292 research outputs found
Approximate Approximations from scattered data
The aim of this paper is to extend the approximate quasi-interpolation on a
uniform grid by dilated shifts of a smooth and rapidly decaying function on a
uniform grid to scattered data quasi-interpolation. It is shown that high order
approximation of smooth functions up to some prescribed accuracy is possible,
if the basis functions, which are centered at the scattered nodes, are
multiplied by suitable polynomials such that their sum is an approximate
partition of unity. For Gaussian functions we propose a method to construct the
approximate partition of unity and describe the application of the new
quasi-interpolation approach to the cubature of multi-dimensional integral
operators.Comment: 29 pages, 17 figure
Computation of volume potentials over bounded domains via approximate approximations
We obtain cubature formulas of volume potentials over bounded domains
combining the basis functions introduced in the theory of approximate
approximations with their integration over the tangential-halfspace. Then the
computation is reduced to the quadrature of one dimensional integrals over the
halfline. We conclude the paper providing numerical tests which show that these
formulas give very accurate approximations and confirm the predicted order of
convergence.Comment: 18 page
Quasi-Freestanding Multilayer Graphene Films on the Carbon Face of SiC
The electronic band structure of as-grown and doped graphene grown on the
carbon face of SiC is studied by high-resolution angle-resolved photoemission
spectroscopy, where we observe both rotations between adjacent layers and
AB-stacking. The band structure of quasi-freestanding AB- bilayers is directly
compared with bilayer graphene grown on the Si-face of SiC to study the impact
of the substrate on the electronic properties of epitaxial graphene. Our
results show that the C-face films are nearly freestanding from an electronic
point of view, due to the rotations between graphene layers.Comment: http://link.aps.org/doi/10.1103/PhysRevB.81.24141
Approximate approximations from scattered data
AbstractThe aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function to scattered data quasi-interpolation. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible, if the basis functions, which are centered at the scattered nodes, are multiplied by suitable polynomials such that their sum is an approximate partition of unity. For Gaussian functions we propose a method to construct the approximate partition of unity and describe an application of the new quasi-interpolation approach to the cubature of multi-dimensional integral operators
Fast computation of elastic and hydrodynamic potentials using approximate approximations
We propose fast cubature formulas for the elastic and hydrodynamic potentials based on the approximate approximation of the densities with Gaussian and related functions. For densities with separated representation, we derive a tensor product representation of the integral operator which admits efficient cubature procedures. We obtain high order approximations up to a small saturation error, which is negligible in computations. Results of numerical experiments which show approximation order O(h2M) , M= 1 , 2 , 3 , 4 , are provided
Approximation of Uncoupled Quasi-Static Thermoelasticity Solutions Based on Gaussians
A fast approximation method to three dimensional equations in quasi-static uncoupled thermoelasticity is proposed. We approximate the density via Gaussian approximating functions introduced in the method approximate approximations. In this way the action of the integral operators on such functions is presented in a simple analytical form. If the density has separated representation, the problem is reduced to the computation of one-dimensional integrals which admit efficient cubature procedures. The comparison of the numerical and exact solution shows that these formulas are accurate and provide the predicted approximation rate 2 , 4 , 6 and 8
Kohn anomaly and interplay of electron-electron and electron-phonon interactions in epitaxial graphene
The interplay of electron-phonon (el-ph) and electron-electron (el-el)
interactions in epitaxial graphene is studied by directly probing its
electronic structure. We found a strong coupling of electrons to the soft part
of the A1g phonon evident by a kink at 150+/-15 meV, while the coupling of
electrons to another expected phonon E2g at 195 meV can only be barely
detected. The possible role of the el-el interaction to account for the
enhanced coupling of electrons to the A1g phonon, and the contribution of el-ph
interaction to the linear imaginary part of the self energy at high binding
energy are also discussed. Our results reveal the dominant role of the A1g
phonon in the el-ph interaction in graphene, and highlight the important
interplay of el-el and el-ph interactions in the self energy of graphene.Comment: accepted to Phys. Rev.
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