179 citations · 826 across the 31 of their papers we have counts for
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Hamilton's equations for a fluid membrane
Riccardo Capovilla, Jemal Guven, Efrain Rojas
Consider a homogenous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibriu…
Hamilton's equations for a fluid membrane: axial symmetry
Riccardo Capovilla, Jemal Guven, Efrain Rojas
Consider a homogenous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can…
Helfrich-Canham bending energy as a constrained non-linear sigma model
Riccardo Capovilla, Jemal Guven
The Helfrich-Canham bending energy is identified with a non-linear sigma model for a unit vector. The identification, however, is dependent on one additional constraint: that the u…
Second variation of the Helfrich-Canham Hamiltonian and reparametrization invariance
Riccardo Capovilla, Jemal Guven
A covariant approach towards a theory of deformations is developed to examine both the first and second variation of the Helfrich-Canham Hamiltonian -- quadratic in the extrinsic c…
Deformations of the geometry of lipid vesicles
Riccardo Capovilla, Jemal Guven, Jose' Antonio Santiago
Consider a closed lipid membrane (vesicle), modeled as a two-dimensional surface, described by a geometrical hamiltonian that depends on its extrinsic curvature. The vanishing of i…
Lipid membranes with an edge
R. Capovilla, J. Guven, J. A. Santiago
Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proport…
Geometry of lipid vesicle adhesion
Riccardo Capovilla, Jemal Guven
The adhesion of a lipid membrane vesicle to a fixed substrate is examined from a geometrical point of view. This vesicle is described by the Helfrich hamiltonian quadratic in mean…
Stresses in lipid membranes
Riccardo Capovilla, Jemal Guven
The stresses in a closed lipid membrane described by the Helfrich hamiltonian, quadratic in the extrinsic curvature, are identified using Noether's theorem. Three equations describ…
Area-Constrained Planar Elastica
G. Arreaga, R. Capovilla, C. Chryssomalakos +1
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quad…