130 research outputs found
Maximally localized Wannier functions in LaMnO3 within PBE+U, hybrid functionals, and partially self-consistent GW: an efficient route to construct ab-initio tight-binding parameters for e_g perovskites
Using the newly developed VASP2WANNIER90 interface we have constructed
maximally localized Wannier functions (MLWFs) for the e_g states of the
prototypical Jahn-Teller magnetic perovskite LaMnO3 at different levels of
approximation for the exchange-correlation kernel. These include conventional
density functional theory (DFT) with and without additional on-site Hubbard U
term, hybrid-DFT, and partially self-consistent GW. By suitably mapping the
MLWFs onto an effective e_g tight-binding (TB) Hamiltonian we have computed a
complete set of TB parameters which should serve as guidance for more elaborate
treatments of correlation effects in effective Hamiltonian-based approaches.
The method-dependent changes of the calculated TB parameters and their
interplay with the electron-electron (el-el) interaction term are discussed and
interpreted. We discuss two alternative model parameterizations: one in which
the effects of the el-el interaction are implicitly incorporated in the
otherwise "noninteracting" TB parameters, and a second where we include an
explicit mean-field el-el interaction term in the TB Hamiltonian. Both models
yield a set of tabulated TB parameters which provide the band dispersion in
excellent agreement with the underlying ab initio and MLWF bands.Comment: 30 pages, 7 figure
The Stokes and Poisson problem in variable exponent spaces
We study the Stokes and Poisson problem in the context of variable exponent
spaces. We prove the existence of strong and weak solutions for bounded domains
with C^{1,1} boundary with inhomogenous boundary values. The result is based on
generalizations of the classical theories of Calderon-Zygmund and
Agmon-Douglis-Nirenberg to variable exponent spaces.Comment: 20 pages, 1 figur
Interpolation in variable exponent spaces
In this paper we study both real and complex interpolation in the recently
introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also
take advantage of some interpolation results to study a trace property and some
pseudodifferential operators acting in the variable index Besov scale
Variable exponent Besov-Morrey spaces
In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.publishe
A pair of positive solutions for the Dirichlet p(z)-Laplacian with concave and convex nonlinearities
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