KPP reaction-diffusion equations with a non-linear loss inside a cylinder

We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a non-linear spacedependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity

Decadal to monthly timescales of magma transfer and reservoir growth at a caldera volcano

International audienceCaldera-forming volcanic eruptions are low-frequency, highimpact events capable of discharging tens to thousands of cubic kilometres of magma explosively on timescales of hours to days, with devastating effects on local and global scales1. Because no such eruption has been monitored during its long build-up phase, the precursor phenomena are not well understood. Geophysical signals obtained during recent episodes of unrest at calderas such as Yellowstone, USA, and Campi Flegrei, Italy, are difficult to interpret, and the conditions necessary for large eruptions are poorly constrained2,3. Here we present a study of pre-eruptive magmatic processes and their timescales using chemically zoned crystals from the 'Minoan' caldera-formingeruption of Santorini volcano,Greece4, which occurred in the late 1600s BC. The results provide insights into how rapidly large silicic systems may pass from a quiescent state to one on the edge of eruption5,6. Despite the large volume of erupted magma4 (40-60 cubic kilometres), and the 18,000-year gestation period between the Minoan eruption and the previous major eruption, most crystals in the Minoan magma record processes that occurred less than about 100 years before the eruption. Recharge of the magma reservoir by large volumes of silicic magma (and some mafic magma) occurred during the century before eruption, and mixing between different silicicmagmabatches was still taking place during the final months. Final assembly of large silicic magma reservoirs may occur on timescales that are geologically very short by comparison with the preceding repose period, with major growth phases immediately before eruption. These observations have implications for the monitoring of long-dormant, but potentially active, caldera systems

Composition and evolution of the melts erupted in 1996 at Karymskoe Lake, Eastern Kamchatka: Evidence from inclusions in minerals

The powerful eruption in the Akademii Nauk caldera on January 2, 1996, marked a new activity phase of Karymsky volcano and became a noticeable event in the history of modern volcanism in Kamchatka. The paper reports data obtained by studying more than 200 glassy melt inclusions in phenocrysts of olivine (Fo82–72), plagioclase (An92–73), and clinopyroxene (Mg# 83–70) in basalts of the 1996 eruption. The data were utilized to estimate the composition of the parental melt and the physicochemical parameters of the magma evolution. According to our data, the parental melt corresponded to low magnesian, highly aluminous basalt (SiO2 = 50.2 wt %, MgO = 5.6 wt %, Al2O3 = 17 wt %) of the mildly potassic type (K2O = 0.56 wt %) and contained much dissolved volatile components (H2O = 2.8 wt %, S = 0.17 wt %, and Cl = 0.11 wt %). Melt inclusions in the minerals are similar in chemical composition, a fact testifying that the minerals crystallized simultaneously with one another. Their crystallization started at a pressure of approximately 1.5 kbar, pro ceeded within a narrow temperature range of 1040 ± 20°C, and continued until a nearsurface pressure of approximately 100 bar was reached. The degree of crystallization of the parental melt during its eruption was close to 55%. Massive crystallization was triggered by H2O degassing under a pressure of less than 1 kbar. Magma degassing in an open system resulted in the escape of 82% H2O, 93% S, and 24% Cl (of their initial contents in the parental melt) to the fluid phase. The release of volatile compounds to the atmosphere during the eruption that lasted for 18 h was estimated at 1.7 × 106 t H2O, 1.4 × 105 t S, and 1.5 × 104 t Cl. The concen trations of most incompatible trace elements in the melt inclusions are close to those in the rocks and to the expected fractional differentiation trend. Melt inclusions in the plagioclase were found to be selectively enriched in Li. The Lienriched plagioclase with melt inclusions thought to originate from cumulate layers in the feeding system beneath Karymsky volcano, in which plagioclase interacted with Lirich melts/brines and was subsequently entrapped and entrained by the magma during the 1996 eruption

Pulsating solutions for multidimensional bistable and multistable equations

We investigate the existence of pulsating front-like solutions for spatially periodic heterogeneous reaction–diffusion equations in arbitrary dimension, in both bistable and more general multistable frameworks. In the multistable case, the notion of a single front is not sufficient to understand the dynamics of solutions, and we instead observe the appearance of a so-called propagating terrace. This roughly refers to a finite family of stacked fronts connecting intermediate stable steady states whose speeds are ordered. Surprisingly, for a given equation, the shape of this terrace (i.e., the involved intermediate states or even the cardinality of the family of fronts) may depend on the direction of propagation