Search

Let $G=(G_j)_{j\ge 0}$ be a strictly increasing linear recurrent sequence of integers with $G_0=1$ having characteristic polynomial $X^{d}-a_1X^{d-1}-\cdots-a_{d-1}X-a_d$. It is well known that each positive integer $\nu$ can be uniquely represented by the so-called greedy expansion $\nu=\varepsilon_0(\nu)G_0+\cdots+\varepsilon_\ell(\nu)G_\ell$ for $\ell \in \mathbb{N}$ satisfying $G_\ell \le \nu < G_{\ell+1}$. Here the digits are defined recursively in a way that $0\le \nu - \varepsilon_{\ell}(\nu) G_\ell - \cdots - \varepsilon_j(\nu) G_j < G_j$ holds for $0 \le j \le \ell$. In the present paper we study the sum-of-digits function $s_G(\nu)=\varepsilon_0(\nu)+\cdots+\varepsilon_\ell(\nu)$ under certain natural assumptions on the sequence $G$. In particular, we determine its level of distribution $x^{\vartheta}$. To be more precise, we show that for $r,s\in\mathbb{N}$ with $\gcd(a_1+\cdots+a_d-1,s)=1$ we have for each $x\ge 1$ and all $A,\varepsilon\in\mathbb{R}_{>0}$ that \[ \sum_{q, Comment: 22 pages, 1 figure, 1 table

International audience

International audience; The growth of faceted crystals occurs often in nature and industry, involving often the presence of flow. The growth of faceted crystals is the result of interface kinetics and diffusion phenomenon. The present paper presents a front tracking interface model based on a cellular automaton approach for the simulation of faceted crystal growth. The current model takes into account the interface kinetics and solute transport by diffusion and convection. The propagation of kinks is modelled by differentiating two growth velocities, one normal and one lateral at each face. The positions of the crystal corners are shifted according to growth of adjacent faces. The hydrodynamics is computed with a two-phase model using a penalty method to model the presence of growing obstacles (the crystals). This model was applied in 2D to the growth of hexagonal Fe 2 Al 5 crystals, so called top dross particles, in a saturated liquid at constant temperature. Qualitative comparison was made between simulation and experimental observation of crystal shape and size. The growth rate was found to be strongly influenced by the flow hydrodynamic induced kinetics.

International audience; Mixed TixSi1−xO2 oxide can exhibit a partial phase separation of the TiO2 and SiO2 phases at the atomic level. The quantification of TiO2-SiO2 mixing in the amorphous material is complicated and was so far done mostly by infrared spectroscopy. We developed a new approach to the fitting of X-ray photoelectron spectroscopy data for the quantification of partial phase separation in amorphous TixSi1-xO2 thin films deposited by plasma enhanced chemical vapour deposition. Several fitting constraints reducing the total number of degrees of freedom in the fits and thus the fit uncertainty were obtained by using core electron binding energies predicted by density functional theory calculations on TixSi1-xO2 amorphous supercells. Consequently, a decomposition of the O1s peak into TiO2, SiO2 and mixed components was possible. The component areas ratios were compared with the ratios predicted by older theoretical models based on the atomic environment statistics and we also developed several new models corresponding to more realistic atomic structure and partial mixing. Based on the comparison we conclude that the studied films are mostly disordered, with only a moderate phase separation.

