Balancing torques in membrane-mediated interactions: Exact results and numerical illustrations
Abstract
Torques on interfaces can be described by a divergence-free tensor which is fully encoded in the geometry. This tensor consists of two terms, one originating in the couple of the stress, the other capturing an intrinsic contribution due to curvature. In analogy to the description of forces in terms of a stress tensor, the torque on a particle can be expressed as a line integral along any contour surrounding the particle. Interactions between particles mediated by a fluid membrane are studied within this framework. In particular, torque balance places a strong constraint on the shape of the membrane. Symmetric two-particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime; in particular, the problem may be solved exactly in the case of two membrane-bound parallel cylinders. This apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane-mediated interactions.
Cite
@article{arxiv.cond-mat/0702340,
title = {Balancing torques in membrane-mediated interactions: Exact results and numerical illustrations},
author = {Martin Michael Mueller and Markus Deserno and Jemal Guven},
journal= {arXiv preprint arXiv:cond-mat/0702340},
year = {2011}
}
Comments
16 pages, 10 figures, REVTeX4 style. The Gaussian curvature term was included in the membrane Hamiltonian; section II.B was rephrased to smoothen the flow of presentation