Defining characteristic length-scales in non-convex domains

Develop a rigorous definition of characteristic length-scales for non-convex domains that can be used in asymptotic electro-diffusion formulas and Neumann Green’s function expansions for voltage calculations.

Background

Asymptotic voltage formulas in this work rely on a characteristic length-scale R, which is well-defined for convex domains through the largest inscribed ball radius.

For non-convex domains with large boundary curvature variations, the appropriate definition of such a characteristic scale is not established, and the authors resort to numerical fitting, indicating a need for a general theoretical framework.