In the attached paper, we have used Variational Analysis techniques (in particular, the theory of epi-convergence) to prove the continuity of maximum-entropy basis functions. In general, for non-smooth functionals, moving objectives and/or constraints, the tools of Newton-Leibniz calculus (gradient, point-convergence) prove to be insufficient; notions of set-valued mappings, set-convergence, etc., are required. Epi-convergence bears close affinity to Gamma- or Mosco-convergence (widely used in the mathematical treatment of martensitic phase transformations). The introductory material on convex analysis and epi-convergence had to be omitted in the revised version; hence the material is by no means self-contained. Here are a few more pointers that would prove to be helpful. Our main point of reference is Variational Analysis by RTR and RJBW; the Princeton Classic Convex Analysis by RTR provides the important tools in convex analysis. For convex optimization, the text Convex Optimization by SB and LV (available online) is excellent. The lecture slides provide a very nice (and gentle) introduction to some of the important concepts in convex analysis. The epigraphical landscape is very rich, and many of the applications would resonate with mechanicians.

On a different topic (non-planar crack growth), we have coupled the x-fem to a new fast marching algorithm. Here are couple of animations on growth of an inclined penny crack in tension (unstructured tetrahedral mesh with just over 12K nodes): larger `time' increment and smaller `time' increment. This is joint-work with Chopp, Bechet and Moes (NSF-OISE project). I will update this page as and when more relevant links are available.

From this Modern Mechanix scan of a 4 page article from the 1924 issue of Popular mechanics, we learn about Lincoln, the inventor!

Biasing reaction pathways with mechanical force, Charles R. Hickenboth, Jeffrey S. Moore, Scott R. White, Nancy R. Sottos, Jerome Baudry & Scott R. Wilson, Nature 446, 423-427 (22 March 2007).

The New York Times Magazine this weekend featured a Harvard undergraduate student from China, and her work to shake up education in China. The article is long, but if you grew up in China, it should be a quick read, and fun. If you grew up in US or Europe, perhaps this is a helpful read, just to learn how other people live.

Appl. Phys. Lett. 90, 133119 (2007)
Mechanics of Precisely Controlled Thin Film Buckling on Elastomeric Substrate

Laguna Beach, CA March 31, 2007 -- Kebaili Corporation a leading California based high-tech company announced today the release of the CPG-500 Series, the industry first compact current pulse generator, specifically designed for electrodeposition applications, such as (direct current) DC plating, pulse plating, and periodic reverse pulse plating for a variety of applications in MEMS and nanotechnology.

The molecular building blocks of a cell include:

What boundary conditions would allow failure to occur in the gauge length and not at or near the clamps? One is not allowed (in suggesting ways of overcoming stress concentation at the clamps) to create defects in the nanotube or nanowire, to configure the region where failure will occur.  Thus, it is not possible (or is it?)  to create an analog of dog-bone specimens by, e.g., milling away part of the nanowire with a focused ion beam, etc., because this creates defects in the nanowire.