Phase transition of compartmentalized surface models

Koibuchi, Hiroshi

doi:10.1140/epjb/e2007-00170-y

Cited by 6 publications

(11 citation statements)

References 32 publications

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“…We find also from the results in Figs.4(a) and 4(b) that the phase transition is not reflected in S 1 /N in contrast to the fluid surface model in Ref. [30], where S 1 /N discontinuously changes at the transition point. The mean square size X 2 is defined by…”

Section: Monte Carlo Techniquesupporting

confidence: 59%

“…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%

“…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: 97%

“…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].…”

Section: Introductionmentioning

confidence: 98%

“…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 Techniquesupporting

confidence: 59%

Section: Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

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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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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Shape transformation transitions of a tethered surface model

Koibuchi

2007

Eur. Phys. J. B

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A surface model of Nambu and Goto is studied statistical mechanically by using the canonical Monte Carlo simulation technique on a spherical meshwork. The model is defined by the area energy term and a one-dimensional bending energy term in the Hamiltonian. We find that the model has a large variety of phases; the spherical phase, the planar phase, the long linear phase, the short linear phase, the wormlike phase, and the collapsed phase. Almost all two neighboring phases are separated by discontinuous transitions. It is also remarkable that no surface fluctuation can be seen in the surfaces both in the spherical phase and in the planar phase. PACS. 64.60.-i General studies of phase transitions -68.60.-p Physical properties of thin films, nonelectronic -87.16.Dg Membranes, bilayers, and vesicles

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Phase transition of compartmentalized surface models

Cited by 6 publications

References 32 publications

Phase Transition of Meshwork Models for Spherical Membranes

Phase Transition of Meshwork Models for Spherical Membranes

Phase structure of a spherical surface model on fixed connectivity meshes

Shape transformation transitions of a tethered surface model

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