International audience; In this work, the structural and mechanical properties of ternary Mo-Al-N alloys are investigated by combining thin film growth experiments and density functional theory (DFT) calculations. Mo 1−x Al x N y thin films (∼300 nm thick), with various Al fractions ranging from x = 0 to 0.5 and nitrogen-to-metal (Al + Mo) ratio ranging from y = 0.78 to 1.38, were deposited by direct-current reactive magnetron cosputtering technique from elemental Mo and Al targets under Ar + N 2 plasma discharges. The Al content was varied by changing the respective Mo and Al target powers, at a fixed N 2 (20 SCCM) and Ar (25 SCCM) flow rate, and using two different substrate temperatures T s = 350 and 500°C. The elemental composition, mass density, crystal structure, residual stress state, and intrinsic (growth) stress were examined by wavelength dispersive x-ray spectroscopy, x-ray reflectivity, x-ray diffraction, including pole figure and sin 2 ψ measurements, and real-time in situ wafer curvature. Nanoindentation tests were carried out to determine film hardness H and elastic modulus E IT , while the shear elastic constant C 44 was measured selectively by surface Brillouin light spectroscopy. All deposited Mo 1−x Al x N y films have a cubic rock-salt crystal structure and exhibit a fiber-texture with a [001] preferred orientation. The incorporation of Al is accompanied by a rise in nitrogen content from 44 to 58 at. %, resulting in a significant increase (2%) in the lattice parameter when x increases from 0 to 0.27. This trend is opposite to what DFT calculations predict for cubic defect-free stoichiometric Mo 1−x Al x N compounds and is attributed to variation in point defect concentration (nitrogen and metal vacancies) when Al substitutes for Mo. Increasing T s from 350 to 500°C has a minimal effect on the structural properties and phase composition of the ternary alloys but concurs to an appreciable reduction of the compressive stress from −5 to −4 GPa. A continuous increase and decrease in transverse sound velocity and mass density, respectively, lead to a moderate stiffening of the shear elastic constant from 130 to 144 GPa with increasing Al fraction up to x = 0.50, and a complex and nonmonotonous variation of H and E IT is observed. The maximum hardness of ∼33 GPa is found for the Mo 0.81 Al 0.19 N 1.13 film, with nitrogen content close to the stoichiometric composition. The experimental findings are explained based on structural and elastic constant values computed from DFT for defect-free and metal-or nitrogen-deficient rock-salt MoAlN compounds.

The Konos Hill and Pagoni Rachi porphyry-epithermal prospects in northeastern Greece are characterized by abundant pyrite that displays important textural and geochemical variations between the various ore stages. It is commonly fine-grained and anhedral in the porphyry-related mineralization (M- and D-type veins), while it forms idiomorphic, medium- to coarse-grained crystals in the late, epithermal style veins (E-type). Porphyry-style pyrite from both prospects is characterized by an enrichment in Co, Se, Cu, and minor Zn, and a depletion in other trace elements, like Bi, Mo, Ag, etc. Pyrite in epithermal-style mineralization is mostly characterized by the presence of As, Bi, Pb, Ni, and Se. Gold in pyrite from all mineralization stages occurs as a non-stoichiometric substituting element, and its abundance correlates with As content. Arsenic in pyrite from Konos Hill records an increase from the porphyry stage to the epithermal stage (along with gold), however, at Pagoni Rachi, the highest Au and As contents are recorded in D-type pyrite and in the epithermal stage. The composition of the studied pyrite marks changes in the physico-chemical conditions of the ore-forming fluids and generally follows the geochemical trends from other porphyry-epithermal systems elsewhere. However, a notable enrichment of Se in the porphyry-style pyrite here is a prominent feature compared to other deposits and can be considered as an exploration tool towards Au-enriched mineralized areas.

The properties of dialdehyde celluloses, which are usually generated by periodate oxidation, are highly dependent on the aldehyde content, i.e. the degree of oxidation (DO). Thus far, the established methods for determining the DO in dialdehyde celluloses lack simplicity or sufficient speed. More than 60 dialdehyde cellulose samples with varying aldehyde content were analysed by near-infrared and Fourier-transform infrared spectroscopy. This was found to be a reliable method for quickly predicting the DO if combined with partial least squares regression (PLSR). The proposed PLSR models can predict the DO with a high determination coefficient (R2) of 99% when applied to a single pulp type and 94% when applied to multiple types. This new approach quickly and reliably determines the DO of dialdehyde celluloses. It can be easily implemented in everyday research to save money, time and resources, especially because the raw datasets and measured DO are provided.

Micro- and nanocrystalline cellulose were extracted from wheat stalk (WS) using different thermomechanical and chemical treatments and characterized by spectroscopic, microscopic and diffraction techniques. The virgin WS fibers were found to be structurally quite similar to the commercial microcrystalline cellulose (MCC). Similar to the commercial one, the MCC extracted from the WS possessed intense infrared (IR) peaks whereas those peaks became more broader in the nanocrystalline cellulose (NCC) of the same origin, which can be attributed to possible breakdown of inter- and intramolecular H-bonding due to strong acid treatment of the MCC. Microscopic results revealed characteristic textures of the MCC and the NCC, the MCC being irregular bundles of the primary crystals bound together with the amorphous phase. The latter was found to disintegrate upon acid hydrolysis giving rise to the rod-shaped nanocrystals having much larger surface area and thus possessing more intense hydrophilic character. The MCC was found to be more stable than the NCC which can be attributed to the presence of protective and binding coating provided by the amorphous cellulosic matter.BIBECHANA 16 (2019) 177-186

