Abstract We provide the first general result for asymptotics of area preserving mean curvature flow in two dimensions showing that flat solutions, starting from any bounded set finite perimeter, converge with exponential rate to a union equally sized disjoint disks. A similar is established also periodic two-phase Mullins–Sekerka flow.

In this paper, we study the null controllability of Mullins equation with control acting on periodic boundary. Firstly, using duality relation between and observability, express condition in terms solution backward adjoint system. After showing existence uniqueness system, determine admissible initial data class since system is not always controllable under these boundary conditions. Finally, s...

The Mullins Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn Hilliard equation. We show that classical solutions exist globally and tend to spheres exponentially fast, provided that they are close to a sphere initially. Our analysis is based on center manifold theory and on maximal regularity. 1998 Academic Press

We prove the convergence of an implicit time discretization for one-phase Mullins-Sekerka equation, possibly with additional non-local repulsion, proposed in [F. Otto, Arch. Rational Mech. Anal. 141 (1998), pp. 63â??103]. Our simple argument shows that limit satisfies equation a distributional sense as well optimal energy-dissipation relation. The proof combines arguments from transport, gradie...

Submitted for the MAR15 Meeting of The American Physical Society Quantitative analysis of actin monomer funneling: how capping protein enhances actin filament growth and nucleation on biomimetic beads1 RUIZHE WANG, ANDERS CARLSSON, Washington University — Capping protein (CP) caps the growing ends of actin filaments and thereby halts their polymerization. However, CP is required for actin-based...

Capping proteins limit actin filament growth, but paradoxically increase actin-based cell motility. This has been attributed to funneling of actin monomers to the filament ends that remain uncapped. Using a reconstituted motility system, Akin and Mullins (2008) now demonstrate that filament capping increases Arp2/3-based nucleation and branching, rather than elevating the rate of filament elong...

In this paper we generalize the degenerate two{phase Stefan problem (Mullins{ Sekerka evolution) to multi{phase systems. We prove a conditional existence result for this evolution problem in the framework of geometric measure theory by using an implicit time discretization. In each time step we solve a variational problem for an energy functional that contains capillarity terms as well as bulk ...