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中国工业与应用数学学会会刊
主管:中华人民共和国教育部
主办:西安交通大学
ISSN 1005-3085  CN 61-1269/O1

工程数学学报 ›› 2017, Vol. 34 ›› Issue (1): 13-20.doi: 10.3969/j.issn.1005-3085.2017.01.002

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关于将飞秒脉冲激光用于纳米金属薄膜传导系统的研究

冯依虎1,   石兰芳2,   莫嘉琪3   

  1. 1- 亳州学院电子与信息工程系,安徽  亳州  236800
    2- 南京信息工程大学数学与统计学院,江苏  南京  210044
    3- 安徽师范大学数学系,安徽  芜湖  241003
  • 收稿日期:2015-06-16 接受日期:2015-11-23 出版日期:2017-02-15 发布日期:2017-04-15
  • 基金资助:
    国家自然科学基金(11202106);安徽省教育厅自然科学基金(KJ2015A347; KJ2015A418; KJ2013B153);安徽省高校优秀青年人才支持重点项目(gxyqZD2016520).

Study of Transfers System for Femtosecond Pulse Laser to Nano Metal Film

FENG Yi-hu1,   SHI Lan-fang2,   MO Jia-qi3   

  1. 1- Department of Electronics and Information Engineering, Bozhou College, Bozhou, Anhui 236800
    2- College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu 210044
    3- Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241003
  • Received:2015-06-16 Accepted:2015-11-23 Online:2017-02-15 Published:2017-04-15
  • Supported by:
    The National Natural Science Foundation of China (11202106); the Natural Science Foundation of the Education Department of Anhui Province (KJ2015A347; KJ2015A418; KJ2013B153); the Key Projects of Outstanding Young Talents of Universities of Anhui Province (gxyqZD2016520).

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面图形.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.

关键词: 飞秒脉冲, 激光, 渐近分析

Abstract:

The solution to a class of nonlinear disturbed transfers system for the femtosecond pulse laser to Nano metal film is obtained by using the asymptotic method. The asymptotic behaviors of corresponding solution to this nonlinear system are discussed. Firstly, the outer solution to the reduced problem is solved. Next, a functional is constructed and its generalized variational is calculated, with its variational equivalent to zero. Thus the Lagrange multiplicator is found. Then, a generalized varitational iteration expansion is constructed by using the varitational principle. Therefore, arbitrary times of iteration expansions for the corresponding system can be solved successively. At the same time, the uniform convergence to the related expansion is accounted by using the variational theory of functional analytic. An example is enumerated, and by using the simulation method, the graphs of surface for its solution are given. From the results obtained in this study, it is validated that the solving method for nonlinear disturbed transfers system to Nano metal film can be provided in a simple and valid manner by using the generalized variational iteration. And it also has a general theoretical value and a wide application potential.

Key words: femtosecond pulse, laser, asymptotic analysis

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