Compressed exponential form for disordered domain wall motion in ultra-thin Au/Co/Au ferromagnetic films

Magnetization reversal in ultra-thin Au/Co/Au films deposited on single crystal silicon (1 0 0) was investigated using Kerr microscopy. In the considered ultra-thin Co films, with a thickness between 0.7 and 1 nm, the coercivity and magnetic anisotropy decrease with decrease in cobalt layer thickness and the magnetization reversal dynamics is dominated by disordered domain wall motion. An analysis of the observed magnetization reversal dynamics is proposed, starting from the Fatuzzo-Labrune model. We show that the relaxation curves of these samples are well described by a function obtained by a technical transformation of Fatuzzo-Labrune model in the regime dominated by domain wall motion.     

Microbial Reduction of Lepidocrocite γ-FeOOH by Shewanella putrefaciens; The Formation of Green Rust

Dissimilatory iron-reducing bacteria (DIRB) couple the oxidation of organic matter or H₂ to the reduction of iron oxides. The bacterial reduction of a most common well-crystallised ferric oxyhydroxide, -FeOOH was investigated using DIRB Shewanella putrefaciens, strain CIP 8040. Experiments were conducted in the presence of neither organic buffer nor phosphate, with formate as electron donor, bicarbonate, and anthraquinone-2,6-disulfonate (AQDS, a humic acid analogue) that influenced the extent of ferric oxide bioreduction. The production of Fe²⁺ was followed with time. The solid phases obtained after bacterial iron reduction were analysed by transmission Mössbauer spectroscopy (TMS) and X-ray diffraction (XRD). Biogenic formation of green rust 1 compound, which contains carbonate anions, [Fe^II ₂Fe^III ₂(OH)₈]²⁺[CO₃ ^2–]^2– was observed. TMS was used to follow the evolution of the green rust abundance during the bacterial culture.     

Separation of unitary representations of connected Lie groups by their moment sets

We show that every unitary representation π of a connected Lie group G is characterized up to quasi-equivalence by its complete moment set.Moreover, irreducible unitary representations π of G are characterized by their moment sets.     

The L p -L q analog of Morgan’s theorem on exponential solvable Lie groups

In this paper, we define an analog of the L ^p -L ^q Morgan’s uncertainty principle for any exponential solvable Lie group G (p, q ∈ [1,+∞]). When G is nilpotent and has a noncompact center, the proof of such an analog is given for p, q ∈ [2,+∞], extending the earlier settings ([2], [4] and [5]). Such a result is only known for some particular restrictive cases so far. We also prove the result for general exponential Lie groups with nontrivial center.     

Propagation of a Dugdale crack at the edge of a half plane

This work deals with the propagation of a Dugdale crack at the edge of a half plane. The corresponding singular integral equation is solved semi-analytically. The expressions of the stress intensity factor and of the crack gap are deduced. A propagation criterion deduced from the revisited Griffith theory (Ferdjani and Marigo in Eur J Mech A Solids 53:1–9, 2015) is applied. The length of the process zone is calculated and compared with the literature results. The presented results show the evolution of the applied load with the crack length for different values of the ratio of the critical length of the Dugdale model to the initial crack length. The shape of the crack gap is also presented. Finally, a comparison between the Griffith and Dugdale models is performed.     

Hausdorff and Packing Spectra,Large Deviations,and Free Energy for Branching Random Walks in {\mathbb{R}^d}

Consider an \({\mathbb{R}^d}\) -valued branching random walk (BRW) on a supercritical Galton Watson tree. Without any assumption on the distribution of this BRW we compute, almost surely and simultaneously, the Hausdorff and packing dimensions of the level sets E(K) of infinite branches in the boundary of the tree (endowed with its standard metric) along which the averages of the BRW have a given closed connected set of limit points K. This goes beyond multifractal analysis, which only considers those level sets when K ranges in the set of singletons \({\{\alpha\}, \alpha \in \mathbb{R}^d}\) . We also give a 0–∞ law for the Hausdorff and packing measures of the level sets E({α}), and compute the free energy of the associated logarithmically correlated random energy model in full generality. Moreover, our results complete the previous works on multifractal analysis by including the levels α which do not belong to the range of the gradient of the free energy. This covers in particular a situation that was until now badly understood, namely the case where a first order phase transition occurs. As a consequence of our study, we can also describe the whole singularity spectrum of Mandelbrot measures, as well as the associated free energy function (or L ^q -spectrum), when a first order phase transition occurs.     

