Membranes

Inclusions on a membrane

red ball Helfrich energy of a membrane with surface tension and bending rigidity:

yellow ball There is considerable literature on the fluctuation-induced interactions between objects on such membrane:

M. Goulian, R. Bruinsma and P. Pincus, Euro. Phys. Lett. 22, 145 (1993)

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E. Noruzifar, J. Wagner, R. Zandi, arXiv:1306.4718 (2013)

yellow ball General form of the interaction for particles of dimension a has the form:

Composition fluctuations of a membrane

red ball Lipid mixtures composing a membrane can exhibit composition fluctuations, possibly poised close to an Ising critical point.

yellow ball The resulting fluctuation-induced interactions are determined (at large separation) by appropriate critical exponents:

B.B. Machta, S.L. Veatch, and J.P. Sethna, Phys. Rev. Lett. 109, 138101 (2012) (circles)

O. A. Vasilyev, E. Eisenriegler, and S. Dietrich, arXiv:1304.4220 (2013) (needles)

yellow ball Appealing to conformal invariance at two dimensional criticality, interactions can be computed for arbitrary shapes:

G. Bimonte, T. Emig, and M. Kardar, arXiv:1307.3993 (2013) (any shape)