The evolution of a foam is determined by drainage flow of the continuous (liquid) phase and coarsening (aging) of the dispersed phase (gas bubbles). Free-drainage experiments with slow- and fast-coarsening gases show markedly different dynamics and elucidate the importance of the coupling of the two effects. Strong coarsening leads to drainage times that are shorter (accelerated drainage) and i...

We study coarsening phenomena observed in discrete, ill-posed diffusion equations that arise in a variety of applications, including computer vision, population dynamics, and granular flow. Our results provide rigorous upper bounds on the coarsening rate in any dimension. Heuristic arguments and numerical experiments we perform indicate that the bounds are in agreement with the actual rate of c...

We have studied the growth dynamics of domains on ternary fluid vesicles composed of saturated (dipalmitoylphosphatidylcholine), unsaturated (dioleoylphosphatidylcholine) phosphatidylcholine lipids, and cholesterol using a fluorescence microscopy. The domain coarsening processes are classified into two types: normal coarsening and trapped coarsening. For the normal coarsening, the domains havin...

This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques, possibly combined with random sampling. A multilevel coarsening technique is proposed which utilizes a hypergraph associated with the data matrix and a graph coa...

Mesoscopic hydrodynamic equations are solved to investigate coarsening dynamics of two interacting nanodroplets on chemically patterned substrates. The effects of different parameters such as the surface chemical pattern, the slip length, the profile of the disjoining pressure, the size of the droplets, and the contact angles on the coarsening are studied. Our results reveal that the presence o...

We have measured the coarsening due to surface tension of radially grown fractal viscous fingering patterns. The patterns at late times depend on the structural form at the onset of coarsening, providing information on the age of the fractal. The coarsening process is not dynamically scale invariant, exhibiting two dynamic length scales that grow as L1(t) approximately t(0.22+/-0.02) and L2(t) ...

ÐThe sidebranching behavior in free dendritic growth into a supercooled melt is investigated through a detailed measurement of the sidebranch structure of succinonitrile (SCN) dendrites using images from the microgravity experiment of Glicksman and co-workers. The measurements show that the sidebranching evolution is divided into two regimes: an initial linear regime and a subsequent non-linear...

We characterize the coarsening dynamics associated with a convective Cahn-Hilliard equation (cCH) in one space dimension. First, we derive a sharp-interface theory through a matched asymptotic analysis. Two types of phase boundaries (kink and anti-kink) arise, due to the presence of convection, and their motions are governed to leading order by a nearest-neighbors interaction coarsening dynamic...

Austenite grain growth in microalloyed steels is governed by the coarsening of fine precipitates present at grain boundaries below the grain coarsening temperature. Zener model is widely used in metals to describe the pinning effect of second phase particles precipitated in the matrix. In this work it has been discussed whether grain boundary or volume diffusion is the rate controlling process ...

Mesh adaptation methods can improve the efficiency and accuracy of solutions to computational modeling problems. In many applications involving quadrilateral and hexahedral meshes, local modifications which maintain the original element type are desired. For triangle and tetrahedral meshes, effective refinement and coarsening methods that satisfy these criteria are available. Refinement methods...