Phase transitions of a tethered membrane model on a torus with intrinsic curvature

Endo, Isao; Koibuchi, Hiroshi

doi:10.1016/j.physleta.2005.11.001

Cited by 12 publications

(24 citation statements)

References 45 publications

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“…The model was known as the one that undergoes a first-order crumpling transition without the boundary condition [39,40,41]. This paper aimed to show how boundary conditions influence the phase transition, and we performed extensive MC simulations on the spherical tethered surfaces up to a size N = 8412.…”

Section: Discussionmentioning

confidence: 99%

“…Studies have also focused on the phase structure of the model with intrinsic curvature [37,38,39,40,41]. It has been shown that the first-order transition can be seen in spherical fluid/tethered surfaces [38,39], tethered surface of disk topology [40], and tethered surface with torus topology [41].…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown that the first-order transition can be seen in spherical fluid/tethered surfaces [38,39], tethered surface of disk topology [40], and tethered surface with torus topology [41].…”

Section: Introductionmentioning

confidence: 99%

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Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries

Koibuchi¹

2006

J. Stat. Mech.

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Abstract. We found that the order for the crumpling transition of an intrinsic curvature model changes depending on the distance between two boundary vertices fixed on the surface of spherical topology. The model is a curvature one governed by an intrinsic curvature energy, which is defined on triangulated surfaces. It was already reported that the model undergoes a first-order crumpling transition without the boundary conditions on the surface. However, the dependence of the transition on such boundary condition is yet to be studied. We have studied in this paper this problem by using the Monte Carlo simulations on surfaces up to a size N = 8412. The first-order transition changes to a second-order one if the distance increases.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries

Koibuchi¹

2006

J. Stat. Mech.

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“…Tethered surface models are defined on triangulated fixed connectivity surfaces representing polymerized biological membranes or membranes in the gel phase [7], and they are classified into a major class of the HPK model [15,16,17,18,19,20,21,22,23,24,25,26]. Fluid surface models are considered a different class of the HPK model defined on dynamically triangulated surfaces representing these biological membranes in the fluid phase, however, we will not discuss the fluid surface model in this paper [27,28,29,30,31,32,33,34].…”

Section: Introductionmentioning

confidence: 99%

First-order phase transition of the tethered membrane model on spherical surfaces

Endo

Koibuchi

2006

Nuclear Physics B

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We found that three types of tethered surface model undergo a first-order phase transition between the smooth and the crumpled phase. The first and the third are discrete models of Helfrich, Polyakov, and Kleinert, and the second is that of Nambu and Goto. These are curvature models for biological membranes including artificial vesicles. The results obtained in this paper indicate that the first-order phase transition is universal in the sense that the order of the transition is independent of discretization of the Hamiltonian for the tethered surface model.

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“…A further issue we consider is whether spherically symmetric electrostatic interactions are capable to break translational, rotational or chiral isometries of the cylinder. Recently, there has been interest to study crystalline systems over constrained geometries such as the surface of spheres, cylinders, and tori [24,25,26]. The generalization to more general curved substrates shows an interesting rich behavior [27].…”

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Spontaneous Chirality via Long-Range Electrostatic Forces

et al. 2007

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We consider a model for periodic patterns of charges constrained over a cylindrical surface. In particular we focus on patterns of chiral helices, achiral rings or vertical lamellae, with the constraint of global electroneutrality. We study the dependence of the patterns' size and pitch angle on the radius of the cylinder and salt concentration. We obtain a phase diagram by using numerical and analytic techniques. For pure Coulomb interactions, we find a ring phase for small radii and a chiral helical phase for large radii. At a critical salt concentration, the characteristic domain size diverges, resulting in macroscopic phase segregation of the components and restoring chiral symmetry. We discuss possible consequences and generalizations of our model. [7,8]. A considerable aspect of these systems is the presence of surface charge heterogeneities or domains [9,10], which arises from the competition of electrostatic forces with segregating forces such as steric, van der Waals, and hydrogen bonding interactions. These surface patterns have been shown to be important for the stability and functionality of the aggregates [2,11,12,13].A key feature in many biological processes is pattern recognition and specificity within isomeric aggregates [14]. Biomolecules exploit repetitive patterning over surfaces, which often breaks some underlying symmetry, in order to increase their functionality [15]. In this context, chiral symmetry (that is the absence of improper rotation axis) is notably interesting: although its role in chemistry and biology is widely recognized [2,16,17,18], its origin in biology is the subject of much debate [19]. Many systems are chiral due to the chirality of its components [19,20]. For instance, colloidal solutions of rodlike viruses provide an intriguing example of chiral structures in liquid crystalline phases [21]. Nevertheless, understanding whether electrostatic interactions alone are capable of producing chiral systems would shed further light on the issue.From a theoretical vantage point, the electrostatic patterning of a system of charges on cylindrical surfaces is however relatively unexplored. Certainly, the effects of long-range electrostatic forces have been widely studied for planar two dimensional systems [22]; also the behavior of short-range interactions over cylindrical geometries has been addressed, such as the Ising model on the cylinder [23]. We analyze here an intermediate case where charges are confined over a cylindrical surface and interact via long-range forces. A further issue we consider is whether spherically symmetric electrostatic interactions are capable to break translational, rotational or chiral isometries of the cylinder. Recently, there has been interest to study crystalline systems over constrained geometries such as the surface of spheres, cylinders, and tori [24,25,26]. The generalization to more general curved substrates shows an interesting rich behavior [27].In this Letter we provide the full phase diagram of lamellar charged patterns on a cylinder, as a...

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Phase transitions of a tethered membrane model on a torus with intrinsic curvature

Abstract: A tethered surface model is investigated by using the canonical Monte Carlo simulation technique on a torus with an intrinsic curvature. We find that the model undergoes a first-order phase transition between the smooth phase and the crumpled one.

Cited by 12 publications

References 45 publications

Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries

Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries

First-order phase transition of the tethered membrane model on spherical surfaces

Spontaneous Chirality via Long-Range Electrostatic Forces

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