The new mineral species arsenmarcobaldiite, Pb12(As3.2Sb2.8) summation=6S21, occurs as black anhedral grains, up to 0.5 mm in size, with metallic lustre, associated with pyrite and minor sphalerite, within layers of granoblastic quartz and accessory baryte embedded in pyrite-rich schist from a small baryte + pyrite prospect at Verzalla, Stazzema, Apuan Alps, Tuscany, Italy. Under the ore microscope, arsenmarcobaldiite is white. It is weakly pleochroic in shades of grey. Anisotropy is distinct, both in air and oil, with rotation tints from brownish to bluish-grey. Reflectance percentages for the four COM wavelengths are [Rmin, Rmax (%), (lamda)]: 32.8, 38.3 (470 nm); 32.2, 37.5 (546 nm); 31.7, 36.9 (589 nm); 31.4, 36.6 (650 nm). Polysynthetic twinning is common and characteristic. Electron microprobe analysis gave (in wt% - average of 19 spot analyses): Ag 0.20(1), Pb 66.34(38), As 6.36(10), Sb 8.93(9), Bi 0.30(5), S 18.00(14), total 100.13(48). On the basis of summationMe = 18 atoms per formula unit, the chemical formula is Ag0.07(1)Pb11.96(5)(As3.17(4)Sb2.74(3)Bi0.05(1))summation5.96S20.97(17), ideally Pb12(As3.2Sb2.8)summation=6S21. The main diffraction lines, corresponding to multiple hkl indices, are [d in Å (relative visual intensity)]: 3.595 (m), 3.429 (m), 3.214 (ms), 3.027 (ms), 2.233 (s), 2.125 (ms), 1.839 (ms). The X-ray diffraction study gave a triclinic unit cell, space group P1, with a = 8.9736(9), b = 29.334(3), c = 8.4925(10) Å, alfa = 98.369(6), beta= 118.705(6), gamma= 90.874(6)O, V = 1930.5(4) Å3 , Z = 2. The crystal structure was solved and refined to R1 = 0.063 on the basis of 6325 reflections with Fo > 4sigma (Fo) and 364 refined parameters. Arsenmarcobaldiite is a new N = 3.5 homologue belonging to the jordanite homologous series and it is the As-dominant isotype of marcobaldiite.

Much of the present-day volume of Earth’s continental crust had formed by the end of the Archean Eon, 2.5 billion years ago, through the conversion of basaltic (mafic) crust into sodic granite of tonalite, trondhjemite and granodiorite (TTG) composition. Distinctive chemical signatures in a small proportion of these rocks, the so-called high-pressure TTG, are interpreted to indicate partial melting of hydrated crust at pressures above 1.5 GPa (>50 km depth), pressures typically not reached in post-Archean continental crust. These interpretations significantly influence views on early crustal evolution and the onset of plate tectonics. Here we show that high-pressure TTG did not form through melting of crust, but through fractionation of melts derived from metasomatically enriched lithospheric mantle. Although the remaining, and dominant, group of Archean TTG did form through melting of hydrated mafic crust, there is no evidence that this occurred at depths significantly greater than the ~40 km average thickness of modern continental crust., Some of Earth’s earliest continental crust has been previously inferred to have formed from partial melting of hydrated mafic crust at pressures above 1.5 GPa (more than 50 km deep), pressures typically not reached in post-Archean continental crust. Here, the authors show that such high pressure signatures can result from melting of mantle sources rather than melting of crust, and they suggest there is a lack of evidence that Earth’s earliest crust melted at depths significantly below 40 km.

