New oscillation and nonoscillation criteria are established for second order linear equations with damping and forcing terms. Examples are given to illustrate the results.

1 . SOME time ago Littlewood and Offordt gave estimates of the number of real roots that an equation of degree n selected at random might be expected to have for various classes of equations in which the coefficients were selected on some probability basis . They found that, when each coefficient was treated on the same basis, the results were practically the same in all cases considered and ag...

This article presents special quadrilateral quadratic refinement elements, which provide geometry and field continuity across Tjunctions where two elements are connected to one side of a larger quadrilateral. The main idea in element refinement is to place one or more nodes outside the element area and to modify element shape functions in order to maintain continuity at refinement edges. Specia...

We construct uniformly bounded solutions for the equations divU = f and curlU = f in the critical cases f ∈ L # (T ,R) and f∈ L # (R,R). Bourgain& Brezis, [BB03, BB07], have shown that there exists no linear construction for such solutions. Our constructions are special cases of a general framework for solving linear equations of the form LU = f , where L is a linear operator densely defined in...

In this article, we present a novel approach for block-structured adaptive mesh refinement (AMR) that is suitable for extreme-scale parallelism. All data structures are designed such that the size of the meta data in each distributed processor memory remains bounded independent of the processor number. In all stages of the AMR process, we use only distributed algorithms. No central resources su...

ION REFINEMENT FOR LARGE SCALE MODEL CHECKING CHAO WANG NEC Laboratories America Princeton, New Jersey GARY D. HACHTEL University of Colorado Boulder, Colorado FABIO SOMENZI University of Colorado Boulder, Colorado Kluwer Academic Publishers Boston/Dordrecht/London

The evolution of negative streamers during electric breakdown of a non-attaching gas can be described by a two-fluid model for electrons and positive ions. It consists of continuity equations for the charged particles including drift, diffusion and reaction in the local electric field, coupled to the Poisson equation for the electric potential. The model generates field enhancement and steep pr...

When performing computational fluid dynamics (CFD) simulations of complex flows, the a priori knowledge of the flow physics and the location of the dominant flow features are usually unknown. For this reason, the development of adaptive remeshing techniques is crucial for large-scale computational problems. Some work has been made recently to provide Nek5000 with adaptive mesh refinement (AMR) ...

We performed a series of three-dimensional numerical simulations of supersonic homogeneous Euler turbulence with adaptive mesh refinement (AMR) and effective grid resolution up to 10243 zones. Our experiments describe nonmagnetized driven supersonic turbulent flows with an isothermal equation of state. Mesh refinement on shocks and shear is implemented to cover dynamically important structures ...