Herleitung der Chowla-Selberg-Formel aus Shimura'schen Periodenrelationen

Ohne Zusammenfassung     

Theoretical study of new acceptor and donor molecules based on polycyclic aromatic hydrocarbons

Functionalized polycyclic aromatic hydrocarbons (PAHs) are an interesting class of molecules in which the electronic state of the graphene-like hydrocarbon part is tuned by the functional group. Searching for new types of donor and acceptor molecules, a set of new PAHs has recently been investigated experimentally using ultraviolet photoelectron spectroscopy (UPS). In this work, the electronic structure of the PAHs is studied theoretically with the help of B3LYP hybrid density functionals. Using the ΔSCF method, electron binding energies have been determined which affirm, specify and complement the UPS data. Symmetry properties of molecular orbitals are analyzed for a categorization and an estimate of the related signal strength. While σ-like orbitals are difficult to detect in UPS spectra of condensed film, calculation provides a detailed insight into the hidden parts of the electronic structure of donor and acceptor molecules. In addition, a diffuse basis set (6-311++G**) was used to calculate electron affinity and LUMO eigenvalues. The calculated electron affinity (EA) provides a classification of the donor/acceptor properties of the studied molecules. Coronene-hexaone shows a high EA, comparable to TCNQ, which is a well-known classical acceptor. Calculated HOMO-LUMO gaps using the related eigenvalues have a good agreement with the experimental lowest excitation energies. TD-DFT also accurately predicts the measured optical gap.     

Observation of the chaotic spin-wave soliton trains in magnetic films

The transition from stationary to chaotic spin-wave soliton trains has been observed. The experiment utilized cw excitation of envelope solitons through self-modulation instability of spin waves. By increasing the spin-wave power, the secondary self-modulation instability succeeded the primary modulation instability, resulting in after-modulation of the soliton train amplitude. Further increase of the spin-wave power led to development of the higher-order instabilities, resulting in formation of the chaotic soliton train.     

Tire footprint analysis depending on the elastokinematics of a multi-link suspension system using multi-body dynamics simulation

An automotive suspension system represents one of the most complex and important systems in a passenger vehicle, which has to ensure a robust and optimized contact between the wheels and the road at any time. For improving a suspension system it is important to take an investigative look at the interaction between suspension, tire and road dynamics. Thus a part of a study into aspects of suspension modeling on multi-body simulations of rear multi-link suspension system dynamics with focus on the tire footprint area is presented in this work. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Minimax problems of discrete optimization invariant under majority operators

A special class of discrete optimization problems that are stated as a minimax modification of the constraint satisfaction problem is studied. The minimax formulation of the problem generalizes the classical problem to realistic situations where the constraints order the elements of the set by the degree of their feasibility, rather than defining a dichotomy between feasible and infeasible subsets. The invariance of this ordering under an operator is defined, and the discrete minimization of functions invariant under majority operators is proved to have polynomial complexity. A particular algorithm for this minimization is described.     

Ionized state of hydroperoxy radical-water hydrogen-bonded complex: (HO2-H2O)+

Ab initio molecular orbital calculations have been employed to characterize the structure and bonding of the (HO2-H2O)+ radical cation system. Geometry optimization of this system was carried out using unrestricted density functional theory in conjunction with the BHHLYP functional and 6-311++G(2df,2p) as well as 6-311++G(3df,3p) basis sets, the second-order M?ller-Plesset perturbation (MP2) method with the 6-311++G(3df,3p) basis set, and the couple cluster (CCSD) method with the aug-cc-pVTZ basis set. The effect of spin multiplicity on the stability of the (HO2-H2O)+ system has been studied and also compared with that of oxygen. The calculated results suggest a proton-transferred hydrogen bond between HO2 and H2O in H3O3+ wherein a proton is partially transferred to H2O producing the O2...H3O+ structure. The basis set superposition error and zero-point energy corrected results indicate that the H3O3+ system is energetically more stable in the triplet state; however, the singlet state of H3O3+ is more stable with respect to its dissociation into H3O+ and singlet O2. Since the resulting proton-transferred hydrogen-bonded complex (O2...H3O+) consists of weakly bound molecular oxygen, it might have important implications in various chemical processes and aquatic life systems.     

Absence of wave packet diffusion in disordered nonlinear systems

We study the spreading of an initially localized wave packet in two nonlinear chains (discrete nonlinear Schr?dinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverges with time. We find that the participation number of a wave packet does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times we find a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wave packet, we rule out the possibility of slow energy diffusion. The dynamical state could approach a quasiperiodic solution (Kolmogorov-Arnold-Moser torus) in the long time limit.     

Modeling and waveform optimization of stick–slip micro-drives using the method of dimensionality reduction

In this paper, the dynamics of piezo-actuated stick–slip micro-drives are studied experimentally and theoretically. First, the stick–slip-based force-generating test stand is introduced, and experimental results are presented. Then, a numerical model is formulated which explicitly includes the dynamics of normal and tangential properties of the contact areas in the frictional driving elements of the drive. The contact forces are simulated using the method of dimensionality reduction. We show that the experimentally observed behavior can be described without using any fitting parameters or assuming any generalized laws of friction if the explicit contact mechanics of the frictional contacts is taken into account. Furthermore, an even simpler model of the drive is developed to get a qualitative understanding of the system. It is employed to gain a new actuation method, which reduces the vibrations of the drive’s runner and therefore enhances its performance.     

Spin-wave eigenmodes of a saturated magnetic square at different precession angles

Using low-loss dielectric magnetic films in combination with space-resolved Brillouin light scattering spectroscopy we have studied nonlinear modification of eigenmode spatial distributions in saturated magnetic squares. We have found that, as the angle of magnetization precession increases, the eigenmode spatial distributions experience significant qualitative changes due to a nonlinear coupling between forming them standing spin waves. We show that the found nonlinear eigenmodes cannot be described by means of the linear theoretical approach even qualitatively.