Axially symmetric membranes with polar tethers
نویسندگان
چکیده
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 6= 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. PACS: 87.16.Dg, 02.40.Hw
منابع مشابه
Axially Symmetric Vibrations of a Liquid-Filled Poroelastic Thin Cylinder Saturated with Two Immiscible Liquids Surrounded by a Liquid
This paper studies axially symmetric vibrations of a liquid-filled poroelastic thin cylinder saturated with two immiscible liquids of infinite extent that is surrounded by an inviscid elastic liquid. By considering the stress free boundaries, the frequency equation is obtained. Particular case, namely, liquid-filled poroelastic cylinder saturated with single liquid is discussed. When the waven...
متن کاملNew Regular Solutions with Axial Symmetry in Einstein-Yang-Mills Theory
We construct new regular solutions in Einstein-Yang-Mills theory. They are static, axially symmetric and asymptotically flat. They are characterized by a pair of integers (k, n), where k is related to the polar angle and n to the azimuthal angle. The known spherically and axially symmetric EYM solutions have k = 1. For k > 1 new solutions arise, which form two branches. They exist above a minim...
متن کاملNew Black Hole Solutions with Axial Symmetry in Einstein-Yang-Mills Theory
We construct new black hole solutions in Einstein-Yang-Mills theory. They are static, axially symmetric and asymptotically flat. They are characterized by their horizon radius and a pair of integers (k, n), where k is related to the polar angle and n to the azimuthal angle. The known spherically and axially symmetric EYM black holes have k = 1. For k > 1, pairs of new black hole solutions appea...
متن کاملAxially-symmetric sheared polymer network liquid crystals.
An axially-symmetric sheared polymer network liquid crystal (SPNLC) device is demonstrated and its performances characterized. Through analyzing the structure of this axially-symmetric SPNLC, we constructed a 3-D model to explain the observed phenomena. The simulation results agree well with the experiment. Two potential applications of such an axially-symmetric SPNLC, namely tunable-focus nega...
متن کامل