R Capovilla and J Guven 2004 J. Phys. A: Math. Gen. 37 5983 doi:10.1088/0305-4470/37/23/003
R Capovilla1 and J Guven2,3
Show affiliationsA covariant approach towards a theory of deformations is developed to examine both the first and second variation of the Helfrich–Canham Hamiltonian—quadratic in extrinsic curvature—which describes fluid vesicles at mesoscopic scales. Deformations are decomposed into tangential and normal components. At first order, tangential deformations may always be identified with a reparametrization; at second order, they differ. The relationship between tangential deformations and reparametrizations, as well as the coupling between tangential and normal deformations, is examined at this order for both the metric and the extrinsic curvature tensors. Expressions for the expansion to second order in deformations of geometrical invariants constructed with these tensors are obtained; in particular, the expansion of the Hamiltonian to this order about an equilibrium is considered. Our approach applies as well to any geometrical model for membranes.
87.16.D- Membranes, bilayers, and vesicles
Issue 23 (11 June 2004)
Received 4 March 2004
Published 25 May 2004
R Capovilla and J Guven 2004 J. Phys. A: Math. Gen. 37 5983
Hans C Fogedby and Alberto Imparato 2009 J. Phys. A: Math. Theor. 42 475004
Albert C Fannjiang 2006 J. Phys. A: Math. Gen. 39 11383
Y. Ideue et al. 2009 ApJ 700 971
J Batle et al 2002 J. Phys. A: Math. Gen. 35 10311
Verne V. Smith et al. 2001 The Astronomical Journal 121 453
Marek Rogatko 1995 Class. Quantum Grav. 12 3115
O Gelhausen et al 2003 J. Phys. D: Appl. Phys. 36 2976
P Heckendorn et al 2009 Environ. Res. Lett. 4 045108
A. Nota et al. 2002 The Astronomical Journal 124 2920