Weakly reinforced pólya urns on countable networks

We study the long-time asymptotics of a network of weakly reinforced P\'olya urns. In this system, which extends the WARM introduced by R. van der Hofstad et. al. (2016) to countable networks, the nodes fire at times given by a Poisson point process. When a node fires, one of the incident edges is selected with a probability proportional to its weight raised to a power $\alpha < 1$, and then this weight is increased by $1$. We show that for $\alpha < 1/2$ on a network of bounded degrees, every edge is reinforced a positive proportion of time, and that the limiting proportion can be interpreted as an equilibrium in a countable network. Moreover, in the special case of regular graphs, this homogenization remains valid beyond the threshold $\alpha = 1/2$.Comment: 9 pages, 2 figures, updated with corrections and journal reference (results unchanged

Temporal relationships between Mg-K mafic magmatism and catastrophic melting of the Variscan crust in the southern part of Velay Complex (Massif Central, France)

Mg-K mafic intrusive rocks are commonly observed during the late stages of the evolution of orogenic belts. The Variscan French Massif Central has many outcrops of these rocks, locally called vaugnerites. Such magmas have a mantle-derived origin and therefore allow discussion of the role of mantle melting and crust-mantle interactions during late-orogenic processes. In the Southern Velay area of the French Massif Central, LA-ICPMS U-Pb dating on zircons and monazites from three vaugnerites and four coeval granites reveals that the two igneous suites formed simultaneously, at c. 305 Ma. This major igneous event followed after an early, protracted melting stage that lasted for 20-30 My and generated migmatites, but the melt was not extracted efficiently and therefore no granite plutons were formed. This demonstrates that widespread crustal anatexis, melt extraction and granite production were synchronous with the intrusion of vaugneritic mantle-derived melts in the crust. The rapid heating and subsequent melting of the crust led to upward flow of partially molten rocks, doming and collapse of the belt.JHS was financially supported by the Spanish grant CGL2008–02864 and the Andalusian grant RNM1595

From high-entropy alloys to complex concentrated alloys

High-entropy alloys (HEAs) and related concept of complex concentrated alloys (CCAs) expand the diversity of the materials world and inspire new ideas and approaches for the design of materials with an attractive combination of properties. Here, we present a critical review of the field with the intent of summarizing the principles underlying their birth and growth. We highlight the major accomplishments and progresses over the last 14 years, especially in the discovery of new microstructures and mechanical properties. Finally, we outline the main challenges and provide guidance for future works

Ultrafine versus coarse grained Al 5083 alloys: From low-cycle to very-high-cycle fatigue

The fatigue performance of coarse and ultrafine-grained (UFG) 5083 Al alloy were compared, from low to very high cycle fatigue. The UFG alloy exhibited cyclic hardening and predominant kinematic hardening. At high plastic strain amplitude (and only in this regime), it showed easier crack initiation and a lower fatigue resistance. Its resistance to HCF was hardly better than that of its coarse grained counterpart until 2.10 6 cycles, but 43% higher in VHCF, until 5.10 8 cycles. Beyond that point, internal crack initiation occurred, and the fatigue resistance of the UFG material decreased, which was explained using Fracture Mechanics

Cadomian S-type granites as basement rocks of the Variscan belt (Massif Central, France): Implications for the crustal evolution of the north Gondwana margin

International audienceFrom the Neoproterozoic to the early Paleozoic, the northern Gondwana margin was sequentially shaped by the Cadomian accretionary and the Variscan collisional orogens which offers the opportunity to investigate the relative extent of crust production/reworking in both geodynamic settings. In the eastern part of the Variscan French Massif Central (FMC), the Velay Orthogneiss Formation (VOF) represents a consistent lithological unit of the pre-Variscan basement and comprises augen gneisses and leucogneisses. Such rocks constitute a unique record of the pre-Variscan magmatic history and bear critical information on the crustal evolution of the northern Gondwana margin.Here, we present whole–rock major and trace element compositions indicating that: (i) the VOF shows a remarkable geochemical homogeneity; (ii) the protolith of the augen gneisses corresponds to strongly peraluminous, “S-type” porphyritic granites originating from partial melting of an Ediacaran sedimentary sequence; (iii) the leucogneisses are former leucogranites generated by fractionation of the magma at the origin of the porphyritic granites; and (iv) the whole suite emplaced at shallow crustal levels (< 7 km). U–Pb LA–(MC–)ICP–MS analyses on zircon yielded similar emplacement ages of c. 542 Ma and a narrow range of εHf(t) clustering around 0 for the protoliths of both augen and leucogneisses. This homogeneous Hf isotope signature, notably uncommon for S-type granites, would originate from a sequential process of: (i) inherited zircon dissolution during melting and ascent in the crust due to Zr-undersaturated conditions, (ii) isotopic homogenization of the melt by advection and elemental/isotopic diffusion, followed by (iii) early saturation upon emplacement owing to rapid cooling at shallow crustal levels.We propose that partial melting of Ediacaran sediments occurred during inversion of a Cadomian back-arc basin and was promoted by the high thermal gradient typical of thinned crust domains. Therefore, the VOF and other Cadomian S-type granitoids from the northern Gondwana margin are indicative of substantial crust reworking away from any proper continental collision zone

