arXiv subjects

Pavel Castro-Villarreal

Publications and source records attributed to Pavel Castro-Villarreal.

20 records · Page 2Linked to original sources

arXiv2007

Inverted catenoids, curvature singularities and tethered membranes

If a catenoid is inverted in any interior point, a deflated compact geometry is obtained which touches at two points (its poles). The catenoid is a minimal surface and, as such, is an equilibrium shape of a symmetric fluid membrane. The conformal symmetry of the Hamiltonian implies that inverted minimal surfaces are also equilibrium shapes. However, they exhibit curvature singularities at their poles. These singularities are associated with external forces pulling the poles together. Unlike the catenoid which is free of stress, there will be stress within the inverted shapes. If the surface area is fixed, reducing the external force induces a transition from a discocyte to a cup-shaped stomatocyte.

cond-mat.soft↗

arXiv2007

Axially symmetric membranes with polar tethers

Axially symmetric equilibrium configurations of the conformally invariant Willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation, not one as would be expected on the basis of axial symmetry. Modulo a translation along the axis, this equation involves a single free parameter c.If c\ne 0, a geometry with spherical topology will possess curvature singularities at its poles. The physical origin of the singularity is identified by examining the Noether charge associated with the translational invariance of the energy; it is consistent with an external axial force acting at the poles. A one-parameter family of exact solutions displaying a discocyte to stomatocyte transition is described.

cond-mat.soft↗