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曲率的形状梯度和经典梯度:微纳米曲面上的驱动力

殷雅俊 陈超 吕存景 郑泉水

殷雅俊, 陈超, 吕存景, 郑泉水. 曲率的形状梯度和经典梯度:微纳米曲面上的驱动力[J]. 应用数学和力学, 2011, 32(5): 509-521. doi: 10.3879/j.issn.1000-0887.2011.05.001
引用本文: 殷雅俊, 陈超, 吕存景, 郑泉水. 曲率的形状梯度和经典梯度:微纳米曲面上的驱动力[J]. 应用数学和力学, 2011, 32(5): 509-521. doi: 10.3879/j.issn.1000-0887.2011.05.001
YIN Ya-jun, CHEN Chao, LV Cun-jing, ZHENG Quan-shui. Shape Gradient and Classical Gradient of Curvatures: Driving Forces on Micro/Nano Curved Surfaces[J]. Applied Mathematics and Mechanics, 2011, 32(5): 509-521. doi: 10.3879/j.issn.1000-0887.2011.05.001
Citation: YIN Ya-jun, CHEN Chao, LV Cun-jing, ZHENG Quan-shui. Shape Gradient and Classical Gradient of Curvatures: Driving Forces on Micro/Nano Curved Surfaces[J]. Applied Mathematics and Mechanics, 2011, 32(5): 509-521. doi: 10.3879/j.issn.1000-0887.2011.05.001

曲率的形状梯度和经典梯度:微纳米曲面上的驱动力

doi: 10.3879/j.issn.1000-0887.2011.05.001
基金项目: 国家自然科学基金资助项目(10872114;10672089;10832005;11072125)
详细信息
    作者简介:

    殷雅俊(1964- ),男,河南人,教授,博士,博士生导师(联系人.Tel:+86-10-62795536;E-mail:yinyj@mail.tsinghua.edu.cn).

  • 中图分类号: O302;O34;O484.2

Shape Gradient and Classical Gradient of Curvatures: Driving Forces on Micro/Nano Curved Surfaces

  • 摘要: 近期的实验和分子动力学模拟均表明:圆锥面上粘附液滴能自发地定向运动,且自发定向运动的方向与粘附面的亲水、疏水性质无关.针对这一重要现象,拟从曲面微纳米力学几何化的角度,提供一般性的理论解释.借助于粒子对势,研究了孤立粒子与微纳米硬曲面之间的相互作用,分析了粒子/硬曲面相互作用的几何学基础.可以证实:(a) 粒子/硬曲面的作用势均具有统一的曲率化形式,均可以统一地表达成曲面平均曲率和Gauss曲率的函数;(b) 基于曲率化的作用势,能够实现曲面微纳米力学的几何化;(c) 曲率与曲率的内蕴梯度构成卷曲空间上的驱动力;(d) 驱动力方向与曲面的亲水、疏水性质无关,解释了自发定向运动实验.
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出版历程
  • 收稿日期:  2010-11-18
  • 修回日期:  2011-03-14
  • 刊出日期:  2011-05-15

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