Experimental research on the Pb phase coarsening of eutectic Pb/Sn flip chip solder joint under current stressing is reported. Phase growth is observed under different current densities and temperatures. Higher current density leads to faster grain coarsening. Based on the test results, a grain coarsening equation including the influence of current density is proposed, dn dn 0 1⁄4 Kjmt. The cur...

High resolution x-ray diffraction using synchrotron radiation was used to characterize GaAs grown by MBE at low temperatures (LT-GaAs). LT-GaAs grown at 225~ is nonstoichiometric and exhibits a 0.15% lattice expansion along the growth direction. Annealing LT-GaAs results in arsenic clusters with a well-defined orientation relationship with the GaAs matrix and a relaxation of the LT-GaAs lattice...

The stochastic Ginzburg-Landau equation in one dimension is the simplest continuum model describing the spatio-temporal evolution of a bistable system in the presence of thermal noise. Relaxation to equilibrium in this model proceeds by coarsening of the field during which regions in the two stables phases separated by localized kinks grow on the average. It is shown that coarsening in the pres...

We report the experimental observation of a submicron cellular structure on the surface of silicon targets eroded by an ion plasma. Analysis by atomic force microscopy allows us to assess the time evolution and show that the system can be described quantitatively by the convective Cahn-Hilliard equation, found in the study of domain coarsening for a large class of driven systems. The space-fill...

Multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing to data science. In this paper we introduce the concept of algebraic distance on hypergraphs and demonstrate its use as an algorithmic component in the coars...

We develop a diffuse interface model to investigate the three dimensional coarsening in thin films. In this model, both strong surface anisotropy with linear Willmore regularization, elastic stresses and deposition are included. The governing equation for the phase field parameter is a sixth order Cahn-Hilliard Equation due to the presence of surface anisotropy and the linear Willmore regulariz...

We study the coarsening dynamics of two- and three-dimensional biaxial nematic liquid crystals, using Langevin dynamics. Unlike previous work, we use a model with no a priori relationship among the three elastic constants associated with director deformations. Biaxial nematics possess four topologically distinct classes of defects, three of which have half-integer charge, while the fourth, whic...

We present a (dynamic) stochastic simulation model for 3D grain morphologies undergoing a grain coarsening phenomenon known as Ostwald ripening. For low volume fractions of the coarsening phase, the classical LSW theory predicts a power-law evolution of the mean particle size and convergence toward self-similarity of the particle size distribution; experiments suggest that this behavior holds a...

Overlap Level of Regular Dual graph (no. elements) coarse grid coarsening coarsening 0 None 56 56 0 4 21 22 0 3 15 12 1 None 16 16 1 4 10 10 1 3 7 7 2 None 14 14 2 4 8 8 2 3 5 5 Table 2 Multigrid iterations for the Airfoil mesh Regular coarsening Dual graph coarsening MG Levels Nodes Dir. B. Overlapping schwarz methods on unstructured meshes using non-matching coarse grids. Domain decomposition...

A stressed thin film on a soft substrate can develop complex wrinkle patterns. The onset of wrinkling and initial growth is well described by a linear perturbation analysis, and the equilibrium wrinkles can be analyzed using an energy approach. In between, the wrinkle pattern undergoes a coarsening process with a peculiar dynamics. By using a proper scaling and two-dimensional numerical simulat...