Flow of partially molten crust controlling construction, growth and collapse of the Variscan orogenic belt: 1 the geologic record of the French Massif Central

We present here a tectonic-geodynamic model for the generation and flow of partially molten rocks and for magmatism during the Variscan orogenic evolution from the Silurian to the late Carboniferous based on a synthesis of geological data from the French Massif Central. Eclogite facies metamorphism of mafic and ultramafic rocks records the subduction of the Gondwana hyperextended margin. Part of these eclogites are forming boudins-enclaves in felsic HP granulite facies migmatites partly retrogressed into amphibolite facies attesting for continental subduction followed by thermal relaxation and decompression. We propose that HP partial melting has triggered mechanical decoupling of the partially molten continental rocks from the subducting slab. This would have allowed buoyancy-driven exhumation and entrainment of pieces of oceanic lithosphere and subcontinental mantle. Geochronological data of the eclogite-bearing HP migmatites points to diachronous emplacement of distinct nappes from middle to late Devonian. These nappes were thrusted onto metapelites and orthogneisses affected by MP/MT greenschist to amphibolite facies metamorphism reaching partial melting attributed to the late Devonian to early Carboniferous thickening of the crust. The emplacement of laccoliths rooted into strike-slip transcurrent shear zones capped by low-angle detachments from c. 345 to c. 310 Ma is concomitant with the southward propagation of the Variscan deformation front marked by deposition of clastic sediments in foreland basins. We attribute these features to horizontal growth of the Variscan belt and formation of an orogenic plateau by gravity-driven lateral flow of the partially molten orogenic root. The diversity of the magmatic rocks points to various crustal sources with modest, but systematic mantle-derived input. In the eastern French Massif Central, the southward decrease in age of the mantle- and crustal-derived plutonic rocks from c. 345 Ma to c. 310 Ma suggests southward retreat of a northward subducting slab toward the Paleotethys free boundary. Late Carboniferous destruction of the Variscan belt is dominantly achieved by gravitational collapse accommodated by the activation of low-angle detachments and the exhumation-crystallization of the partially molten orogenic root forming crustal-scale LP migmatite domes from c. 305 Ma to c. 295 Ma, coeval with orogen-parallel flow in the external zone. Laccoliths emplaced along low-angle detachments and intrusive dykes with sharp contacts correspond to the segregation of the last melt fraction leaving behind a thick accumulation of refractory LP felsic and mafic granulites in the lower crust. This model points to the primordial role of partial melting and magmatism in the tectonic-geodynamic evolution of the Variscan orogenic belt. In particular, partial melting and magma transfer (i) triggers mechanical decoupling of subducted units from the downgoing slab and their syn-orogenic exhumation; (ii) the development of an orogenic plateau by lateral flow of the low-viscosity partially molten crust; and, (iii) the formation of metamorphic core complexes and domes that accommodate post-orogenic exhumation during gravitational collapse. All these processes contribute to differentiation and stabilisation of the orogenic crust

Tectonic erosion and crustal relamination during the India-Asian continental collision: Insights from Eocene magmatism in the southeastern Gangdese belt

Understanding the processes of tectonic erosion and crustal relamination during continental collision has important implications for the growth and differentiation of the continental crust. The discrepancy in isotopic compositions between the pre- and syn-collision magmatic rocks from the Gangdese belt in south Tibet provides an opportunity for studying these processes during the India-Asian collision. The Nyingchi granites and Confluence hornblende gabbros from the eastern Gangdese belt have zircon U-Pb ages of ca. 50 Ma. The Nyingchi granites have high Sr/Y and (Dy/Yb)N ratios, indicating that the magma was generated under eclogite-facies conditions. Their Sr-Nd-Pb-Hf isotopic compositions require significant incorporation of ancient supracrustal materials from the Gangdese belt and the Indian continent. The Confluence hornblende gabbros display arc-like trace element patterns but have enriched Sr-Nd-Pb-Hf isotopic compositions compared with those from the Jurassic-Cretaceous arc magmatic rocks, indicating significant input of ancient components into their mantle sources. The occurrence of the Cenozoic felsic metamorphic rocks in the lower crust of the Gangdese belt allows us to propose that the Nyingchi high Sr/Y granites were derived from partial melting of relaminated crustal materials which were removed from the Gangdese belt by tectonic erosion and the subducted Indian continent. The Confluence gabbros were sourced from lithospheric mantle which was metasomatized by inputs from relaminated crustal materials derived from the Gangdese belt and the subducted Indian continent. The estimated tectonic erosion rate is 150–188 km3/km/my, indicating significant crustal loss occurred during continental collision. Our study demonstrates that tectonic erosion and crustal relamination play an important role in the refinement of the composition of continental crust during continental collision

