Anomalous dispersion in the Belousov-Zhabotinsky reaction: Experiments and modeling

We report results on dispersion relations and instabilities of traveling waves in excitable systems. Experiments employ solutions of the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction confined to thin capillary tubes which create a pseudo-one-dimensional system. Theoretical analyses focus on a three-variable reaction-diffusion model that is known to reproduce qualitatively many of the experimentally observed dynamics. Using continuation methods, we show that the transition from normal, monotonic to anomalous, single-overshoot dispersion curves is due to an orbit flip bifurcation of the solitary pulse homoclinics. In the case of “wave stacking”, this anomaly induces attractive pulse interaction, slow solitary pulses, and faster wave trains. For “wave merging”, wave trains break up in the wake of the slow solitary pulse due to an instability of wave trains at small wavelength. A third case, “wave tracking” is characterized by the non-existence of solitary waves but existence of periodic wave trains. The corresponding dispersion curve is a closed curve covering a finite band of wavelengths.     

Stochastic homogenization of a class of monotone eigenvalue problems

Stochastic homogenization (with multiple fine scales) is studied for a class of nonlinear monotone eigenvalue problems. More specifically, we are interested in the asymptotic behaviour of a sequence of realizations of the form

Pseudomonotone operators and the Bregman Proximal Point Algorithm

To permit the stable solution of ill-posed problems, the Proximal Point Algorithm (PPA) was introduced by Martinet (RIRO 4:154–159, 1970) and further developed by Rockafellar (SIAM J Control Optim 14:877–898, 1976). Later on, the usual proximal distance function was replaced by the more general class of Bregman(-like) functions and related distances; see e.g. Chen and Teboulle (SIAM J Optim 3:538–543, 1993), Eckstein (Math Program 83:113–123, 1998), Kaplan and Tichatschke (Optimization 56(1–2):253–265, 2007), and Solodov and Svaiter (Math Oper Res 25:214–230, 2000). An adequate use of such generalized non-quadratic distance kernels admits to obtain an interior-point-effect, that is, the auxiliary problems may be treated as unconstrained ones. In the above mentioned works and nearly all other works related with this topic it was assumed that the operator of the considered variational inequality is a maximal monotone and paramonotone operator. The approaches of El-Farouq (JOTA 109:311–326, 2001), and Schaible et al. (Taiwan J Math 10(2):497–513, 2006) only need pseudomonotonicity (in the sense of Karamardian in JOTA 18:445–454, 1976); however, they make use of other restrictive assumptions which on the one hand contradict the desired interior-point-effect and on the other hand imply uniqueness of the solution of the problem. The present work points to the discussion of the Bregman algorithm under significantly weaker assumptions, namely pseudomonotonicity [and an additional assumption much less restrictive than the ones used by El-Farouq and Schaible et al. We will be able to show that convergence results known from the monotone case still hold true; some of them will be sharpened or are even new. An interior-point-effect is obtained, and for the generated subproblems we allow inexact solutions by means of a unified use of a summable-error-criterion and an error criterion of fixed-relative-error-type (this combination is also new in the literature).     

Electronic and geometric properties of Au nanoparticles on Highly Ordered Pyrolytic Graphite (HOPG) studied using X-ray Photoelectron Spectroscopy (XPS) and Scanning Tunneling Microscopy (STM)

Au nanoparticles grown on mildly sputtered Highly Ordered Pyrolytic Graphite (HOPG) surfaces were studied using Scanning Tunneling Microscopy (STM) and X-ray Photoelectron Spectroscopy (XPS). The results were compared with those of Ag nanoparticles on the same substrate. By varying the defect densities of HOPG and the Au coverages, one can create Au nanoparticles in various sizes. At high Au coverages, the structures of the Au films significantly deviate from the ideal truncated octahedral form: the existence of many steps between different Au atomic layers can be observed, most likely due to a high activation barrier of the diffusion of Au atoms across the step edges. This implies that the particle growth at room temperature is strongly limited by kinetic factors. Hexagonal shapes of Au structures could be identified, indicating preferential growth of Au nanostructures along the (111) direction normal to the surface. In the case of Au, XPS studies reveal a weaker core level shift with decreasing particle size compared to the 3d level in similarly sized Ag particles. Also taking into account the Auger analysis of the Ag particles, the core level shifts of the metal nanoparticles on HOPG can be understood in terms of the metal/substrate charge transfer. Ag is (partially) positively charged, whereas Au negatively charged on HOPG. It is demonstrated that XPS can be a useful tool to study metal-support interactions, which plays an important role for heterogeneous catalysis, for example.     