Magnetite is a common accessory phase in various types of ore deposits. Its trace element content has proven to have critical implications regarding petrogenesis and as guides in the exploration for ore deposits in general. In this study we use LA-ICP-MS (laser ablation-inductively coupled plasma-mass spectrometry) analyses of trace elements to chemically characterize magnetite from the Pagoni Rachi Cu&ndash, Mo&ndash, Re&ndash, Au porphyry-style prospect, Thrace, northern Greece. Igneous magnetite mostly occurs as euhedral grains, which are commonly replaced by hematite in fresh to propylitic-altered granodiorite porphyry, whereas, hydrothermal magnetite forms narrow veinlets or is disseminated in sodic/potassic-calcic altered (albite + K-feldspar + actinolite + biotite + chlorite) granodiorite porphyry. Magnetite is commonly associated with chalcopyrite and pyrite and locally exhibits martitization. Laser ablation ICP-MS analyses of hydrothermal magnetite yielded elevated concentrations in several trace elements (e.g., V, Pb, W, Mo, Ta, Zn, Cu, and Nb) whereas Ti, Cr, Ni, and Sn display higher concentration in its magmatic counterpart. A noteworthy enrichment in Mo, Pb, and Zn is an unusual feature of hydrothermal magnetite from Pagoni Rachi. High Si, Al, and Ca values in a few analyses of hydrothermal magnetite imply the presence of submicroscopic or nano-inclusions (e.g., chlorite, and titanite). The trace element patterns of the hydrothermal magnetite and especially the decrease in its Ti content reflect an evolution from the magmatic towards the hydrothermal conditions under decreasing temperatures, which is consistent with findings from analogous porphyry-style deposits elsewhere.

International audience; Greece contains several gem corundum deposits set within diverse geological settings, mostly within the Rhodope (Xanthi and Drama areas) and Attico-Cycladic (Naxos and Ikaria islands) tectono-metamorphic units. In the Xanthi area, the sapphire (pink, blue to purple) deposits are stratiform, occurring within marble layers alternating with amphibolites. Deep red rubies in the Paranesti-Drama area are restricted to boudinaged lenses of Al-rich metapyroxenites alternating with amphibolites and gneisses. Both occurrences are oriented parallel to the ultra-high pressure/high pressure (UHP/HP) Nestos suture zone. On central Naxos Island, colored sapphires are associated with desilicated granite pegmatites intruding ultramafic lithologies (plumasites), occurring either within the pegmatites themselves or associated metasomatic reaction zones. In contrast, on southern Naxos and Ikaria Islands, blue sapphires occur in extensional fissures within Mesozoic metabauxites hosted in marbles. Mineral inclusions in corundums are in equilibrium and/or postdate corundum crystallization and comprise: spinel and pargasite (Paranesti), spinel, zircon (Xanthi), margarite, zircon, apatite, diaspore, phlogopite and chlorite (Naxos) and chloritoid, ilmenite, hematite, ulvospinel, rutile and zircon (Ikaria). The main chromophore elements within the Greek corundums show a wide range in concentration: the Fe contents vary from (average values) 1099 ppm in the blue sapphires of Xanthi, 424 ppm in the pink sapphires of Xanthi, 2654 ppm for Paranesti rubies, 4326 ppm Minerals 2019, 9, 49 2 of 41 for the Ikaria sapphires, 3706 for southern Naxos blue sapphires, 4777 for purple and 3301 for pink sapphire from Naxos plumasite, and finally 4677 to 1532 for blue to colorless sapphires from Naxos plumasites, respectively. The Ti concentrations (average values) are very low in rubies from Paranesti (41 ppm), with values of 2871 ppm and 509 in the blue and pink sapphires of Xanthi, respectively, of 1263 ppm for the Ikaria blue sapphires, and 520 ppm, 181 ppm in Naxos purple, pink sapphires, respectively. The blue to colorless sapphires from Naxos plumasites contain 1944 to 264 ppm Ti, respectively. The very high Ti contents of the Xanthi blue sapphires may reflect submicroscopic rutile inclusions. The Cr (average values) ranges from 4 to 691 ppm in the blue, purple and pink colored corundums from Naxos plumasite, is quite fixed (222 ppm) for Ikaria sapphires, ranges from 90 to 297 ppm in the blue and pink sapphires from Xanthi, reaches 9142 ppm in the corundums of Paranesti, with highest values of 15,347 ppm in deep red colored varieties. Each occurrence has both unique mineral assemblage and trace element chemistry (with variable Fe/Mg, Ga/Mg, Ga/Cr and Fe/Ti ratios). Additionally, oxygen isotope compositions confirm their geological typology, i.e., with, respectively δ 18 O of 4.9 ± 0.2‰ for sapphire in plumasite, 20.5‰ for sapphire in marble and 1‰ for ruby in mafics. The fluid inclusions study evidenced water free CO 2 dominant fluids with traces of CH 4 or N 2 , and low CO 2 densities (0.46 and 0.67 g/cm 3), which were probably trapped after the metamorphic peak. The Paranesti, Xanthi and central Naxos corundum deposits can be classified as metamorphic sensu stricto (s.s.) and metasomatic, respectively, those from southern Naxos and Ikaria display atypical magmatic signature indicating a hydrothermal origin. Greek corundums are characterized by wide color variation, homogeneity of the color hues, and transparency, and can be considered as potential gemstones.

