Narrow Results

The shape of the solid lipid monolayer domain surrounded by a fluid phase is of considerable interest from both physical and mathematical points of view. Here, we report two new results about this topic. First, we find an exact analytical solution to an approximated shape equation that we derived recently. This solution can well-describe the kidney- and boojum-like domains that abound in lipid monolayer. Second, we derive an exact domain shape equation by a direct variation of domain energy without any artificial cutoff. We find no continuous solutions that satisfy this shape equation due to the divergence of its coefficients, which is rooted in the continuous description of electrostatic dipoles.

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

When making an isotropic elastic shell into a curving tube, the crimp energy and bending energy determine the equilibrium shapes of the tube. In this study, we established a model to explore the elastic behavior of a tube made of an elastic shell. Two typical shapes: torus shape and periodic shape are discussed by studying the equilibrium shape equations in the planar case. Our study reveals that the crimp energy for an isotropic elastic tube is innegligible and will induce abundant shapes. It also reveals that varicose vein is more likely to occur when the blood vessels become thicker, which is in accordance with the clinic experiments.

The shape of the solid lipid monolayer domain surrounded by a fluid phase is of considerable interest from both physical and mathematical points of view. Here, we report two new results about this topic. First, we find an exact analytical solution to an approximated shape equation that we derived recently. This solution can well-describe the kidney- and boojum-like domains that abound in lipid monolayer. Second, we derive an exact domain shape equation by a direct variation of domain energy without any artificial cutoff. We find no continuous solutions that satisfy this shape equation due to the divergence of its coefficients, which is rooted in the continuous description of electrostatic dipoles.

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