4 papers · 1 filter
The pinning effect of dilute defects
William M Feldman, Inwon C Kim
We consider the Bernoulli free boundary problem with ``periodic defects", or a periodic array of compactly supported inhomogeneities. First we study the problem with a single defec…
Rate independent capillary motion on a narrow Wilhelmy plate
Carson Collins, William M Feldman
We study a rate independent energetic model of the Wilhelmy plate experiment in capillarity. The evolution is driven by vertical motions of the plate. We show stability of energy s…
Global Well-Posedness of a Nonlinear Fokker-Planck Type Model of Grain Growth
Batuhan Bayir, Yekaterina Epshteyn, William M Feldman
Most technologically useful materials spanning multiple length scales are polycrystalline. Polycrystalline microstructures are composed of a myriad of small crystals or grains with…
Compactness for via concentration-compactness
William M Feldman, Kerrek Stinson
Motivated by variational models for fracture, we provide a new proof of compactness for functions without a priori bounds on the function itself. Our proof is based on the…