Phase Transition of a Skeleton Model for Surfaces

Koibuchi, Hiroshi

doi:10.1007/11816102_24

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…Meshwork models in [23,24] has no vertex inside the compartments, which have finite size n. The phase structure of such meshwork model of finite n is considered to be dependent on the elasticity of junctions [23,24]. Therefore, it is interesting to study the dependence of the surface fluctuation transition on n in the meshwork model, where the elasticity of junctions is identical to that in the model of this Letter.…”

Section: Discussionmentioning

confidence: 99%

Phase structure of a spherical surface model on fixed connectivity meshes

Koibuchi¹

2007

Physics Letters A

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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.

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Section: Discussionmentioning

confidence: 99%

Phase structure of a spherical surface model on fixed connectivity meshes

Koibuchi¹

2007

Physics Letters A

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“…The chains in our model share the two-dimensional Gaussian bond potential S 1 and the two-dimensional bending energy S J at the boundaries, which are the junctions. However, the two-dimensional S 1 seems to play no significant role in the transition, because a skeleton surface model with a one-dimensional bond potential also undergoes a phase transition [26]. It is expected that the skeleton surface model has a phase transition even without S 1 as in HPK model [17].…”

Section: Discussionmentioning

confidence: 99%

Phase Transition of Triangulated Spherical Surfaces with Elastic Skeletons

Koibuchi

2007

J Stat Phys

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A first-order transition is numerically found in a spherical surface model with skeletons, which are linked to each other at junctions. The shape of the triangulated surfaces is maintained by skeletons, which have a one-dimensional bending elasticity characterized by the bending rigidity b, and the surfaces have no two-dimensional bending elasticity except at the junctions. The surfaces swell and become spherical at large b and collapse and crumple at small b. These two phases are separated from each other by the first-order transition. Although both of the surfaces and the skeleton are allowed to self-intersect and, hence, phantom, our results indicate a possible phase transition in biological or artificial membranes whose shape is maintained by cytoskeletons.

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Section: Introductionmentioning

confidence: 99%

“…Following to these considerations, we studied a meshwork model in [31] and reported some preliminary results on the phase structure. In this paper, we study two types of meshwork models including the one in [31] on relatively large sized surfaces. The first model in this paper is characterized by elastic junctions and is identical to the model in [31], while the second model is characterized by rigid junctions, which are hexagonal (or pentagonal) rigid plates.…”

Section: Introductionmentioning

confidence: 99%

Phase Transition of Meshwork Models for Spherical Membranes

Koibuchi

2007

J Stat Phys

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We have studied two types of meshwork models by using the canonical Monte Carlo simulation technique. The first meshwork model has elastic junctions, which are composed of vertices, bonds, and triangles, while the second model has rigid junctions, which are hexagonal (or pentagonal) rigid plates. Two-dimensional elasticity is assumed only at the elastic junctions in the first model, and no two-dimensional bending elasticity is assumed in the second model. Both of the meshworks are of spherical topology. We find that both models undergo a first-order collapsing transition between the smooth spherical phase and the collapsed phase. The Hausdorff dimension of the smooth phase is H ≃ 2 in both models as expected. It is also found that H ≃ 2 in the collapsed phase of the second model, and that H is relatively larger than 2 in the collapsed phase of the first model, but it remains in the physical bound, i.e., H < 3. Moreover, the first model undergoes a discontinuous surface fluctuation transition at the same transition point as that of the collapsing transition, while the second model undergoes a continuous transition of surface fluctuation. This indicates that the phase structure of the meshwork model is weakly dependent on the elasticity at the junctions.

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Phase Transition of a Skeleton Model for Surfaces

Cited by 3 publications

References 18 publications

Phase structure of a spherical surface model on fixed connectivity meshes

Phase structure of a spherical surface model on fixed connectivity meshes

Phase Transition of Triangulated Spherical Surfaces with Elastic Skeletons

Phase Transition of Meshwork Models for Spherical Membranes

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