A hypergeometric function approach to the persistence problem of single sine-Gordon breathers

It is shown that for an interesting class of perturbation functions, at most one of the continuum of sine-Gordon breathers can persist for the perturbed equation. This question is much more subtle than the question of persistence of large portions of the family, because analytic continuation arguments in the amplitude parameter are no longer available. Instead, an asymptotic analysis of the obstructions to persistence for large Fourier orders is made, and it is connected to the asymptotic behaviour of the Taylor coefficients of the perturbation function by means of an inverse Laplace transform and an integral transform whose kernel involves hypergeometric functions in a way that is degenerate in that asymptotic analysis involves a splitting monkey saddle. Only first order perturbation theory enters into the argument. The reasoning can in principle be carried over to other perturbation functions than the ones considered here.

     

Numerical study on the fluid-structure interaction in a model aquatic canopy flow

This work presents numerical simulations and selected results of the flow over aquatic canopies, consisting of artificial flexible rectangular blades, arranged in a well-defined order. The results obtained with three different Reynolds and Cauchy numbers are compared with experimental data achieving good agreement. The considered range of Cauchy numbers represents three different types of canopies ranging from rigid up to highly flexible plants. The transient flow data and blade positions are statistically analyzed to gain deeper understanding of the complex physical processes for this kind of fluid structure interaction. For example, the correlation of role of large scale motion of the flexible blades in conjunction with coherent vortex structures of the flow is addressed. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability criteria for positive linear discrete-time systems

Positivity - We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have...     

Convex interval interpolation with cubic splines,II

The problem of convex interval interpolation with cubicC ¹-splines has an infinite number of solutions, if it is solvable at all. For selecting one of the solutions a regularized mean curvature is minimized. The arising finite dimensional constrained program is solved numerically by means of a dualization approach.Dedicated to Professor Julius Albrecht on the occasion of his 65th birthday.     

Sum factorization of the static condensed Helmholtz equation in a three-dimensional spectral element discretization

We propose a factorization technique for the Helmholtz operator of a static condensed, three-dimensional, cartesian spectral-element discretization, that yields linear complexity in the number of degrees of freedom. We then compare its performance to a reference implementation of the conventional, unfactorized approach. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A multiwave range test for obstacle reconstructions with unknown physical properties

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A ‘range test’ for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533–547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhäuser, Basel, 1986, pp. 93–102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Göttingen, 1999]. In particular, we propose a new version of the Kirsch–Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.     

The combination technique and some generalisations

The combination technique has repeatedly been shown to be an effective tool for the approximation with sparse grid spaces. Little is known about the reasons of this effectiveness and in some cases the combination technique can even break down. It is known, however, that the combination technique produces an exact result in the case of a projection into a sparse grid space if the involved partial projections commute.

The performance of the combination technique is analysed using a projection framework and the C/S decomposition. Error bounds are given in terms of angles between the spanning subspaces or the projections onto these subspaces. Based on this analysis modified combination coefficients are derived which are optimal in a certain sense and which can substantially extend the applicability and performance of the combination technique.     

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.     

A field-theoretic study of the Regge-eikonal model. II

A previous study of the Regge-eikonal model in φ³ is extended to QED. First we define a reggeon amplitude that is built up by tower diagrams, and then study multiregge exchange by use of Gribov's reggeon calculus. The situation is essentially the same as in φ³: The eikonal approximation is the true high-energy and weak coupling limit (s → ∞, α ln s = fixed), but it breaks down outside of the weak-coupling limit. This confirms that the eikonal approximation as a model for Regge-cuts is not justifiable by field-theoretic arguments because of the neglect of inelastic intermediate states.     

Simultaneous Raman and fluorescence spectroscopy of single conjugated polymer chains

Simultaneous surface enhanced Raman scattering (SERS) and fluorescence is demonstrated from single conjugated polymer chains. As resonance enhancement of SERS depends on the spectral overlap of the polymer's absorption and the incident laser, resonance Raman and fluorescence effectively probe the absorbing and emitting part of the polymer, respectively. The optical phonon energies change along the polymer chain, providing a window to spatially track excited state relaxation. Whereas a mean spatial redistribution of the excitation is witnessed by a change in vibronic fingerprint following interchromophoric energy transfer, intrachromophoric exciton self-trapping leaves the vibrations unchanged.