Adventures in Mathematical Modelling.
University of Buffalo and Caltech physicists proposed a broadening of Hertz's contact theory through modelling the connections between the geometry of the contact region of adjacent elastic objects with axial symmetry and the magnitude and behaviour of the nonlinear repulsive force between them. Different surface geometries offer possibilities through which energy propagation can be modified through particle design. The model has potential applications for energy transport, localisation, and dispersion in granular systems and in the development of VLSI circuits.
A lay-friendly briefing on the research from "Nanowerk:"
For those interested in the mathematical and technical details, the original article is available below from the Caltech library: