微/纳米曲面的曲率和曲率梯度诱发的驱动力研究

项目名称： 微/纳米曲面的曲率和曲率梯度诱发的驱动力研究

项目编号： No.11272175

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 殷雅俊

作者单位： 清华大学

项目金额： 82万元

中文摘要： 本项目探索微/纳米曲面上独特的驱动力机制- - 由曲率和曲率梯度诱发的几何驱动力。申请人以两类现象- - 即生物膜纳米管上的输运现象和微米锥面上的液滴定向运动现象- - 为研究背景,以微/纳米尺度上普遍存在的短程相互作用为物理基础，以卷曲空间上的微分（Riemann）几何为几何形式，探索微/纳米曲面力学。拟达成如下研究目标：（1）揭示两类现象背后共同的空间形式和物理本质；（2）提出以曲率和曲率梯度为要素的几何驱动力概念，实证几何驱动力在微/纳米曲面上的普遍存在性；（3）澄清粒子与曲面相互作用的基本模式，实现"粒子/曲面"相互作用势的曲率化；（4）基于曲率化作用势和几何驱动力，实现微/纳米曲面力学的几何化；（5）证实如下命题：微/纳米曲面力学中的尺度效应，主要是由空间卷曲诱导的几何效应；微分（Riemann）几何化的微/纳米曲面力学，是大、小尺度上统一的力学，是自然而然地实现了跨尺度的力学。

中文关键词： 微/纳米曲面；曲率；曲率梯度；驱动力；

英文摘要： This project is confined to the unique driving mechanism on micro/nano curved surfaces - - the geometric driving force induced by curvatures and curvature gradients. The transportations on biomembrane nanotubes and the spontenious directional movements of droplets on micro conic tubes form the background of the research. The short-range interactions existing universally in micro/nano scales is taken as the physical basement, and the differential (Riemann) geometry in curved spaces is selected as the geometrical framework. On the above basements the mechanics on micro/nano curved surfaces is explored. The following objectives are approached. (1) The unified space form and unified phisical mechanism for the transportation on biomembrane nanotubes and the spontenious directional movements of droplets on micro conic tubes are revealed. (2) The concept of geometrical driving forces induced by curvatures and curvature gradients is defined. The universal existence of geometrical driving forces on micro/nano curved surfaces is confirmed. (3) The foundmental modes of the interactions between particles and curved surfaces are clearified. The curcature-based potentials for "particle/curved surface" interactions are derived. (4) Based on the curvature-baed potentials and the geometrical driving forces, the geometrilization

英文关键词： micro/nano curved surfaces；curvatures；curvature gradients；driving forces；