10 papers · 1 filter
A domain decomposition method for the directional contact angle hysteresis interval on doubly periodic rough surfaces
Zijie Lin, William M Feldman, Braxton Osting
We study wetting on a doubly periodic rough surface in three dimensions. Although the liquid-vapor interface meets the solid at the local Young's angle, microscale roughness can ca…
Solutions of the Bernoulli one-phase problem with a defect
William M Feldman, Inwon C Kim
We study the far-field behavior of solutions of the one-phase Bernoulli free boundary problem in the exterior of a ball, and of entire solutions with a single compactly supported i…
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…
An obstacle approach to rate independent droplet evolution
William M Feldman, Inwon C Kim, Norbert Požár
We consider a toy model of rate independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We introduce a notion…
Minimizing movements solutions for a monotone model of droplet motion
Carson Collins, William M Feldman
We study the uniqueness and regularity of minimizing movements solutions of a droplet model in the case of piecewise monotone forcing. We show that such solutions evolve uniquely o…
On the geometry of rate independent droplet evolution
William M Feldman, Inwon C. Kim, Norbert Požár
We introduce a toy model for rate-independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We consider a notion…
Liquid Drops on a Rough Surface
William M. Feldman, Inwon C. Kim
We consider a liquid drop sitting on a rough solid surface at equilibrium, a volume constrained minimizer of the total interfacial energy. The large-scale shape of such a drop stro…