Phase Transition of Triangulated Spherical Surfaces with Elastic Skeletons

Koibuchi, Hiroshi

doi:10.1007/s10955-007-9287-z

Cited by 8 publications

(26 citation statements)

References 26 publications

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“…We should note that the results H col of both models are in sharp contrast to that of the compartmentalized model in Ref. [29], because the compartmentalized surface is completely collapsed in the collapsed phase. The specific heat for S 2 of model 1 is defined by…”

Section: Monte Carlo Techniquecontrasting

confidence: 56%

“…Thus, the triangulated surfaces for constructing the meshwork are identical to the lattices for the surface models in [29,30]. Therefore, the size of meshwork can be characterized by the expression similar to the one for those compartmentalized surface models in [29,30].…”

Section: Modelsmentioning

confidence: 99%

“…In fact, the phase structure of skeleton models is partly understood [29,30]. The numerical results show that the phase structure of the surface fluctuation phenomenon in the fixed-connectivity conventional surface model remains almost unchanged even when the compartmentalized structure was introduced [29]. On the contrary, in a dynamically triangulated fluid surface model the phase structure considerably changes if the free diffusion of vertices is confined inside the compartments, which are introduced as an inhomogeneous structure [30].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the conventional homogeneous surface model mentioned above can be extended to an inhomogeneous one by including a cytoskeletal structure [28,29,30]. In fact, the phase structure of skeleton models is partly understood [29,30].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Monte Carlo Techniquecontrasting

confidence: 56%

Section: Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase Transition of Meshwork Models for Spherical Membranes

Koibuchi

2007

J Stat Phys

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Spherical Surface Models with Directors

Koibuchi

2009

J Stat Phys

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A triangulated spherical surface model is numerically studied, and it is shown that the model undergoes phase transitions between the smooth phase and the collapsed phase. The model is defined by using a director field, which is assumed to have an interaction with a normal of the surface. The interaction between the directors and the surface maintains the surface shape. The director field is not defined within the two-dimensional differential geometry, and this is in sharp contrast to the conventional surface models, where the surface shape is maintained only by the curvature energies. We also show that the interaction makes the Nambu-Goto model well-defined, where the bond potential is given by the area of triangles; the Nambu-Goto model is well-known as an ill-defined one even when the conventional two-dimensional bending energy is included in the Hamiltonian.

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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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Phase Transition of Triangulated Spherical Surfaces with Elastic Skeletons

Cited by 8 publications

References 26 publications

Phase Transition of Meshwork Models for Spherical Membranes

Phase Transition of Meshwork Models for Spherical Membranes

Spherical Surface Models with Directors

Phase structure of a spherical surface model on fixed connectivity meshes

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