A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids

We study a Dirichlet boundary value problem associated to an anisotropic differential operator on a smooth bounded of $\Bbb R^N$. Our main result establishes the existence of at least two different non-negative solutions, provided a certain parameter lies in a certain range. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with adequate variational methods and a variant of Mountain Pass lemma.Comment: Proceedings A of the Royal Society of London, in pres

Calculation of model Hamiltonian parameters for LaMnO_3 using maximally localized Wannier functions

Maximally localized Wannier functions (MLWFs) based on Kohn-Sham band-structures provide a systematic way to construct realistic, materials specific tight-binding models for further theoretical analysis. Here, we construct MLWFs for the Mn e_g bands in LaMnO_3, and we monitor changes in the MLWF matrix elements induced by different magnetic configurations and structural distortions. From this we obtain values for the local Jahn-Teller and Hund's rule coupling strength, the hopping amplitudes between all nearest and further neighbors, and the corresponding reduction due to the GdFeO_3-type distortion. By comparing our results with commonly used model Hamiltonians for manganites, where electrons can hop between two "e_g-like" orbitals located on each Mn site, we find that the most crucial limitation of such models stems from neglecting changes in the underlying Mn(d)-O(p) hybridization.Comment: 15 pages, 11 figures, 3 table

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

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

DNA Damage during G2 Phase Does Not Affect Cell Cycle Progression of the Green Alga Scenedesmus quadricauda

DNA damage is a threat to genomic integrity in all living organisms. Plants and green algae are particularly susceptible to DNA damage especially that caused by UV light, due to their light dependency for photosynthesis. For survival of a plant, and other eukaryotic cells, it is essential for an organism to continuously check the integrity of its genetic material and, when damaged, to repair it immediately. Cells therefore utilize a DNA damage response pathway that is responsible for sensing, reacting to and repairing damaged DNA. We have studied the effect of 5-fluorodeoxyuridine, zeocin, caffeine and combinations of these on the cell cycle of the green alga Scenedesmus quadricauda. The cells delayed S phase and underwent a permanent G2 phase block if DNA metabolism was affected prior to S phase; the G2 phase block imposed by zeocin was partially abolished by caffeine. No cell cycle block was observed if the treatment with zeocin occurred in G2 phase and the cells divided normally. CDKA and CDKB kinases regulate mitosis in S. quadricauda; their kinase activities were inhibited by Wee1. CDKA, CDKB protein levels were stabilized in the presence of zeocin. In contrast, the protein level of Wee1 was unaffected by DNA perturbing treatments. Wee1 therefore does not appear to be involved in the DNA damage response in S. quadricauda. Our results imply a specific reaction to DNA damage in S. quadricauda, with no cell cycle arrest, after experiencing DNA damage during G2 phase