Self–regularization by projection for noisy pseudodifferential equations of negative order

It is well known, that pseudodifferential equations of negative order considered in Sobolev spaces with small smoothness indices are ill–posed. On the other hand, it is known that efficient discretization schemes with properly chosen discretization parameters allow to obtain a regularization effect for such equations. The main accomplishment of the present paper is the principle for the adaptive choice of the discretization parameters directly from noisy discrete data. We argue that the combination of this principle with wavelet–based matrix compression techniques leads to algorithms which are order–optimal in the sense of complexity.     

Wavelet filtering to study mixing in 2D isotropic turbulence

This paper presents the application of coherent vortex simulation (CVS) filtering, based on an orthogonal wavelet decomposition of vorticity, to study mixing in 2D homogeneous isotropic turbulent flows. The Eulerian and Lagrangian dynamics of the flow are studied by comparing the evolution of a passive scalar and of particles advected by the coherent and incoherent velocity fields, respectively. The former is responsible for strong mixing and produces the same anomalous diffusion as the total flow, due to transport by the coherent vortices, while mixing in the latter is much weaker and corresponds to classical diffusion.     

Connection Formulas for Second Order Differential Equations with a Complex Parameter and Having an Arbitrary Number of Turning Points

We consider the differential equation on a finite interval I, where I contains m turning points, that is here, zeros of ?. Using asymptotic estimates proved by R. E. LANGER for solutions of (*) for intervals containing only one turning point we derive asymptotic estimates (for ρ → ) for a special fundamental system of solutions of (*) in I. The results obtained are fundamental for the investigation of eigenvalue problems defined by (*) and suitable boundary conditions.     

111In(111Cd) quadrupole interaction in the chalcogenide spinel CdCr2Se4

The¹¹¹Cd quadrupole coupling in the spinel CdCr₂Se₄ is investigated by TDPAC after different sample treatments. The experiments are consistent with Se vacancies causing the non-cubic probe environments and with the assumption that the majority of the¹¹¹In atoms are positioned at A-sites.     

Electronic structure of Sc2AC (A=Al, Ga, In, Tl)

Using ab initio calculations, we have studied Sc₂AC with A=Al, Ga, In and Tl. We show that C 2p and Sc 3d as well as A p and Sc 3d states are hybridized, but the antibonding states in the vicinity of the Fermi level weaken the overall bonding. In terms of the chemical bonding, the influence of the size of the A element is minute. Furthermore, the bulk modulus of the corresponding binary transition metal carbide is not conserved in these phases. Therefore, Sc₂AC can be classified as weakly coupled MAX phases according to Sun and co-workers [Z. Sun, D. Music, R. Ahuja, S. Li, J.M. Schneider, Phys. Rev. B 70 (2004) 092102]. It is our ambition that these calculations will stimulate experimental research on these compounds.     

Soft x-ray laser spectroscopy on trapped highly charged ions at FLASH

In a proof-of-principle experiment, we demonstrate high-resolution resonant laser excitation in the soft x-ray region at 48.6 eV of the 2 (2)S(1/2) to 2 (2)P(1/2) transition of Li-like Fe23+ ions trapped in an electron beam ion trap by using ultrabrilliant light from Free Electron Laser in Hamburg (FLASH). High precision spectroscopic studies of highly charged ions at this and upcoming x-ray lasers with an expected accuracy gain up to a factor of a thousand, become possible with our technique, thus potentially yielding fundamental insights, e.g., into basic aspects of QED.