the nonlinear viscoelastic beam equation with past history memory where g(u_t) is a damping like | u_t | ^ru_t and f(u) is a source term like | u | ^αu ? | u | ^βu, by considering 0 ≤ β < α and r > 0. Copyright © 2014 John Wiley & Sons, Ltd.     

Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser

Single-pass free-electron lasers constitute an example of systems with long-range interactions. The light-particle interplay leading to the power growth and successive relaxation towards a quasi-stationary state is governed by the Vlasov equation. A maximum entropy principle inspired to Lynden-Bell's theory of “violent relaxation" for the Vlasov equation can be invoked to analytically characterize the behaviour of the saturated system. In particular, we here concentrate on the case of coherent harmonic generation obtained from an externally seeded free-electron laser and provide a simple strategy to predict the laser intensity as well as the final electron-beam energy distribution.     

一种超混沌映射的单双参量自适应同步

利用参量自适应法实现了超混沌系统Kawakami映射的同步.通过严密的数学推导,给出了Kawakami映射在单参量自适应下实现同步的充分条件,并在双参量自适应控制下系统同样实现了同步.数值模拟结果显示,该映射输出具有类似于白噪声的宽谱特性,因此比较适合用于保密通信.     

受迫振动非线性特性的教学拓展

受迫振动在大学物理和大学物理实验中均是重点教学内容,为了使学生更加深入理解受迫振动的非线性特性,本文基于波耳共振仪所涉及的非线性因素和实验数据,对受迫振动方程进行非线性修正,利用数值分析探讨其非线性特性.通过引入硬弹簧型杜芬方程,探讨系统由周期性运动进入混沌状态的演化,将受迫振动中相对稳定的平衡点与奇异吸引子进行类比,...     

广义神经传播方程的整体吸引子

使用Galerkin方法,结合Sobolev空间理论和不等式技巧,给出了广义神经传播方程解的存在唯一性定理,然后利用吸引子存在性定理,采用半群方法证明了方程整体吸引子的存在性.     

Theory of particle transport phenomena during fatigue and time-dependent fracture of materials based on mesoscale dynamics and their practical applications

In this work, the mesoscale mechanics of metals, which links their microscopic physics and macroscopic mechanics, was established. For practical applications, the laws for quantitatively predicting life of cycle and time-dependent fracture behavior such as fatigue, hydrogen embrittlement, and high-temperature creep were derived using particle transport phenomena theories such as dislocation group dynamics, hydrogen diffusion, and vacancy diffusion. Furthermore, these concepts were also applied for estimating the degree of viscoelastic deterioration of blood vessel walls, which is dominated by a time-dependent mechanism, and for the diagnosis of aneurysm accompanied by the viscoelastic deterioration of the blood vessel wall. In these theories, new mechanical indexes were derived as dominant factors for predicting the life of fatigue crack growth and the time-dependent fracture of notched specimens of materials such as hydrogen embrittlement and high-temperature creep. Furthermore, as an example of a practical application, these theories were applied to estimate the degree of viscoelastic deterioration and chaotic motions of blood vessel walls, which are closely related to blood vessel diseases such as atherosclerosis and aneurysm. Moreover, new indexes to diagnose them were also proposed for clinical applications.     

基于图像重组和比特置乱的多图像加密

针对现有多图像加密算法只能同时加密多张同类型同大小的图像,适用范围不广、实用性差等问题,提出一种基于图像重组和比特置乱的多图像加密算法.该算法通过将任意数量、不同大小和不同类型的图像重新组合成新多灰度图,一次完成同时加密,极大提高了加密效率和适用范围.首先,依次提取所有待加密图像像素值重新组合出N张m×n新灰度图,并将其转化成m×n×8N二进制矩阵.然后,采用3D比特置乱方式,对高位页进行行列比特置乱,低位页进行整页比特置乱.最后,进行异或扩散操作,得到密文图像.高低位分开置乱提高了算法的抗噪声能力,最终密文信息熵达到7.999以上,很好地掩盖了明文的统计特性.构造一种新型Logistic与广义三阶Fibonacci级联的混沌系统产生随机序列,增加了初值和控制参数范围,扩大了密钥空间,使其达到8×10^84以上,极大地提高了抗穷举攻击能力.既提高了序列随机性,又同时保留了低维混沌系统的快速性.结合明文哈希值(SHA-256)产生密钥,明文像素值发生微小改变后密文像素值变化率达到0.996以上,极大地提高了的明文敏感性和算法抗选择明文攻击的能力.实验分析表明,提出的多图像加密算法安全性高、实用性强.