Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling
Open Access
- 25 April 2017
- Vol. 6 (2), 10
- https://doi.org/10.3390/axioms6020010
Abstract
We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping from a two-dimensional parameter space M to the three-dimensional Euclidean space . The metric variable , which is always fixed to the Euclidean metric , can be extended to a more general non-Euclidean metric on M in the continuous model. The problem we focus on in this paper is whether such an extension is well defined or not in the discrete model. We find that a discrete surface model with a nontrivial metric becomes well defined if it is treated in the context of Finsler geometry (FG) modeling, where triangle edge length in M depends on the direction. It is also shown that the discrete FG model is orientation asymmetric on invertible surfaces in general, and for this reason, the FG model has a potential advantage for describing real physical membranes, which are expected to have some asymmetries for orientation-changing transformations.
This publication has 28 references indexed in Scilit:
- Finsler Geometry Modeling of Phase Separation in Multi-Component MembranesPolymers, 2016
- Monte Carlo studies of a Finsler geometric surface modelPhysica A: Statistical Mechanics and its Applications, 2014
- Self-Contact and Instabilities in the Anisotropic Growth of Elastic MembranesPhysical Review Letters, 2010
- Polymorphism of vesicles with multi-domain patternsSoft Matter, 2009
- Membrane Simulation Models from Nanometer to Micrometer ScaleJournal of the Physics Society Japan, 2009
- Theory of the thermal magnetocapacitance of multicomponent silicate glasses at low temperaturePhilosophical Magazine, 2004
- Fluctuating nematic elastomer membranesPhysical Review E, 2003
- The statistical mechanics of membranesPhysics Reports, 2001
- Landau Theory of the Crumpling TransitionPhysical Review Letters, 1988
- Phase transitions in flexible polymeric surfacesPhysical Review A, 1987