Multigrid algorithm from cyclic reduction for Markovian queueing networks

A multigrid method based on cyclic reduction strategy is proposed to solve huge, nonsymmetric singular linear systems arising from Markovian queueing networks. A simple way to construct the matrix-dependent prolongation and restriction operators is presented in this paper. Numerical results for multiple queues are given to illustrate the efficiency and robustness of our methods.     

Molecular model studies based on ab initio calculations of nucleophilic and electrophilic addition‐substitution reactions focused on carbon–halogen compounds

We describe with molecular model studies based on the intrinsic parameters of van't Hoff's regular tetrahedron nucleophilic and electrophilic addition‐substitution reactions via a selected reaction coordinate for the displacement of carbon. Geometries of stable, intermediate transition complexes or transition states are compared with the corresponding ab initio values. Specific attention is given on the hypervalent and nonhypervalent character of carbon supported by ab initio calculations, our model consideration and experimental evidence. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Understanding the interaction of multi-walled carbon nanotubes with mutagenic organic pollutants using computational modeling and biological experiments

Carbon nanotubes (CNTs) are very promising materials to remove pollutants from the environment. To develop safe, efficient technologies, it is necessary to understand the mechanisms of interaction between CNTs and pollutants. This requires innovative, interdisciplinary approaches. Detailed chemical analysis of the CNTs along with computational modeling can provide important information about the mechanisms of interaction. If biological experiments are included in these studies, useful complementary information is obtained. To exemplify the use of this approach, we present a case study in which detailed calculations and the Salmonella mutagenicity assay were applied to elucidate how multi-walled CNTs interact with 1-nitropyrene, an important mutagenic pollutant.     

Spectral and Indo-Molecular Orbital Studies of n →∗ Transitions in Symmetric Diazines

Abstract

Experimental and theoretical (INDO-MO) studies of n → transitions have been carried out for seven symmetric diazines. In all cases, there is very good agreement between the theoretical predictions and experimental observations on the symmetry of the lowest energy n→? singlet state.     

Variational Properties of the Solutions for Second-Order Differential Equations and Systems on Semi-Line

In this article, an abstract theory regarding variational properties of the fixed points of contractions and Perov contractions is applied to boundary value problems on semi-line for second-order differential equations and systems. The main result states that under suitable conditions the unique solution of such a system is a Nash-type equilibrium of the corresponding energy functionals.     

Theoretical model for the transverse interference pattern of GRIN optical fiber using a laser sheet of light

A new technique (El-Ghandoor et al., Opt. Laser Technol. 31(7) (1999) 481–488) has been applied to study the shape of transverse interference fringes, instead of multiple beam Fizeau fringes (Marhic, Stein, Appl. Phys. Lett. 35 (1975) 1678–1682), from a GRIN optical fiber. In this technique, a laser light sheet is used to illuminate and pass directly through the optical fiber. Theoretical expressions are derived for the optical path differences of three groups of interference beams. The first one passes through the cladding, the core, and then the cladding once again; the second passes through the cladding only, and the third passes through the surrounding air. Theoretical expressions for the shape of transverse interference fringes formed across isotropic non-absorbing optical fibers are also calculated.     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.