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Archiv der Mathematik -     

Über die Wertannahme der Ahlfors Funktion in beliebigen Gebieten

Let B be a domain ?? that supports nonconstant bounded analytic functions, let pe B. In [1] S.Fisher posed the question: Does the Ahlforsfunction for B and p map a maximal B onto the unit disc D? We give an example of a maximal B such that in B F(z) omits two values of D.     

13C-NMR-Spektroskopie von Cyclopropenonen und Cyclopropenyliumionen (Cyclopropenonchemie: VII)

The carbon-13 NMR spectra of thirteen cyclopropenones, two cyclopropenethiones, five related cyclopropenylium salts and three cyclobutenediones are tabulated and discussed.     

Modelling Spirals of Silence and Echo Chambers by Learning from the Feedback of Others

What are the mechanisms by which groups with certain opinions gain public voice and force others holding a different view into silence? Furthermore, how does social media play into this? Drawing on neuroscientific insights into the processing of social feedback, we develop a theoretical model that allows us to address these questions. In repeated interactions, individuals learn whether their opinion meets public approval and refrain from expressing their standpoint if it is socially sanctioned. In a social network sorted around opinions, an agent forms a distorted impression of public opinion enforced by the communicative activity of the different camps. Even strong majorities can be forced into silence if a minority acts as a cohesive whole. On the other hand, the strong social organisation around opinions enabled by digital platforms favours collective regimes in which opposing voices are expressed and compete for primacy in public. This paper highlights the role that the basic mechanisms of social information processing play in massive computer-mediated interactions on opinions.     

Synchronization and complex dynamics of oscillators with delayed pulse coupling

Finger on the pulse: A systematic experimental study of pulse-coupled chemical oscillators with delay has confirmed a surprisingly large number of theoretical and mathematical predictions (see the dynamics for a pair of pulse-coupled oscillators; AP=antiphase (AP) and IP=in-phase oscillations, C=complex bursting dynamics, and OS=oscillator suppression). These results have implications for neuroscience and other biological fields.     

Weak equivalence principle from a spontaneously broken gauge theory of gravity

Further consequences of a finite topological field theory for gravity based on the SL(5,R) gauge group are reported. After symmetry breaking, it induces four-dimensional Einstein spaces with a cosmological constant related to the tiny scale of the symmetry breaking. It is shown that not only a ‘background’ metric emerges from a Higgs-like mechanism, but also consistently the geodesic equation central to Einstein?s equivalence principle. In next order of the symmetry breaking scale, the induced torsion could even provoke a tiny Lorentz violation.     

Nonlocal control of pulse propagation in excitable media

We study the effects of nonlocal control of pulse propagation in excitable media. As ageneric example for an excitable medium the FitzHugh-Nagumo model with diffusion in theactivator variable is considered. Nonlocal coupling in form of an integral term with aspatial kernel is added. We find that the nonlocal coupling modifies the propagatingpulses of the reaction-diffusion system such that a variety of spatio-temporal patternsare generated including acceleration, deceleration, suppression, or generation of pulses,multiple pulses, and blinking pulse trains. It is shown that one can observe these effectsfor various choices of the integral kernel and the coupling scheme, provided that thecontrol strength and spatial extension of the integral kernel is appropriate. In addition,an analytical procedure is developed to describe the stability borders of the spatiallyhomogeneous steady state in control parameter space in dependence on the parameters of thenonlocal coupling.     

Phosphor thermometry at the surface of single reacting large-diameter spherical coke particles to characterise combustion for packed bed furnaces

Packed-bed furnaces fired with large-diameter coke are important in high-temperature material processing industries such as lime and iron production. The combustion conditions are complicated by the presence of an ash layer surrounding the coke particle that remains intact during passage through the furnace and alters oxygen diffusion and heat transfer to the reacting particle core. The objective of this study is to determine the surface temperature of this ash layer using lifetime-based phosphor thermometry during combustion of single spherical 38 mm diameter coke particles in a high temperature tube furnace. Time traces of the coke particle core temperature and mass conversion rate do not significantly differ between experiments performed with and without the phosphor layer, indicating that the presence of the phosphor particles does not alter the overall combustion behaviour. Surface temperatures of up to 950 °C are measured and correlated with the fuel mass conversion rate. When the coke particle starts to react the surface temperature is up to 100 °C higher than that of the core. As the reaction front progresses toward the centre, the core temperature exceeds the surface temperature by 200 °C due to the insulating effect of the ash layer. The surface temperature of the ash layer decreases with time due to the steadily decreasing fuel mass conversion rate. The method and results can be used to provide key validation data for shrinking-core combustion models, for example by constraining the unknown transport properties of the ash layer, thereby assisting the development of complete packed-bed furnace simulations for process optimisation.