Next: Acknowledgments Up: Main Previous: Refinements
A conceptually and computationally simple numerical technique for computing mean interfacial curvature has been demonstrated. The procedure requires no detailed information about the shape of the interface, and consists of determining the portion of volume enclosed by a template sphere (or circle in 2D) that lies on one side of the interface. The mean curvature of the interface, relative to the phase lying on the opposite side, is then approximately linear in this computed volume. Higher-order correction terms to the linear approximation have been shown to be negligibly small in most cases for appropriate choice of the template radius. Application of the procedure to digitized representations of interface images are straightforward and yield accurate estimates of the spatial distribution of curvature along interfaces, although errors in individual measurements arise from the discrete representation of the interface. These errors can all be reduced by refining the pixel grid, at the expense of increased memory allocation and CPU time. Incorporation of a burning algorithm has been shown to provide greater accuracy in regions having sharp curvature fluctuations, like those along sharp crack-like features. A simple extension of the algorithm allows accurate computation of the interface orientation relative to a fixed reference frame.