A novel iterative combinatorial nanoscale search based on the application of cross-sectional synchrotron X-ray nanodiffraction and cross-sectional nanoindentation is used to refine the relationship between deposition conditions, microstructure and properties of nanostructured TiAlN thin films. Using three iterative steps, a nanolamellar TiAlN thin film with a maximal hardness of ∼36 GPa is developed., Because of the tremendous variability of crystallite sizes and shapes in nano­materials, it is challenging to assess the corresponding size–property relationships and to identify microstructures with particular physical properties or even optimized functions. This task is especially difficult for nanomaterials formed by self-organization, where the spontaneous evolution of microstructure and properties is coupled. In this work, two compositionally graded TiAlN films were (i) grown using chemical vapour deposition by applying a varying ratio of reacting gases and (ii) subsequently analysed using cross-sectional synchrotron X-ray nanodiffraction, electron microscopy and nanoindentation in order to evaluate the microstructure and hardness depth gradients. The results indicate the formation of self-organized hexagonal–cubic and cubic–cubic nanolamellae with varying compositions and thicknesses in the range of ∼3–15 nm across the film thicknesses, depending on the actual composition of the reactive gas mixtures. On the basis of the occurrence of the nanolamellae and their correlation with the local film hardness, progressively narrower ranges of the composition and hardness were refined in three steps. The third film was produced using an AlCl3/TiCl4 precursor ratio of ∼1.9, resulting in the formation of an optimized lamellar microstructure with ∼1.3 nm thick cubic Ti(Al)N and ∼12 nm thick cubic Al(Ti)N nanolamellae which exhibits a maximal hardness of ∼36 GPa and an indentation modulus of ∼522 GPa. The presented approach of an iterative nanoscale search based on the application of cross-sectional synchrotron X-ray nanodiffraction and cross-sectional nanoindentation allows one to refine the relationship between (i) varying deposition conditions, (ii) gradients of microstructure and (iii) gradients of mechanical properties in nanostructured materials prepared as thin films. This is done in a combinatorial way in order to screen a wide range of deposition conditions, while identifying those that result in the formation of a particular microstructure with optimized functional attributes.

X-ray nanodiffraction is used to evaluate axial and tangential residual stress distributions in a W thin film deposited on the scalloped inner wall of a through-silicon via. The results reveal oscillatory stress distributions which correlate well with the scallop wavelength and morphology., Synchrotron X-ray nanodiffraction is used to analyse residual stress distributions in a 200 nm-thick W film deposited on the scalloped inner wall of a through-silicon via. The diffraction data are evaluated using a novel dedicated methodology which allows the quantification of axial and tangential stress components under the condition that radial stresses are negligible. The results reveal oscillatory axial stresses in the range of ∼445–885 MPa, with a distribution that correlates well with the scallop wavelength and morphology, as well as nearly constant tangential stresses of ∼800 MPa. The discrepancy with larger stress values obtained from a finite-element model, as well as from a blanket W film, is attributed to the morphology and microstructural nature of the W film in the via.

DPDAK is a software for simple and fast on- and offline reduction and analysis of X-ray scattering data. It is an open-source software with a plug-in structure allowing tailored extensions., X-ray scattering experiments at synchrotron sources are characterized by large and constantly increasing amounts of data. The great number of files generated during a synchrotron experiment is often a limiting factor in the analysis of the data, since appropriate software is rarely available to perform fast and tailored data processing. Furthermore, it is often necessary to perform online data reduction and analysis during the experiment in order to interactively optimize experimental design. This article presents an open-source software package developed to process large amounts of data from synchrotron scattering experiments. These data reduction processes involve calibration and correction of raw data, one- or two-dimensional integration, as well as fitting and further analysis of the data, including the extraction of certain parameters. The software, DPDAK (directly programmable data analysis kit), is based on a plug-in structure and allows individual extension in accordance with the requirements of the user. The article demonstrates the use of DPDAK for on- and offline analysis of scanning small-angle X-ray scattering (SAXS) data on biological samples and microfluidic systems, as well as for a comprehensive analysis of grazing-incidence SAXS data. In addition to a comparison with existing software packages, the structure of DPDAK and the possibilities and limitations are discussed.