Solving symmetric mixed-model multi-level just-in-time scheduling problems

The generation of leveled production schedules is of high importance for mixed-model assembly lines whose parts and materials are supplied just-in-time by multi-level production processes. The Output Rate Variation problem is the standard mathematical representation of this complex level scheduling problem and has been extensively studied by research thus far. This work identifies novel symmetries in solution sequences of this problem class and shows how these insights can be used to improve exact solution procedures presented in the literature. The effectiveness of the modifications is evaluated by a computational study.     

Driving student-centred calculus: results of a comprehensive case study for Kaizen learning in the Sultanate of Oman

The art of teaching freshmen students is undergoing a rapid paradigm change. Classical forms of teaching are not applicable any more and an unmanageable offer of new multimedia tools and concepts is glutting the market. Moreover, compared to previous courses, the class size triples. In view of these challenges, we implemented a new teaching concept best described as Kaizen learning. By Kaizen learning, we define a teaching philosophy that is based on a concise mix of short learning units (with feedback loops and tests) and of carefully chosen repetitions (also with feedback loops and tests) to calibrate a course for the students. Here, this intensive blended, student-centred learning paradigm is analysed together with its direct impact on the students’ performance. This case study leads to easy-to-implement key drivers for successfully teaching science in Oman, such as (1) human–human interaction, (2) clearly communicated expectations, (3) avoidance of a short-term learning attitude, (4) a no-calculator policy, (5) continuous Kaizen learning, and (6) balanced combination of traditional teaching and e-learning.     

L 2-\overline{\partial}-Cohomology groups of some singular complex spaces

Let X be a pure n-dimensional (where n≥2) complex analytic subset in ? ^N with an isolated singularity at 0. In this paper we express the L ²-(0,q)- $\overline{\partial}$ -cohomology groups for all q with 1≤q≤n of a sufficiently small deleted neighborhood of the singular point in terms of resolution data. We also obtain identifications of the L ²-(0,q)- $\overline{\partial}$ -cohomology groups of the smooth points of X, in terms of resolution data, when X is either compact or an open relatively compact complex analytic subset of a reduced complex space with finitely many isolated singularities.     

Exceptional Components

For a wild acyclic quiver Q, Kerner introduced the notion of exceptional components for the Auslander–Reiten quiver of Q over an algebraically closed field k. He then defined two invariants for these exceptional components and asked whether these invariants coincide for each exceptional component. He showed that for each exceptional component there is a related hereditary factor algebra B of the path algebra kQ. He then proved that B is tame or representation finite and asked whether the representation finite case does occur, at all. We will answer both of Kerner's questions.     

Bifurcation of critical points for continuous families of C 2 functionals of Fredholm type

Given a continuous family of C ² functionals of Fredholm type, we show that the nonvanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial critical points but also allows to estimate the number of bifurcation points along the branch. We use this result for several parameter bifurcation, estimating the number of connected components of the complement of the set of bifurcation points in the parameter space and apply our results to bifurcation of periodic orbits of Hamiltonian systems. By means of a comparison principle for the spectral flow, we obtain lower bounds for the number of bifurcation points of periodic orbits on a given interval in terms of the coefficients of the linearization.     

Fluctuations in the quark-meson model for QCD with isospin chemical potential

We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and   isospin chemical potentials, _μB${\mu }_B$ and _μI${\mu }_I$. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite _μB=3μ${\mu }_B=3\mu$ introduces an additional dimension to the phase diagram as compared to two-color QCD, however. At zero temperature, the (_μI,μ${\mu }_I,\mu$) plane of this phase diagram is strongly constrained by the “Silver Blaze problem.” In particular, the onset of pion condensation must occur at _μI=_mπ/2${\mu }_I=m_{\pi }/2$, independent of μ   as long as μ+_μI$\mu +{\mu }_I$ stays below the constituent quark mass of the QM model or the liquid-gas transition line of nuclear matter in QCD. In order to maintain this relation beyond mean field it is crucial to compute the pion mass from its timelike correlator with the FRG in a consistent way.