Applying Methods from Differential Geometry to Devise Stable and Persistent Air Layers Attached to Objects Immersed in Water

作     者：Wilfried Konrad Christian Apeltauer Jrg Frauendiener Wilhelm Barthlott Anita Roth-Nebelsick 

作者机构：Institute for Geosciences University of Tubingen D-72016 Tubingen Germany Department of Mathematics and Statistics University of Otago Dunedin 9054 New Zealand Centre of Mathematics for Applications University of Oslo NO-0317 Oslo Norway Nees Institute for Biodiversity of Plants University of Bonn D-53115 Bonn Germany State Museum of Natural History Stuttgart Rosenstein 1 D-70191 Stuttgart Germany 

出 版 物：《Journal of Bionic Engineering》 (仿生工程学报（英文版）)

年 卷 期：2009年第6卷第4期

页      面：350-356页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：funded by grants from the Deutsche Forschungsgemeinschaft the Bundesministerium für Bildung und Forschung and the Landesgraduiertenfrderungsgesetz des Landes Baden-Württemberg 

主　　题：interfaces air layers differential geometry stability persistence Salvinia 

摘      要：We describe a few mathematical tools which allow to investigate whether air-water interfaces exist(under prescribed conditions)and are mechanically stable and temporally *** terms of physics,air-water interfaces are governed by the Young-Laplace *** they are surfaces of constant mean curvature which represent solutions of a nonlinear elliptic partial differential *** explicit solutions of this equation can be obtained only in very special cases,it is -under moderately special circumstances-possible to establish the existence of a solution without actually solving the differential *** also derive criteria for mechanical stability and temporal persistence of an air *** we calculate the lifetime of a non-persistent air ***,we apply these tools to two examples which exhibit the symmetries of 2D *** examples can be viewed as abstractions of the biological model represented by the aquatic fern Salvinia.