Area-constrained planar elastica

Arreaga, Guillermo; Capovilla, Riccardo; Chryssomalakos, Chryssomalis; Guven, Jemal

doi:10.1103/physreve.65.031801

Cited by 62 publications

(100 citation statements)

References 24 publications

(25 reference statements)

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“…The fields we consider are the local composition and the local curvature of the membrane [11][12][13]. These couple through the composition-dependent material properties [14][15][16][17][18], which dictate the energetics of bending and stretching the membrane.…”

Section: B Simulation Modelmentioning

confidence: 99%

Competition between line tension and curvature stabilizes modulated phase patterns on the surface of giant unilamellar vesicles: A simulation study

2013

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When prepared in the liquid-liquid coexistence region, the four component lipid system distearoyl-phosphatidylcholine (DSPC)/dioleoyl-phosphatidylcholine (DOPC)/palmitoyl,oleoylphosphatidylcholine (POPC)/Cholesterol with certain ratios of DOPC and POPC shows striking modulated phase patterns on the surface of giant unilamellar vesicles (GUVs). In this simulation study we show that the morphology of these patterns can be explained by the competition of line tension (which tends to favor large round domains) and curvature, as specified by the Helfrich energy functional. In this study we use a Monte-Carlo simulation on the surface of a GUV to determine the equilibrium shape and phase morphology. We find that the patterns arising from these competing interactions very closely approximate those observed, the patterned morphologies represent thermodynamically stable configurations, and that the geometric nature of these patterns is closely tied to the relative and absolute values of the model parameters.

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Section: B Simulation Modelmentioning

confidence: 99%

Competition between line tension and curvature stabilizes modulated phase patterns on the surface of giant unilamellar vesicles: A simulation study

2013

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“…One would expect to require two integrations of the curvature to reconstruct the corresponding loop; remarkably, none is needed. This was shown in [16]. Here, it will be shown how this comes about using the conservation of the effective stress.…”

Section: An Identity For Rigid Loops Enclosing a Fixed Areamentioning

confidence: 82%

“…The 'σ' identities which were identified in [16] are reproduced in a very direct way. The latter of the two identities implies that…”

Section: An Identity For Rigid Loops Enclosing a Fixed Areamentioning

confidence: 85%

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Laplace pressure as a surface stress in fluid vesicles

Guven

2006

J. Phys. A: Math. Gen.

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Consider a surface, enclosing a fixed volume, described by a free-energy depending only on the local geometry; for example, the Canham-Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on the surface is determined completely by geometry. In equilibrium, its divergence is proportional to the Laplace pressure, normal to the surface, maintaining the constraint on the volume. It is shown that this source itself can be expressed as the divergence of a positiondependent surface stress. As a consequence, the equilibrium can be described in terms of a conserved effective surface stress. Various non-trivial geometrical consequences of this identification are explored. In a cylindrical geometry, the cross-section can be viewed as a closed planar Euler elastic curve. With respect to an appropriate centre the effective stress itself vanishes; this provides a remarkably simple relationship between the curvature and the position along the loop. In two or higher dimensions, it is shown that the only geometry consistent with the vanishing of the effective stress is spherical. It is argued that the appropriate generalization of the loop result will involve null stresses.

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“…Explicit equations in the case of fluid membranes are presented. In section (4), we use the alternative method introducing auxiliary variables to regain the Euler-Lagrange equations of section (2). The equations of elastic curves in presence of long range forces, constrained to surfaces are presented.…”

Section: Introductionmentioning

confidence: 99%

Elastic Curves and Surfaces Under Long-Range Forces: A Geometric Approach

Santiago

Chacón‐Acosta

González-Gaxiola

2013

Int. J. Mod. Phys. B

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Using classical differential geometry, the problem of elastic curves and surfaces in the presence of long-range interactions Φ, is posed. Starting from a variational principle, the balance of elastic forces and the corresponding projections n i · ∇Φ, are found. In the case of elastic surfaces, a force coupling the mean curvature with the external potential, KΦ, appears; it is also present in the shape equation along the normal principal in the case of curves. The potential Φ contributes to the effective tension of curves and surfaces and also to the orbital torque. The confinement of a curve on a surface is also addressed, in such a case, the potential contributes to the normal force through the terms −κΦ−n·∇Φ. In general, the equation of motion becomes integro-differential that must be numerically solved.

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Area-constrained planar elastica

Cited by 62 publications

References 24 publications

Competition between line tension and curvature stabilizes modulated phase patterns on the surface of giant unilamellar vesicles: A simulation study

Competition between line tension and curvature stabilizes modulated phase patterns on the surface of giant unilamellar vesicles: A simulation study

Laplace pressure as a surface stress in fluid vesicles

Elastic Curves and Surfaces Under Long-Range Forces: A Geometric Approach

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