Internal phase transition induced by external forces in Finsler geometric model for membranes

Hiroshi Koibuchi and Andrey Shobukhov
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Hiroshi Koibuchi: Department of Mechanical and Systems Engineering, National Institute of Technology, Ibaraki College, Nakane 866 Hitachinaka, Ibaraki 312-8508, Japan
Andrey Shobukhov: #x2020;Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Leninskiye Gory, MSU, 2-nd Educational Building, Russia

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 04, 1-15

Abstract: In this paper, we numerically study an anisotropic shape transformation of membranes under external forces for two-dimensional triangulated surfaces on the basis of Finsler geometry. The Finsler metric is defined by using a vector field, which is the tangential component of a three-dimensional unit vector σ corresponding to the tilt or some external macromolecules on the surface of disk topology. The sigma model Hamiltonian is assumed for the tangential component of σ with the interaction coefficient λ. For large (small) λ, the surface becomes oblong (collapsed) at relatively small bending rigidity. For the intermediate λ, the surface becomes planar. Conversely, fixing the surface with the boundary of area A or with the two-point boundaries of distance L, we find that the variable σ changes from random to aligned state with increasing of A or L for the intermediate region of λ. This implies that an internal phase transition for σ is triggered not only by the thermal fluctuations, but also by external mechanical forces. We also find that the frame (string) tension shows the expected scaling behavior with respect to A∕N (L∕N) at the intermediate region of A (L) where the σ configuration changes between the disordered and ordered phases. Moreover, we find that the string tension γ at sufficiently large λ is considerably smaller than that at small λ. This phenomenon resembles the so-called soft-elasticity in the liquid crystal elastomer, which is deformed by small external tensile forces.

Keywords: Triangulated surfaces; Finsler geometry; membranes; Monte Carlo simulations (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S012918311650042X

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