An H1Galerkin mixed finite element method is discussed for a class of second order hyperbolic problems. It is proved that the Galerkin approximations have the same rates of convergence as in the classical mixed method, but without LBB stability condition and quasi-uniformity requirement on the finite element mesh. Compared to the results proved for one space variable, the L∞(L2)-estimate of the...

The Optoelectronic Technology Consortium (OETC) 16 Gbit/s, 32-channel parallel fiber optic bus introduces new requirements for modeling and simulation of an optical bus which were not present for previous single-channel optical link systems. These requirements include the simulation of the statistical variation in component parameters, timing skew, and crosstalk. Due to the required simulation ...

Achieving homogeneous phase transition and uniform charge distribution is essential for good cycle stability and high capacity when phase conversion materials are used as electrodes. Herein, we show that chemical lithiation of bulk 2H-MoS2 distorts its crystalline domains in three primary directions to produce mosaic-like 1T' nanocrystalline domains, which improve phase and charge uniformity du...

Two new quasi-linear elliptic systems of partial differential equations to automatically generate twodimensional boundary conforming structured grids are formulated. One of the new systems generates grids with near-uniform cell areas. The other produces meshes with near-uniform coordinate line spacings. In both cases, the resulting grids conform to complex boundaries with severe singularities w...

Random number sequences are used in a wide range of applications such as simulation, sampling, numerical analysis, cryptography, and recreation. The quality of random number sequences is critical to the correctness of these applications. Many statistical tests have been developed to test various characteristics of random number generators such as randomness, independence, uniformity, etc. Most ...

Szemerédi’s Regularity Lemma proved to be a very powerful tool in extremal graph theory with a large number of applications. Chung [Regularity lemmas for hypergraphs and quasi-randomness, Random Structures and Algorithms 2 (1991), 241–252], Frankl and Rödl [The uniformity lemma for hypergraphs, Graphs and Combinatorics 8 (1992), 309–312, Extremal problems on set systems, Random Structures and A...

This research describes the goals, design and implementation of a quasi natural gradient, laboratory scale, sand tank (aquifer) model experiment. The model was used to study the transport of an inorganic tracer (Chloride) in groundwater, within a tropical aquifer (porous medium) material. Three-dimensional sand tank (1.8 m × 0.3 m × 0.8 m) experiments were conducted to investigate contaminant t...