Fractal and nonfractal shapes in two-dimensional vesicles

doi:10.1016/0167-2789(89)90180-2

Physica D: Nonlinear Phenomena

Volume 38, Issues 1–3, September 1989, Pages 112-118

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Abstract

Ongoing collaborative work on the statistical mechanics of two-dimensional vesicles is reviewed with emphasis on the range of fractal and nonfractal shapes exhibited by the bead-and-tether model of a closed membrane which also embodies an osmotic pressure difference, Δp, and a bending rigidity modulus, κ; Monte Carlo simulations and scaling analyses are described. Flaccid vesicles, with Δp=κ=0, represent closed self-avoiding rings; their mean area, 〈A〉, scales with the mean square size, 〈R_G²〉; their mean shape is close to elliptical. Inflated, Δp > 0 vesicles become circular; deflated, Δp<0 vesicles collapse to form branched polymers. The vesicle shapes appear to vary continuously with the scaling combination ΔpN^2ν, where N is the number of monomers/beads and $ν= 34$ . For Δp <0 and $κ K_{B} T$ large relative to N³ a range of characteristic nonfractal shapes or cytotypes appears.

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Fractal and nonfractal shapes in two-dimensional vesicles

Abstract

Nucl. Phys. B (Proc. Suppl.)

J. Math. Chem.

Phys. Rev. Lett.

Phys. Rev. Lett.

J. Phys. A