Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling
We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping r from a two-dimensional parameter space M to the three-dimensional Euclidean space R 3 . The metric variable g a b , which is always fixed to the Eu...
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MDPI AG
2017-04-01
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| Series: | Axioms |
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| Online Access: | http://www.mdpi.com/2075-1680/6/2/10 |
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| author | Evgenii Proutorov Hiroshi Koibuchi |
| author_facet | Evgenii Proutorov Hiroshi Koibuchi |
| author_sort | Evgenii Proutorov |
| collection | DOAJ |
| description | We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping r from a two-dimensional parameter space M to the three-dimensional Euclidean space R 3 . The metric variable g a b , which is always fixed to the Euclidean metric δ a b , 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. |
| first_indexed | 2024-12-10T05:21:19Z |
| format | Article |
| id | doaj.art-92483ff9c3354c2884a1cbba63f42c00 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-10T05:21:19Z |
| publishDate | 2017-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-92483ff9c3354c2884a1cbba63f42c002022-12-22T02:00:47ZengMDPI AGAxioms2075-16802017-04-01621010.3390/axioms6020010axioms6020010Orientation Asymmetric Surface Model for Membranes: Finsler Geometry ModelingEvgenii Proutorov0Hiroshi Koibuchi1Department of Physics, Cherepovets State University, Pr. Lunacharskii 5, Cherepovets 162600, RussiaNational Institute of Technology, Ibaraki College, Nakane 866, Hitachinaka, Ibaraki 312-8508, JapanWe study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping r from a two-dimensional parameter space M to the three-dimensional Euclidean space R 3 . The metric variable g a b , which is always fixed to the Euclidean metric δ a b , 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.http://www.mdpi.com/2075-1680/6/2/10triangulated surface modelmembranesHelfrich and Polyakovnon-Euclidean metricFinsler geometrydirection-dependent lengthorientation symmetry/asymmetry |
| spellingShingle | Evgenii Proutorov Hiroshi Koibuchi Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling Axioms triangulated surface model membranes Helfrich and Polyakov non-Euclidean metric Finsler geometry direction-dependent length orientation symmetry/asymmetry |
| title | Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling |
| title_full | Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling |
| title_fullStr | Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling |
| title_full_unstemmed | Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling |
| title_short | Orientation Asymmetric Surface Model for Membranes: Finsler Geometry Modeling |
| title_sort | orientation asymmetric surface model for membranes finsler geometry modeling |
| topic | triangulated surface model membranes Helfrich and Polyakov non-Euclidean metric Finsler geometry direction-dependent length orientation symmetry/asymmetry |
| url | http://www.mdpi.com/2075-1680/6/2/10 |
| work_keys_str_mv | AT evgeniiproutorov orientationasymmetricsurfacemodelformembranesfinslergeometrymodeling AT hiroshikoibuchi orientationasymmetricsurfacemodelformembranesfinslergeometrymodeling |