Separation of Coadjoint Orbits of Generalized Diamond Lie Groups

Mathematical Notes - Let $$G$$ be a type I connected and simply connected generalized diamond Lie group defined as the semidirect product of a $$d$$ -dimensional Abelian Lie group $$N$$ with...     

Structure refinement, dielectric, pyroelectric and Raman characterizations of Ba1−xLax(1−y)/2Euxy/2Nax/2TiO3 solid solution

The perovskite-type oxides Ba_1−xLa_x(1−y)/2Eu_xy/2Na_x/2TiO₃ (0?x?0.5 and xy=0.04) were synthesized and characterized by X-ray diffraction as well as dielectric measurements and Raman spectroscopy. The crystal structure of these ceramics has been determined by the Rietveld refinement powder X-ray diffraction data at room temperature. These compounds crystallize at room temperature in tetragonal space group P4mm for 0?x?0.1 and in the cubic group for 0.2?x?0.5. The phase transition temperature T_C (or T_m) decreases as x content increases. The degree of diffuseness of the phase transition is more pronounced for higher x content, implying the existence of a composition-induced diffuse phase transition of the ceramics with x?0.1. The evolution of the Raman spectra was studied as a function of various compositions at room temperature. The polarization state was checked by pyroelectric measurements.     

Monitoring structural transformation of hydroxy-sulphate green rust in the presence of sulphate reducing bacteria

The activities of bacterial consortia enable organisms to maximize their metabolic capabilities. This article assesses the synergetic relationship between iron reducing bacteria (IRB), Shewanella putrefaciens and sulphate reducing bacteria (SRB) Desulfovibrio alaskensis. Thus, the aim of this study was first to form a biogenic hydroxy-sulpahte green rust GR2( $ {\text{SO}}_{{\text{4}}} ^{{2 - }} The activities of bacterial consortia enable organisms to maximize their metabolic capabilities. This article assesses the synergetic relationship between iron reducing bacteria (IRB), Shewanella putrefaciens and sulphate reducing bacteria (SRB) Desulfovibrio alaskensis. Thus, the aim of this study was first to form a biogenic hydroxy-sulpahte green rust GR2() through the bioreduction of lepidocrocite by S. putrefaciens and secondly to investigate if sulfate anions intercalated in the biogenic GR2() could serve as final electron acceptor for a sulfate reducing bacterium, D. alaskensis. The results indicate that the IRB lead to the formation of GR2() and this mineral serve as an electron acceptor for SRB. GR2() precipitation and its transformation was demonstrated by using X-ray diffraction (DRX), M?ssbauer spectroscopy (TMS) and transmission electron spectroscopy (TEM). These observations point out the possible acceleration of steel corrosion in marine environment in presence of IRB/SRB consortia.     

Chemical stability of hydroxysulphate green rust synthetised in the presence of foreign anions: carbonate, phosphate and silicate

Hydroxysulphate green rust species were precipitated in the presence of various anions. is stable at ∼pH 7 and is transformed into a mixture of magnetite and ferrous hydroxide when the pH raised at ∼12. In the presence of carbonate species, is partially transformed into a mixture of magnetite and siderite at ∼pH 8.5. This transformation is stopped when silicate anions are present in the solution. As already observed for phosphate anions, the adsorption of silicate anions on the lateral faces of the crystals may explain this stabilization effect. Sulphate anions are easily exchanged by carbonate species at ∼pH 10.5. In contrast, anionic exchange between sulphate and phosphate anions was not observed.