L’évolution de la croute continentale vue par le zircon, résultats et limites de l’approche à partir de l’exemple du Massif Central français

The formation of the continental crust is a major consequence of Earth differentiation. Understanding how the crust formed and evolved through time is paramount to locate the vast mineral deposits hosted therein and address its influence on the global climate, ultimately affecting the development of terrestrial life. Recent advances on the topic of continental crust evolution benefited from improvements of analytical techniques enabling in situ measurements of U-Pb- Hf-O isotope compositions in zircon, a widespread accessory mineral of continental igneous rocks. The time constrains derived from the U-Pb chronometer coupled with the petrogenetic information retrieved from Hf-O isotope signatures are currently used to unravel the diversity and succession of magmatic events affecting the continental crust at the regional and global scales. This study reconstructs the evolutionary path followed by the crust segment today exposed in the eastern part of the French Massif Central (FMC), a portion of the Variscan belt of Western Europe, with the aim to investigate the potential flaws of the zircon record of crust evolution. In this scope, the origin and geodynamic significance of the constituent FMC lithological units are tackled by combining conventional petrological observations with zircon U-Pb-Hf-O isotope data. The results obtained following this integrated approach are then confronted to the conclusions that would have been drawn solely from zircon isotopic signatures, taken out of their petrological context, as is commonly performed in studies investigating crust evolution. The oldest rocks of the FMC correspond to Ediacaran (590_550 Ma) meta-sediments deposited in back-arc basins along the northern Gondwana margin. Such basins were fed by a mixed detritus originating from the adjacent Cadomian magmatic arc and a distal Gondwana source, presumably the Sahara Metacraton. Partial melting of these meta-sediments at the Ediacaran/Cambrian boundary led to voluminous S-type granitic magmatism, pinpointing a first major crust reworking event in the FMC. The origin of anatexis likely stems from the transient thickening of the hot, back-arc crust caused by the flattening of the Cadomian subduction. Subordinate melting of the depleted backarc mantle at that time is also documented. During the Lower Paleozoic, rifting of the northern Gondwana provoked coeval crust and (limited) mantle melting. Mantle-derived igneous rocks show markedly diverse trace element and isotopic signatures, consistent with a very heterogeneous mantle source pervasively modi_ed by the Cadomian subduction. Finally, the Variscan collision resulted in crustal melting as evidenced by the emplacement of S-type granites and the formation of migmatite domes, the spatial distribution of which being partly controlled by the crustal architecture inherited from pre-orogenic events. Synchronous intrusion of mafic mantle-derived magmas and their differentiates testify for Variscan post-collisional new continental crust production in the FMC. Two major inconsistencies exist between these results and the zircon record. First, zircon Hf model ages would point to substantial Mesoproterozoic crust formation in the FMC whereas more than 60% of the crust is actually Neoproterozoic in age. Second, new additions to the continental crust volume during the Variscan orogeny are not recorded even though 5 to 10% of the exposed crust formed at that time. The origin of both discrepancies inherently lies in the mixed isotopic signature carried by many zircon grains. Such equivocal information can only be detected when additional petrological constrains on the zircon host rocks are available and provide guidance in interpreting the zircon record of crust evolutionLa formation de la croute continentale est une des conséquences majeures de la différenciation de la Terre. Les avancées récentes dans la compréhension de ce phénomène résultent de l’amélioration des techniques analytiques permettant la mesure in situ des compositions isotopiques en U-Pb-Hf-O de grains de zircon, minéral abondant dans les roches crustales. Cette étude reconstitue l’histoire du segment de croute affleurant dans l’est du Massif Central français (MCF), portion de la chaine Varisque d’Europe de l’Ouest, dans le but d’évaluer les limites d’utilisation des zircons pour retracer l’évolution crustale. L’origine et la signification géodynamique des principales unités lithologiques du MCF ont été étudiées en combinant les approches classiques de la pétrologie avec des données isotopiques U-Pb-Hf-O acquises sur zircon. Deux incohérences majeures existent entre nos résultats et les conclusions tirées de l’étude des zircons considérés hors de leur contexte pétrologique, approche généralement suivie pour analyser l’évolution crustale. Les âges modèles calculés à partir des données Hf suggèrent une importante croissance crustale au Mésoproterozoique dans le MCF, en contradiction avec le fait que 60% de la croute locale soit d’âge Néoproterozoïque. De plus, 5 à 10% de la croute du MCF a été formée durant l’orogènese Varisque sans que cela ne soit enregistré par le zircon. Dans les deux cas, ces incohérences résultent du caractère hybride des signatures isotopiques portées par les zircons. Celles-ci ne peuvent être correctement détectées et interprétées qu’en disposant de données pétrologiques complémentaires sur les roches contenant les grains analysé