Surface tension of membranes depending on the boundary shape

Abstract

In this paper, we study the boundary effect on the surface (or frame) tension of elastic membrane surface models. The frame tension generally depends only on the projected area of the boundary over which the surface spans. However, from a spin model analogy, the frame tension is expected to be dependent also on the boundary shape at the continuous transition point. We confirm this expectation using the following fixed-connectivity and tethered surface models: the surface model of Helfrich and Polyakov and a surface model with deficit angle term. We also discuss the reason why this expectation is worthwhile to study.

arXiv comment19 pages, 7 figures

References in corpus (15)

• The Statistical Mechanics of Membranes
• The Theory of Dynamical Random Surfaces with Extrinsic Curvature
• Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size
• Anisotropic surface tension of buckled fluid membrane
• First-order transition of tethered membranes in 3d space
• Modeling and Simulation of Liquid Crystal Elastomers
• Modeling elastic instabilities in nematic elastomers
• First order phase transitions in polymerized phantom membranes
• Polymerized Membranes, a Review
• Finsler geometry modeling and Monte Carlo study of 3D liquid crystal elastomer
• Universal behavior of crystalline membranes: crumpling transition and Poisson ratio of the flat phase
• Phase transition of surface models with intrinsic curvature
• Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime
• Monte Carlo studies of triangulated spherical surfaces in the two-dimensional space
• Dependence of the surface tension on the shape of surface boundary