A limiting distribution for maxima of discrete stationary triangular arrays with an application to risk due to avalanches

In this paper, we generalize earlier work dealing with maxima of discrete random variables. We show that row-wise stationary block maxima of a triangular array of integer valued random variables converge to a Gumbel extreme value distribution if row-wise variances grow sufficiently fast as the row-size increases. As a by-product, we derive analytical expressions of normalising constants for most classical unbounded discrete distributions. A brief simulation illustrates our theoretical result. Also, we highlight its usefulness in practice with a real risk assessment problem, namely the evaluation of extreme avalanche occurrence numbers in the French Alps.     

Thermosolutal mixed convection and flow-reversal in an inclined parallel-plate channel

The steady-state laminar mixed convection of a binary gas mixture in a parallel-plate channel is investigated. The channel walls are subjected to different combinations of first-type thermal and solutal boundary conditions and different wall inclinations have been considered. A second-order accurate control-volume based numerical scheme is used for the resolution. In parallel with the numerical investigation, the governing conservation equations are also simplified for fully developed conditions and are shown to be controlled by a single parameter. An exact analytical solution is obtained for the main flow variables and transfer rates and serves as a validation tool for the numerical model. In addition, it establishes a criterion based on the two Grashof numbers, the Reynolds number and the channel inclination for the existence of a reversed flow.     

Identification of markers of thermal processing (“roasting”) in aqueous extracts of Coffea arabica L. seeds through NMR fingerprinting and chemometrics

Roasting of Coffea arabica L. seeds gives rise to chemical reactions that produce more than 800 compounds, some being responsible for the desired organoleptic properties for which the beverage called “coffee” is known. In the industry, the “roasting profile,” that is, the times and temperatures applied, is key to influence the composition of roasted coffee beans and the flavour of the beverage made from them. The impact of roasting on the chemical composition of coffee has been the subject of numerous studies, including by nuclear magnetic resonance (NMR) spectroscopy. However, the roasting equipment and profiles applied in these studies are often far from real industrial conditions. In this work, the effects of two critical technological parameters of the roasting process, namely, the “development time” (the period of time after the “first crack,” a characteristic noise due to seed disruption) and the final roasting temperature on coffee extracts, were investigated. Seeds were roasted at pilot scale according to 13 industrial roasting profiles and extracted in D₂O. The extracts were analysed by ¹H NMR experiments. The NMR spectra were compared using (a) quantitative analysis of main signals by successive orders of magnitude and (b) chemometric tools (principal component analysis, partial least squares and sparse-orthogonal partial least squares analysis). This allowed to identify compounds, which may serve as markers of roasting and showed that changes in chemical composition can be detected even for slight change in final temperature (~1°C) or in total roasting time (~25 s).