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...

A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a U (1) × U (1) group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, t...

Langmuir films (LFs) on water have long been studied for their interest for basic science and their numerous applications in chemistry, physics, materials science and biology. We present here A-resolution synchrotron X-ray studies of the structure of stearic acid LFs on a liquid mercury surface. At low coverage, P 110 A/mol, a 2D gas phase of flat-lying molecules is observed. At high coverage, ...

We report on numerical experiments using adaptive sparse grid dis-cretization techniques for the numerical solution of scalar hyperbolic conservation laws. Sparse grids are an eecient approximation method for functions. Compared to regular, uniform grids of a mesh parameter h contain h ?d points in d dimensions, sparse grids require only h ?1 jloghj d?1 points due to a truncated , tensor-produc...

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...

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor fiowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid ...

The problem of article is cubic spline-interpolation of functions having high gradient regions. It is shown that uniform grids are inefficient to be used. In case of piecewise-uniform grids, concentrated in the boundary layer, for cubic spline interpolation are announced asymptotically exact estimates on a class of functions with an exponential boundary layer. There are obtained results showing...

The problem of adaptation of structured 2-D grids to a control function is investigated. We aim to create a grid with highly stretched and nearly orthogonal cells in regions of control function’s singularities of thin-layer type. Adaptation is performed by optimizing a mesh quality functional via node-movement. Construction of the functional is specifically investigated. The presented functiona...

We present a practical approach for the numerical solution of the Reynolds averaged Navier-Stokes (RANS) equations using high-order discontinuous Galerkin methods. Turbulence is modeled by the Spalart-Allmaras (SA) one-equation model. We introduce an artificial viscosity model for SA equation which is aimed at accommodating high-order RANS approximations on grids which would otherwise be too co...