I describe an adaptive h-reenement method for solving reaction-diiusion systems in three space dimensions on hexahedral grids. These grids typically have irregular (hanging) nodes. Solutions are calculated using Galerkin's method with a piecewise trilinear basis in space and a BDF code in time. New a posteriori error indicators based on interpolation error estimates for irregular grids are used...

In this paper, dynamic modeling of a double layer cylindrical functionally graded (FG) microshell is considered. Modeling is based on the first-order shear deformation theory (FSDT), and the equations of motion are derived using the Hamilton's principle. It assumes that functionally graded length scale parameter changes along the thickness. Generalized differential quadrature method (GDQM) is u...

A new type of grid turbulence generator, the 3D sparse (3DS), is a co-planar arrangement co-frames each containing different length scale elements [Malik, N. A. US Patent No. 9,599,269 B2 (2017)] and possessing much bigger parameter space than flat 2D fractal square (2DF). Using DNS we compare characteristics (mean flow, intensity, energy spectrum) generated by types 3DS grids. The peak intensi...

We propose the split-diffuse (SD) algorithm that takes the output of an existing dimension reduction algorithm, and distributes the data points uniformly across the visualization space. The result, called the topic grids, is a set of grids on various topics which are generated from the free-form text content of any domain of interest. The topic grids efficiently utilizes the visualization space...

In this paper we present eg-GRIDS, an algorithm for inducing context-free grammars that is able to learn from positive sample sentences. The presented algorithm, similar to its GRIDS predecessors, uses simplicity as a criterion for directing inference, and a set of operators for exploring the search space. In addition to the basic beam search strategy of GRIDS, eg-GRIDS incorporates an evolutio...

this paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. the graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. nonlocal governing equations of motion for this double-layer graphene s...

We derive an expansion for the fundamental solution of Laplace’s equation in flat-ring cyclide coordinates three-dimensional Euclidean space. This is a double series products functions that are harmonic interior and exterior coordinate surfaces which peanut shaped orthogonal to flat-rings. These internal external expressed terms Lamé—Wangerin functions. Using solution, we addition theorem azimu...

Recent research using high-resolution magnetic field data to examine the interior structures of MHD shocks in interplanetary space and in the magnetotail led to a surprising discovery that a slow-mode shock is often followed by an adjoining rotational discontinuity layer on the postshock side. The thickness of each layer is of the order of a few ion inertial lengths. Such a compound structure i...

In [5], we studied convergence and the structure of the error for several projection methods when the spatial variable was kept continuous . In this paper, we address similar problems for the fully discrete case when the spatial variable is discretized using the staggered grid. We prove that the numerical solution has full accuracy upto the boundary, despite the fact that there are numerical bo...