项目名称: 纳米材料性质定量分析中的反问题
项目编号: No.11471284
项目类型: 面上项目
立项/批准年度: 2015
项目学科: 数理科学和化学
项目作者: 徐翔
作者单位: 浙江大学
项目金额: 68万元
中文摘要: 本项目致力于研究纳米材料 (nano-material) 力学性质的定量分析。纳米材料由于其结构的特殊性,在机械性能包括弹性模量、刚度等方面与传统的块状材料(bulk-material)有显著不同。由于纳米材料尺寸非常小(1-100nm),因此定量分析它们的性质也是极具挑战性的课题。本项目中,我们拟建立一个基于欧拉-伯努利方程并且带有随机源项的一个新的模型来定量分析纳米材料的力学性质,不仅可以有效地克服纳米材料制备中产生的非均一性,而且还可以去除测量工具产生的系统性误差,得到更为精确的结果。在数学上,可以将该问题看成偏微分方程反演系数及源项的反问题。因此我们借助于反问题理论与算法来对该问题的解决给予理论支持。
中文关键词: 反问题;正则化方法;参数识别;随机源项
英文摘要: In this research project, we propose to investigate mechanical properties of nanomaterials quantitatively. Due to its special structure, nanomaterials are quite different from those conventional bulk materials including elasticity,stiffness, hardness and etc. Though nanoscience and nanotechnology made a great progress in past two decades, there are still many challenges on quantifying physical properties due to its small size, non-uniformity and high level noise of measurements. In this project, we propose a novel model based on Euler-Bernoulli equation with a stochastic source to quantify mechanical properties of nano-materials, which expects more accurate results. Mathematically, the problem could be formulated as an inverse coefficient and source problem in partial differential equations. Therefore, we intend to utilize methods developed in inverse problems to deal with it. Moreover, the methods studied here could be applied for more inverse problems.
英文关键词: Inverse Problems;Regularization method;Parameter identification;random source