Closed, Two Dimensional Surface Dynamics

Frontiers in Physics

Svintradze, David V.¹ 

[1] School of Health Sciences, University of Georgia, Georgia

关键词: Shape dynamics;    Differential Geometry;    membrane dynamics;    micelles;    fluid film dynamics;   

DOI  :  10.3389/fphy.2018.00136

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

We present dynamic equations for two dimensional closed surfaces and analytically solve it for some simplified cases. We derive final equations for surface normal motions by two different ways. The solution of the equations of motions in normal direction indicates that any closed, two dimensional, homogeneous surface with time invariable surface energy density adopts constant mean curvature shape when it comes in equilibrium with environment. In addition, we show that the shape equation is an approximate solution to our equation of motion in the normal direction and is valid for stationary or near to stationary shapes. As an example, we apply the formalism to analyze equilibrium shapes of micelles and explain why they adopt spherical, lamellar and cylindrical shapes. Theoretical calculation for micellar optimal radius is in good agreement with all atom simulations and experiments.

【 授权许可】

CC BY