As the length scale of sample dimensions is reduced to the micron and sub-micron scales, the strength of various materials has been observed to increase with decreasing size, a fact commonly referred to as the ‘sample size effect’. In this work, the influence of temperature on the sample size effect in copper is investigated using in situ microcompression testing at 25, 200 and 400 °C in the SEM on vacuum-annealed copper structures, and the resulting deformed structures were analysed using X-ray μLaue diffraction and scanning electron microscopy. For pillars with sizes between 0.4 and 4 μm, the size effect was measured to be constant with temperature, within the measurement precision, up to half of the melting point of copper. It is expected that the size effect will remain constant with temperature until diffusion-controlled dislocation motion becomes significant at higher temperatures and/or lower strain rates. Furthermore, the annealing treatment of the copper micropillars produced structures which yielded at stresses three times greater than their un-annealed, FIB-machined counterparts., Philosophical Magazine, 96 (32-34), ISSN:1478-6443, ISSN:1941-5869

The full strain tensor present in a 2 · 2 · 6 μm3 sized germanium micro pillar was measured by X-ray microdiffraction Laue during in situ loading. Initial orientation gradients, residual strains and diffraction peak streaking were found negligible. The obtained strain values from Laue pattern analysis have been used to calculate the deviatoric stress tensor. The collected patterns show a pillar rotation and a build-up of shear stress components acting parallel to the contact surface of the flat punch, which is both an indication for misalignment of the sample and counter-body during loading. Based on the assumption of stress free pillar-side faces the full stress tensor was further evaluated. The stresses acting in loading direction derived from the Laue patterns compared to engineering stresses calculated from the continuously recorded signal of the load cell are in agreement within 9%. The discrepancy is explained by the initial experimental misalignment of the pillar with respect to the counter-body. Finally, difficulties arising during such an in situ experiment are discussed. Keywords: In situ micro compression, Experimental micromechanics, Synchrotron radiation, Laue microdiffraction

cited By 5; International audience; The copoly(2-oxazoline) pNonOx80-stat-pDc=Ox20 can be synthesized from the cationic ring-opening copolymerization of 2-nonyl-2-oxazoline NonOx and 2-dec-9′-enyl-2-oxazoline Dc=Ox in the ionic liquid n-hexyl methylimidazolium tetrafluoroborate under microwave irradiation in 250g/batch quantities. The polymer precipitates upon cooling, enabling easy recovery of the polymer and the ionic liquid. Both monomers can be obtained from fatty acids from renewable resources. pNonOx80-stat-pDc=Ox20 can be used as polymer in a photoresist (resolution of 1μm) based on UV-induced thiol-ene reactions. © 2015 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

International audience; As a result of its influence on heat transfer between cast part and mould, air gap formation is an important problem for many casting processes. The general explanation for gap formation is that, as a result of stresses and distortions that are created from inhomogeneous cooling, shrinkage of the casting and expansion of the mould occur. In this paper, different thermomechanical approaches are applied to a well defined casting process using three commercial and one inhouse codes and their predictions are compared with experimental findings. The experimental data were obtained from the solidification and subsequent cooling of cylindrical castings of eutectic Al-13%Si and ternary Al-7%Si-0.3%Mg alloys. Based on these findings, the major differences between the predictions of the models and the actual formation of the air gap are discussed

International audience; This book highlights emerging diffraction studies of strain and dislocation gradients with mesoscale resolution, which is currently a focus of research at laboratories around the world. While ensemble-average diffraction techniques are mature, grain and subgrain level measurements needed to understand real materials are just emerging. In order to understand the diffraction signature of different defects, it is necessary to understand the distortions created by the defects and the corresponding changes in the reciprocal space of the non-ideal crystals. Starting with a review of defect classifications based on their displacement fields, this book then provides connections between different dislocation arrangements, including geometrically necessary and statistically stored dislocations, and other common defects and the corresponding changes in the reciprocal space and diffraction patterns. Subsequent chapters provide an overview of microdiffraction techniques developed during the last decade to extract information about strain and dislocation gradients. X-ray microdiffraction is a particularly exciting application compared with alternative probes of local crystalline structure, orientation and defect density, because it is inherently non-destructive and penetrating.

