KIDNEY-BOOJUM-LIKE SOLUTIONS AND EXACT SHAPE EQUATION OF SOLID-LIKE DOMAINS IN LIPID MONOLAYER

摘要

The shape of solid lipid monolayer domain surrounded by a fluid phase is of considerableinterest from physical and mathematical points of view. Here we report two new resultsabout this topic. First, we obtain an exact analytical solution to an approximated shapeequation that was derived by us recently [Phys. Rev. Lett. 93, 206101 (2004)]. Thissolution can well describe the kidney- and boojum-like domains that abound in lipidmonolayer. Second, we derive an exact domain shape equation by a direct variationof domain energy without any artificial cutoff. We find that no continuous solutionssatisfies this shape equation due to the divergence of its coefficients, which is rooted inthe continuous description of electrostatic dipoles.