A Parallel Iterative Method for Computing Molecular Absorption Spectra

We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of "dominant products" to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamical polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a a matrix-free GMRES method to determine the (interacting) density response. The resulting code is about one order of magnitude faster than our previous full-matrix method. This acceleration makes the speed of our TDDFT code comparable with codes based on Casida's equation. The implementation of our method uses hybrid MPI and OpenMP parallelization in which load balancing and memory access are optimized. To validate our approach and to establish benchmarks, we compute spectra of large molecules on various types of parallel machines. The methods developed here are fairly general and we believe they will find useful applications in molecular physics/chemistry, even for problems that are beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.Comment: 20 pages, 17 figures, 3 table

Cosmic Ray Nuclei (CRN) detector investigation

The Cosmic Ray Nuclei (CRN) detector was designed to measure elemental composition and energy spectra of cosmic radiation nuclei ranging from lithium to iron. CRN was flown as part of Spacelab 2 in 1985, and consisted of three basic components: a gas Cerenkov counter, a transition radiation detector, and plastic scintillators. The results of the experiment indicate that the relative abundance of elements in this range, traveling at near relativistic velocities, is similar to those reported at lower energy

Remarks on an occurence of Orobanche hederae VAUCHER ex DUBY (Ivy Broomrape) in Dortmund, a rare plant species in North Rhine-Westphalia

Es wird über ein rezentes Vorkommen von Orobanche hederae (Efeu-Sommerwurz, Efeu-Würger) in Dortmund- Lütgendortmund berichtet sowie eine Einschätzung bezüglich der Herkunft, der Gefährdung und des floristischen Status dieses Vorkommens vorgenommen. Des Weiteren wird die pflanzengeografische Bedeutung des Fundes, speziell für den Ballungsraum Ruhrgebiet, aber auch für Westfalen insgesamt, diskutiert. Ferner wird eine Übersicht über die jüngsten Funde der Art in Nordrhein-Westfalen in den letzten zehn Jahren geliefert.This article reports a new occurrence of the rare parasitical plant species Orobanche hederae VAUCHER ex DUBY (Ivy Broomrape) in the city of Dortmund (Westphalia). A description and discussion of the origin, the threat of the current location and the importance of this finding in relation to the flora of the Ruhr Region and North Rhine- Westphalia will be given. Furthermore, an overview of occurrences of this species in North Rhine-Westphalia for the last ten years is provided

On Presburger arithmetic extended with non-unary counting quantifiers

We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting, and exact-counting quantifiers, all applied to tuples of variables. Further, the residue in modulo-counting quantifiers is given as a term. Our main result shows that satisfaction for this logic is decidable in two-fold exponential space. If only threshold- and exact-counting quantifiers are allowed, we prove an upper bound of alternating two-fold exponential time with linearly many alternations. This latter result almost matches Berman's exact complexity of first-order logic without counting quantifiers. To obtain these results, we first translate threshold- and exact-counting quantifiers into classical first-order logic in polynomial time (which already proves the second result). To handle the remaining modulo-counting quantifiers for tuples, we first reduce them in doubly exponential time to modulo-counting quantifiers for single elements. For these quantifiers, we provide a quantifier elimination procedure similar to Reddy and Loveland's procedure for first-order logic and analyse the growth of coefficients, constants, and moduli appearing in this process. The bounds obtained this way allow to replace quantification in the original formula to integers of bounded size which then implies the first result mentioned above. Our logic is incomparable with the logic considered recently by Chistikov et al. They allow more general counting operations in quantifiers, but only unary quantifiers. The move from unary to non-unary quantifiers is non-trivial, since, e.g., the non-unary version of the H\"artig quantifier results in an undecidable theory