International audience; The Matongo carbonatite intrusion belongs to the Neoproterozoic Upper Ruvubu alkaline plutonic complex (URAPC), that is located in Burundi along the western branch of the East African Rift. Beside the Matongo carbonatite, the URAPC alkaline complex comprises feldspathoidal syenites, diorites, quartz-bearing syenites and granites. Three main facies have been recognized in the Matongo carbonatite: (1) Sövites represent the dominant facies. Two varieties have been recognized. A scarce coarse-grained sövite (sövite I), which is altered and poorly enriched in REE (4 < ΣREE < 8 ppm), is encountered in highly fractured zones. A fine-grained sövite (sövite II), which is made of saccharoidal calcite, commonly associated with apatite, aegirine and amphibole, is abundant in the intrusion. Sövite II is enriched in LREE (442 < ΣREE < 1550 ppm, 49 < LaN/YbN < 175). (2) Ferrocarbonatites, that form decimeter-wide veins crosscutting the sövites, are characterized by a LREE enriched patterns (225 < ΣREE < 1048 ppm, 17 < LaN/YbN < 64). (3) K-feldspar and biotite-rich fenite facies (silicocarbonatites) have been recognized at the contact between the carbonatites and the country rock. They are likewise LREE-enriched (134 < ΣREE < 681 ppm, 25 < LaN/YbN < 46). Additionaly, "late" hydrothermal MREE-rich carbonatite veinlets can be found in sövite I. They are characterized by moderate enrichment in REE (ΣREE = 397 ppm), with a MREE-humped pattern (LaN/YbN = 3.7). The different facies represent the typical magmatic evolution of a carbonatite, while the silicocarbonatites are interpreted as resulting from the fenitisation of the country host-rocks. In addition, the most REE-depleted and fractionated facies, i.e. the coarse-grained sövite facies and the "late" calcite veinlets testify for hydrothermal processes that occurred after carbonatite emplacement and result from REE mobilization and redistribution. Large idiomorphic zircon crystals (megacrysts), found in the vicinity of the carbonatite can directly be related to the carbonatite evolution. They have been dated at 705.5 ± 4.5 Ma (U-Pb concordant age, LA-ICP-MS). Similar zircon megacrysts of the Lueshe carbonatite (DRCongo) have been dated and give a concordant age at 798.5 ± 4.9 Ma (U-Pb, LA-ICP-MS). Considering that an extensional tectonic regime occured at that time in Central Africa - what remains debated - both ages could relate to different stages of Rodinia breakup, with uprise of mantle-derived magmas along Palaeoproterozoic lithospheric zones of weakness.

We consider the restless Markov bandit problem, in which the state of each arm evolves according to a Markov process independently of the learner's actions. We suggest an algorithm that after $T$ steps achieves $\tilde{O}(\sqrt{T})$ regret with respect to the best policy that knows the distributions of all arms. No assumptions on the Markov chains are made except that they are irreducible. In addition, we show that index-based policies are necessarily suboptimal for the considered problem., In proceedings of The 23rd International Conference on Algorithmic Learning Theory (ALT 2012)

International audience; In this paper, we study the problem of estimating the mean values of all the arms uniformly well in the multi-armed bandit setting. If the variances of the arms were known, one could design an optimal sampling strategy by pulling the arms proportionally to their variances. However, since the distributions are not known in advance, we need to design adaptive sampling strategies to select an arm at each round based on the previous observed samples. We describe two strategies based on pulling the arms proportionally to an upper-bound on their variances and derive regret bounds for these strategies. %on the excess estimation error compared to the optimal allocation. We show that the performance of these allocation strategies depends not only on the variances of the arms but also on the full shape of their distributions.

International audience; Variations of the Earthfs magnetic field during the first millennium BC in western Europe remain poorly constrained, especially archaeointensity changes. Three salt-kilns (MOA, MOB and MOC) sampled in Moyenvic (Lorraine, eastern France) have been studied to provide new reference data. Each kiln has been dated by radiocarbon to originate from the Early Iron Age or Hallstatt period (between VIII and Vth Century BC). Rock magnetic experiments and hysteresis results suggest the predominance of pseudo-single domain (PSD) Ti-poor magnetite. Archaeomagnetic directions obtained by thermal and alternating field demagnetizations have high mean inclination (close to 70.) and declination (between 19 and 31.). A first set of classical Thellier.Thellier experiments was conducted on 46 samples with a laboratory field almost parallel to the direction of the characteristic remanent magnetization (ChRM). Only 24 of these specimens present a linear NRM.TRM plot. For other specimens, NRM.TRM plots are concave-up with positive pTRM checks. The very large dispersion observed between the determined palaeointensity values suggests some artefacts have not been fully recognized. A second set of Thellier experiments was conducted on 34 sister specimens with the laboratory field applied quasi-perpendicular to the ChRM. In these cases,mineralogical evolutions during heating and chemical remanent magnetization acquisitions have been clearly recognized, despite positive pTRM checks. The concave-up shapes of NRM.TRM plots appear mainly due to mineralogical alteration rather than to the presence of PSD.MD grains. For the entire set of samples the success rate of the palaeointensity determinations is very low with 80 per cent of the samples rejected. Nevertheless, reliable mean archaeointensities have been obtained for two of the three kilns (MOA, 80.1 } 14.5 ƒÊT and MOB, 86.6 } 6.9 ƒÊT at the latitude of Paris). The high field strength and the archaeomagnetic directions determined, combined with previous published data, provide further evidence for important changes of the Earth magnetic field in Europe during the first half of the first millennium BC. These large variations of the geomagnetic field during the Iron Ages indicate that archaeomagnetism is highly suitable for dating of structures from this period.

