Ein allgemeiner Vierscheitelsatz für ebene Jordankurven

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Über gewisse lineare Transformationen

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Plasmon dispersion in Al atk≦k F using electron energy loss spectroscopy

We find a quasi quadratic dispersion of the plasmon up to _p = 28 eV atk=1.77 Å^–1 with no levelling off contrary to other measurements. We usedk-scans at constant energy loss andE-scans at constant wave vector, which yield different dispersions of the plasmon peak maximum because of the finite halfwidth. The levelling off in plasmon dispersion observed previously is due to multiple scattering events, which obscure the plasmon dispersion inE-scans.We confirmed the anisotropy of the dispersion coefficient by investigating polycrystalline samples of different orientation.     

Surface enhanced Raman scattering (SERS): Annealing the silver substrate

Silver films, deposited at 120 K in UHV, were slowly warmed to room temperature, Characteristic intensity variations of the inelastic background (I), of disorder induced Raman scattering from phonons (II) and of the SERS signal from adsorbed pyridine have been observed. In the case of (I) and (II) these are explained by the bulk concentration of point defects, in the SERS case by annealing of atomic scale surface roughness.     

A higher-order large-scale regularity theory for random elliptic operators

We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coefficient case. This result can be seen as the qualitative side of a large-scale C^k,α-regularity theory, which in the present work is developed in the form of a corresponding C^k,α-“excess decay” estimate: For a given a-harmonic function u on a ball B_R, its energy distance on some ball B_r to the above space of a-harmonic functions that grow at most like a polynomial of degree k has the natural decay in the radius r above some minimal radius r₀.

Though motivated by stochastic homogenization, the contribution of this paper is of purely deterministic nature: We work under the assumption that for the given realization a of the coefficient field, the couple (φ, σ) of scalar and vector potentials of the harmonic coordinates, where φ is the usual corrector, grows sublinearly in a mildly quantified way. We then construct “kth-order correctors” and thereby the space of a-harmonic functions that grow at most like a polynomial of degree k, establish the above excess decay, and then the corresponding Liouville principle.