Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling
Department of Physics, Cherepovets State University, Pr. Lunacharskii 5, Cherepovets 162600, Russia
National Institute of Technology, Ibaraki College, Nakane 866, Hitachinaka, Ibaraki 312-8508, Japan
Author to whom correspondence should be addressed.
Academic Editors: Emil Saucan and David Gu
Received: 21 March 2017 / Revised: 14 April 2017 / Accepted: 19 April 2017 / Published: 25 April 2017
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 is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Proutorov, E.; Koibuchi, H. Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling. Axioms 2017, 6, 10.
Proutorov E, Koibuchi H. Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling. Axioms. 2017; 6(2):10.
Proutorov, Evgenii; Koibuchi, Hiroshi. 2017. "Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling." Axioms 6, no. 2: 10.
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