The Method of Fundamental Solutions for Stokes flows with a free surface

We investigate the use of the Method of Fundamental Solutions (MFS) for solving Stokes flow problems with a free surface. We apply the method to the creeping planar Newtonian extrudate-swell problem and study the effect of the surface tension on the free surface. The results are in good agreement with existing finite element and boundary element solutions. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 667–678, 1998     

Phase transition thresholds for some Friedman-style independence results

We classify the phase transition thresholds from provability to unprovability for certain Friedman-style miniaturizations of Kruskal's Theorem and Higman's Lemma. In addition we prove a new and unexpected phase transition result for ε₀. Motivated by renormalization and universality issues from statistical physics we finally state a universality hypothesis. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Disproof of a conjecture about independent branchings in k-connected directed graphs

For each k ≥ 3, we construct a finite directed strongly k-connected graph D containing a vertex t with the following property: For any k spanning t-branchings, B₁, …, B_k in D (i. e., each B_i is a spanning tree in D directed toward t), there exists a vertex x ≠ t of D such that the k, x, t-paths in B₁, …, B_k are not pairwise openly disjoint. This disproves a well-known conjecture of Frank. © 1995, John Wiley & Sons, Inc.