关于将飞秒脉冲激光用于纳米金属薄膜传导系统的研究

发布时间：2018-05-23 21:55

本文选题：飞秒脉冲 + 激光　；参考：《工程数学学报》2017年01期

【摘要】：本文是利用渐近方法求解一类飞秒脉冲激光纳米金属薄膜传导非线性扰动系统,并讨论该非线性系统对应解的渐近性态.首先,求出了退化问题的解.其次,构造一个泛函,计算它的广义变分,令其变分为零.从而得到了Lagrange乘子.然后利用变分原理,构造出一个广义变分迭代式.因此,可依次求出相应系统解任意次精度的渐近展开式.同时,利用泛函分析变分原理,论述了相应展开式的一致收敛性.并举出了相应的例子,得到了它的渐近解并通过模拟方法给出了其解的曲而图形.通过本文的研究,证实了对纳米金属薄膜传导这类非线性扰动系统的求解方法简单有效,并具有一般意义和广泛的应用前景.
[Abstract]:In this paper, the asymptotic method is used to solve a class of nonlinear perturbation systems induced by femtosecond pulsed laser nanometallic thin films, and the asymptotic behavior of the corresponding solutions of the nonlinear systems is discussed. First, the solution of the degenerate problem is obtained. Secondly, a functional is constructed and its generalized variation is calculated so that its variation is zero. The Lagrange multiplier is obtained. Then a generalized variational iteration is constructed by using the variational principle. Therefore, the asymptotic expansions of the corresponding system for arbitrary order accuracy can be obtained in turn. At the same time, the uniform convergence of the corresponding expansions is discussed by using the variational principle of functional analysis. An example is given, its asymptotic solution is obtained and the curve and graph of its solution are given by means of simulation. Through the research in this paper, it is proved that the method of solving the nonlinear perturbation system such as nanometallic thin film conduction is simple and effective, and has general significance and wide application prospect.
【作者单位】：亳州学院电子与信息工程系;南京信息工程大学数学与统计学院;安徽师范大学数学系;
【基金】：国家自然科学基金(11202106) 安徽省教育厅自然科学基金(KJ2015A347;KJ2015A418;KJ20138153) 安徽省高校优秀青年人才支持重点项目(gxyqZD2016520)~~
【分类号】：O175

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