Relaxation Patterns in Supercooled Liquids from Generalized Mode-Coupling Theory

The mode-coupling theory of the glass transition treats the dynamics of supercooled liquids in terms of two-point density correlation functions. Here we consider a generalized, hierarchical formulation of schematic mode-coupling equations in which the full basis of multipoint density correlations is taken into account. By varying the parameters that control the effective contributions of higher-order correlations, we show that infinite hierarchies can give rise to both sharp and avoided glass transitions. Moreover, small changes in the form of the coefficients result in different scaling behaviors of the structural relaxation time, providing a means to tune the fragility in glass-forming materials. This demonstrates that the infinite-order construct of generalized mode-coupling theory constitutes a powerful and unifying framework for kinetic theories of the glass transition

Asymptotics for the long-time evolution of kurtosis of narrow-band ocean waves

In this paper we highlight that extreme events such as freak waves are a transient phenomenon in keeping with the old fisherman tale that these extreme events seem to appear out of nowhere. Janssen (J. Phys. Oceanogr., vol. 33, 2003, pp. 863-884) obtained an evolution equation for the ensemble average of the excess kurtosis, which is a measure for the deviation from normality and an indicator for nonlinear focusing resulting in extreme events. In the limit of a narrow-band wave train, whose dynamics is governed by the two-dimensional nonlinear Schrödinger (NLS) equation, the excess kurtosis is under certain conditions seen to grow to a maximum after which it decays to zero for large times. This follows from a numerical solution of the problem and also from an analytical solution presented by Fedele (J. Fluid Mech., vol. 782, 2015, pp. 25-36). The analytical solution is not explicit because it involves an integral from initial time to actual time. We therefore study a number of properties of the integral expression in order to better understand some interesting features of the time-dependent excess kurtosis and the generation of extreme events.</p

Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost complete characterization of the critical behavior of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure

Construction of data-driven models to predict the occurrence of planktonic species in the North-Sea

Marine habitat suitability models typically predict the potential distribution of organisms based on basic abiotic variables such as salinity, oxygen concentrations, temperature fluctuations (Gogina & Zettler, 2010) or sediment class information (Degraer et al., 2008; Willems et al., 2008). Recently, Dachs & Méjanelle (2010) claimed that the modification of biota composition due to marine pollution is a factor to be taken into account in marine habitat suitability models. Although the anthropogenic pressure on the environment has been exponentially increasing during the last six decades (Dachs & Méjanelle, 2010), the global effect of human inputs on oceanic phytoplankton remains unknown (Echeveste et al., 2010). A limited number of studies have assessed the impact of anthropogenic stressors on phytoplankton in marine environments at a global level (Faust et al., 2003; Magnusson et al.,2008). In order to fill this knowledge gap, this research tries to determine to what extent pollution data can be used to predict the occurrence of the phytoplanktonic organisms compared to basic abiotic variables. Here we explored this issue by developing classification trees relating physical-chemical variables with the occurrence of the potential harmful toxic algae Odontella sinensis