形变张量的特征值与Boussinesq方程组的正则性估计

讨论了二维及三维满足周期边界条件的Boussinesq方程初边值问题的局部正则解在有限时间内爆破的可能性.在二维情况下,用形变张量的特征值给出温度梯度的L2估计,从中看出若流体微团变形的速率大,则解爆破的可能性就大.在三维情况下,用形变张量的特征值和温度的偏导给出涡量的L2估计,从中发现若流体微团在大部分时间内一般是平面拉伸,且温度的偏导较小时,解爆破的可能性就大;若一般是线性拉伸,温度的偏导又不任意增大时,解爆破的可能性就小.     

NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD

A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.     

MD simulation for nanocrystals

Molecular dynamic (MD) provided anab initio simulation for nano-scale mechanical behavior of materials, provided that the inter-atomic potential is accurately prescribed. MD is particularly suitable in simulating the formation, the deformation, and the evolution of nanocrystals under a fast strain rate. To tackle large scale system and nano-seconds time duration, parallel algorithm is desired. The present paper reviews the recent advances in MD simulation for nanocrystals rithm is desired. The present paper reviews the recent advances in MD simulation for nanocrstals with attention focused on the applications toward nanomechanics. The examined issues are: formation of nanocrystalline metals, nanoindentation on nancorystals, fast deformation of nanocrystals, orderdisorder transition, and nano-particle impact. The project supported by the National Natural Science Foundation of China (101212202 and 90205023)     

腔镜形变对圆筒组合型CO_2激光器模式的影响

针对具有锁相结构的圆筒组合型CO2激光器,分析了其注入锁定的原理,利用等价条形腔理论,建立了分析其输出基模的数学模型。利用该模型,研究了不同形变量对圆筒形腔输出基模的影响。结果表明,为了获得与注入光束模式类似的光场分布,复曲面镜与圆筒形谐振腔中平面镜镜面中心的形变量应控制在0.07倍波长以内。同时,分析在不同腔镜参数情况下腔镜形变对输出模式造成的影响,其结果有利于进一步优化谐振腔的参数设计。     

胡克定律探究实验装置的改进

利用自制胡克定律探究实验装置对新课标中"探究弹簧弹力与形变量之间的关系"实验进行了改进,改进后的实验装置能直接在坐标纸上绘出弹簧弹力与形变量之间的对应关系点,通过拟合可得到F-x曲线,求拟合直线的斜率可求出被测弹簧的劲度系数.改进后的实验装置得出的实验结果与新课标教材中描述的现象一致.     

形变碳纳米管中水的输运行为研究

水分子通过碳纳米管的运输行为对认识生命的新陈代谢活动、海水淡化和纳米运输器件有着重要的参考作用.本文通过分子动力学的方法研究了水分子通过形变碳纳米管的运输行为,即椭圆柱状碳纳米管的离心率e对管内水分子输运的影响.结果发现椭圆柱状碳纳米管的离心率对管内水分子的偶极矩概率分布、径向函数分布和流量有重要的影响作用.分析认为碳纳米管的形变使管内水分子的偶极矩态及其运输状态发生变化;同时也发现在一定范围内通过改变碳纳米管的形状能起到分子开关的作用.     

SOLITARY WAVES IN FINITE DEFORMATION ELASTIC CIRCULAR ROD

A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.     

若干高维可积和不可积模型的严格解

可积和不可积模型可以描述自然科学中的诸多现象, 寻找高维非线性模型的严格解已成为可积系统的一个重要研究内容. 结合达布变换法和多线性分离变量法, 可以得到多个(2+1)维非线性模型包含任意函数的严格解, 通过选取不同的任意函数, 构造这些非线性模型新的相互激发模式. 进一步推广了形变映射理论, 建立了变系数 场和sine-Gordon以及双sine-Gordon场的形变映射关系, 从而得到高维不可积模型包含任意函数的新严格解. 对任意函数的不同选择, 构造了sine-Gordon和双sine-Gordon可积模型丰富的局域解和周期解, 如多solitoff解及其周期波推广、周期形变的蛇形孤波解以及变模的拟周期解等.     

小实验大道理 ——从热缩片小制品DIY看高分子材料的熵致形变

A little experiment concerning the pyrocondensation materials was introduced in this paper. The aim was to help the public understand the principles of entropy induced deformation of polymer materials.     

转动中的材料形变检测方法探讨

扇叶因转动会产生形变,引起形变的参数主要由扇叶的形状以及旋转速度构成。本文主要介绍了寻找转动中材料形变的相应规律而设计的一系列实验及实验成果展示。不同于现有的观测方式,实验创新性地运用光学锁相成像技术获得的周期运动物体的准静态图像来定量测量形变程度,分析并找出相应规律,极大地降低了测试成本,在工程设计、产品检测等方面有着积极重要的意义。