How bees and foams respond to curved confinement:Level set boundary representations in the Surface Evolver

We investigate the equilibrium properties of a single area-minimising bubble trapped between two narrowly-separated parallel curved plates. We begin with the simple case of a bubble trapped between concentric spherical plates. We develop a model that shows that the surface tension energy of the bubble is lower when confined between spherical plates as compared to a bubble trapped between flat plates. We confirm our findings by comparing against Surface Evolver simulations. Next, we derive a simple model for a bubble between arbitrarily curved parallel plates. The energy is found to be higher when the local Gaussian curvature of the plates is negative and lower when the curvature is positive. To check the validity of the model we consider a bubble trapped between concentric tori. In the toroidal case we find that the sensitivity of the bubble's energy to the local curvature acts as a geometric potential capable of driving bubbles from regions with negative to positive curvature

Varicose Veins on the Internet

AbstractObjectives: to evaluate the quality of information on the Internet concerning varicose veins.Design: review of retrieved pamphlets and their scoring for educational value. Materials: a sample of 41 documents were retrieved from the Internet using four ««search engines»». Methods: characteristics, including country of origin, authorship, length, and presence of references were recorded. Based on factors such as disease summary, treatment options and complications a weighted score was created by two independent observers.Results: eleven documents were published by an academic institution or professional organisation. Twenty-seven documents originated from private practice groups, the source of three was unidentifiable. The median weighted score was 21.5 (interquartile range: 7.5–48.5). Scores originating from non-profit making organisations were significantly higher than those from private practice groups (44.5 vs 13, p=0.04). The length of the document showed a significant positive correlation with its educational quality as measured by the information score (r=0.82, p<0.001). Conclusion: there is a plethora of data concerning varicose veins on the Internet. Some documents offer comprehensive information but many are confusing or misleading. Longer pamphlets and information presented by non-profit making organisations are more reliable than short documents and information offered by private medical groups