Wednesday, September 12, 2012

1209.2141 (Jemal Guven et al.)

Force dipoles and local defects on flat fluid membranes    [PDF]

Jemal Guven, Pablo Vázquez-Montejo
An exact description is provided of a flat fluid membrane locally deformed by external normal forces bringing two points on the surface together. The conformal symmetry of the two-dimensional bending energy is used to identify the distribution of energy as well as the stress established in the membrane. Logarithmic curvature singularities in the surface geometry at the points of contact signal the presence of external forces. Whereas the total energy is independent of the distance S between the two points, as measured along the surface, the magnitude of the forces is shown to vary inversely with S. The geometry behaves near each of the singularities as a biharmonic monopole, in the region between them as a surface of constant mean curvature, and asymptotically as a biharmonic quadrupole. Radial tension is accompanied by lateral compression, both near the poles and asymptotically, with a crossover from tension to compression displayed between the two singularities.
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