Sharp oscillation and nonoscillation tests for delay dynamic equations

In this paper, we give new sufficient conditions for both oscillation and nonoscillation of the delay dynamic equation where and satisfy τ(t) ≤ σ(t) for all large t and . As an important corollary, we obtain the time scale invariant integral condition for nonoscillation: for all large t. Also, with some examples, we show that newly presented results are sharp.     

Mechanics of atoms interacting with a carbon nanotorus: optimal configuration and oscillation behaviour

In this paper, we investigate a carbon nanotorus as a caged molecular structure interacting with an atom. Assuming that the atom is located along the central axis perpendicular to the torus, the interaction energy of the system is determined using the continuum approximation together with the Lennard-Jones potential. This approach avoids the intensive computational calculations that are involved in other modelling approaches. Numerical results are presented in terms of dimensionless variables. The results show that the optimal major radius of the torus has a linear relationship with its minor radius when the atom is symmetrically situated along the torus axis. When the atom is offset from this axis, the minimum energy location shifts away from the centre as the ratio of the major and minor radii exceeds the value of 0.90. Finally, the oscillatory behaviour for the carbon atom is investigated. Our findings predict a novel nano-oscillator which can produce frequencies in the gigahertz range.     

Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.     

Oscillation theorems for symplectic difference systems

We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same problem was treated and an essential ingredient was to establish the concept of the multiplicity of a focal point. But there was still a rather restrictive condition needed, which is eliminated here by using the concept of finite eigenvalues (or zeros) from the theory of matrix pencils.     

激光核聚变与高功率激光:历史与进展

回顾激光聚变近50年来的发展历程,评述聚变物理与高功率激光驱动器的研究进展,展望聚变能源未来前景.     

高阶变系数函数方程的非振动解

给出一类高阶非线性函数方程的一些新的非振动准则,并且给出了在差分方程中的若干应用,结果改进和推广了近期文献的某些结果.     

Oscillation criteria and asymptotic properties of solutions of third‐order nonlinear neutral differential equations

The main goal of this article is to study the asymptotic properties and oscillation of the third‐order neutral differential equations with discrete and distributed delay. We give several theorems and related examples to illustrate the applicability of these theorems. Copyright © 2014 John Wiley & Sons, Ltd.     

二维柱坐标系辐射输运方程保球对称的离散纵标格式

 离散纵标格式是计算辐射输运方程的常用格式之一. 但是, 传统的离散纵标格式求解二维柱坐标系辐射输运方程模拟一维球对称问题时, 会出现明显的非对称现象, 球对称性被破坏. 针对该问题, 本文分析了传统离散纵标格式不能够保持球对称性的原因, 提出了空间基于柱坐标系、方向基于球坐标系的辐射输运方程, 并对该方程设计了新的离散纵标格式, 从理论上证明了当空间网格取球对称剖分时该离散格式能够保持一维球对称性的充分必要条件. 通过对真空球区域辐射输运、与物质耦合辐射输运等球对称算例的数值模拟, 验证了该格式的保球对称性, 球对称误差能够达到机器精度. 非对称辐射驱动模型以及非对称网格剖分条件下的数值模拟等算例也取得了较好的结果.