The existence of weak solutions to the continuous coagulation equation with multiple fragmentation is shown for a class of unbounded coagulation and fragmentation kernels, the fragmentation kernel having possibly a singularity at the origin. This result extends previous ones where either boundedness of the coagulation kernel or no singularity at the origin for the fragmentation kernel were assumed.

The Lycian and Antalya ophiolite complexes in SW Turkey represent fragments of oceanic lithosphere emplaced following the closure of the Neotethys Ocean during the Late Cretaceous. The peridotites from both of these ophiolites have compositions ranging from relatively undepleted lherzolites to highly depleted harzburgites and display a diverse suite of geochemical signatures indicative of both anhydrous, mid-ocean ridge (MOR)-type and hydrous, supra-subduction zone (SSZ)-type melting regimes. Whole-rock major and trace element systematics and mineral chemistry indicate that the MOR- and SSZ-type peridotites represent the residues from 5-9% and 13-25% of mantle melting, respectively, and display evidence for a multi-stage evolution of an oceanic lithosphere. Olivine-orthopyroxene-spinel equilibria indicate that the clinopyroxene-bearing, MOR- type peridotites are moderately reduced with their oxygen fugacity (fO(2)) ranging from -2.22 to -1.44 log units relative to the FMQ (fayalite-magnetite-quartz) buffer and are similar to abyssal peridotites, while more refractory, SSZ-type harzburgites and dunites (

Least squares fitting of point sets to lines, planes, curves and surfaces is carried out using eigenvalues and eigenvectors to find the major principal moment of inertia axis of a point set taken as representing the mass distribution of a rigid body. This engineering geometric approach produces identical results when compared to methods of conventional minimization using partial derivatives with respect to linear equation coefficients. Extending the approach to the fitting of conics and quadrics achieves great computational advantage over conventional leastsquares optimization of Euclidean, as opposed to algebraic distance. The results, though imperfect, provide a starting point for iterations that will converge rapidly. Often, if enough points are given and these do not deviate wildly from the fit shape type selected, the result is satisfactory without resorting to further improvement.

International audience; The construction of a secular variation (SV) reference curve for a region for which little or no archaeomagnetic directions are available is presented here. A SV curve is illustrated for Austria, centred on Radstadt (47.38°N, 13.45°E) and based on data from sites in other countries less than 500 km away. The published data were selected on site characteristics of N = 3 and k = 50, and dated within 400 yr. This yielded 170 directions from which a SV curve was derived using Bayesian techniques. The obtained reference curve represents the past 2300 yr. New data, mainly from Austria, substantiate this curve and confirm the validity of the techniques employed which can, therefore, be applied for similar situations. Another test has been made using the German reference curve for dating the Austrian archaeological sites, here a systematic shift to older times in the order 30­110 yr occurs.

à paraître; International audience; In this paper we consider a particular class of problems called multiarmed gambler bandits (MAGB) which constitutes a modified version of the Bernoulli MAB problem where two new elements must be taken into account: the budget and the risk of ruin. The agent has an initial budget that evolves in time following the received rewards, which can be either +1 after a success or −1 after a failure. The problem can also be seen as a MAB version of the classic gambler's ruin game. The contribution of this paper is a preliminary analysis on the probability of being ruined given the current budget and observations, and the proposition of an alternative regret formulation, combining the classic regret notion with the expected loss due to the probability of being ruined. Finally, standard state-of-the-art methods are experimentally compared using the proposed metric.