Phase structure of a spherical surface model on fixed connectivity meshes

Abstract

An elastic surface model is investigated by using the canonical Monte Carlo simulation technique on triangulated spherical meshes. The model undergoes a first-order collapsing transition and a continuous surface fluctuation transition. The shape of surfaces is maintained by a one-dimensional bending energy, which is defined on the mesh, and no two-dimensional bending energy is included in the Hamiltonian.

Non-trivial effect of the in-plane shear elasticity on the phase transitions of fixed-connectivity meshwork models

“…The result indicates that the transition of surface fluctuations is of first-order, because ν almost satisfies ν = 1. This is a remarkable result distinguishing model 1 in this paper from the model in [18], where the transition of surface fluctuations is reported to be of second-order. Therefore, we understand that the in-plane shear elasticity strengthens the transition of surface fluctuations in the surface model with one-dimensional bending energy.…”

“…The linear surface of the model in [19] consists of oblong surfaces, and the planar surface consists of both regular triangles and oblong ones. No energy cost is necessary for the in-plane deformations in both of the models in [18,19]. For this reason, we expect that the in-plane energy makes a nontrivial effect on the transitions.…”

“…In this article, we have investigated how the in-plane shear elasticity influences the transitions observed in two-types of the meshwork models in [18] and [19]. The models are described as follows: The surface shape of the first model in [18] is maintained by a one-dimensional bending energy and by the Gaussian bond potential, while the surface shape of the second model in [19] is maintained by the one-dimensional bending energy and by the Nambu-Goto potential. One of the transitions in the model of [18] is called the collapsing transition, which is of first-order and separates the smooth phase from the collapsed phase at finite bending rigidity.…”

“…The models are described as follows: The surface shape of the first model in [18] is maintained by a one-dimensional bending energy and by the Gaussian bond potential, while the surface shape of the second model in [19] is maintained by the one-dimensional bending energy and by the Nambu-Goto potential. One of the transitions in the model of [18] is called the collapsing transition, which is of first-order and separates the smooth phase from the collapsed phase at finite bending rigidity. The other is a continuous one called the transition of surface fluctuations.…”

“…The well-definedness of the model in [19] is due to the onedimensional bending energy, and a variety of shapes makes the model very different from the conventional ones in [10], which have only the smooth phase and the collapsed phase. The models in [18,19] are also different form the surface models with cytoskeletal structures in [21,22], because the length L between the junctions of the models in [18,19] is L = 1 in the unit of bond length while that of the models in [21,22] is L > 1.…”