Topological "Shape" in Micellar Dynamics

For micelles, "shape" is prominent in rheological computations of fluid flow, but this "shape" is often expressed too informally to be useful for rigorous analyses. We formalize topological "shape equivalence" of micelles, both globally and locally, to enable visualization of computational fluid dynamics. Although topological methods in visualization provide significant insights into fluid flows, this opportunity has been limited by the known difficulties in creating representative geometry. We present an agile geometric algorithm to represent the micellar shape for input into fluid flow visualizations. We show that worm-like and cylindrical micelles have formally equivalent shapes, but that visualization accentuates unexplored differences. This global-local paradigm is extensible beyond micelles.