Equilibrium Shape Equations Research Articles

Equilibrium shape equation and possible shapes of carbon nanotubes.

The elastic free energy of carbon nanotubes grown by iron-catalyzed decomposition of acetylene is introduced to describe the possible tubular shapes. The equilibrium shape equation can be obtained by the first variation of the elastic free energy of the slightly distorted tube. The model is consistent with both stable and metastable shapes observed in our experiments. The results are due to the fluctuation of growth conditions, such as the pressure, temperature, and composition of the vapor. \textcopyright{} 1996 The American Physical Society.

Anchor ring-vesicle membranes.

A family of the exact and analytical solutions of the equilibrium shape equation of vesicle membranes is found. They are anchor rings with generating circles of radii in the ratio 1/ \ensuremath{\surd}2 . It is shown that these ring vesicles are stable for some negative values of their spontaneous curvatures, such that experimental construction of such vesicles seems possible. A discussion shows that a positive Gauss-curvature elastic modulus favors the formation of these special vesicles.