In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of wealth among individuals. For this equation the stationary state can be easily derived and shows a Pareto power law tail. Numerical results confirm the previous analysis.

International audienceHerein, we report on a three-component supra molecular hybrid system built from specific recognition processes involving a Dawson-type polyoxometalate (POM) ,P2W18O62](6-), a cationic electron-rich cluster [Ta6Br12(H2O)(6)](2+), and gamma-cyclodextrin (gamma-CD). Such materials have been investigated using a bottom-up approach by studying the specific interactions between gamma-CD and both types of inorganic units. Their ability to interact has been investigated in the solid state by single-crystal X-ray diffraction (XRD) and in solution using multinuclear NMR methods (including DOSY, EXSY, and COSY), electrospray ionization mass and UV-vis spectroscopies, electrochemistry, and isothermal titration calorimetry experiments. Single-crystal XRD analysis reveals that POM:gamma-CD constitutes a highly versatile system which gives aggregates with 1:1, 1:2, and 1:3 stoichiometry. Surprisingly, these arrangements exhibit a common feature wherein the gamma-CD moiety interacts with the Dawson-type POMs through its primary face. We present also the first structural model involving an octahedral-type metallic cluster with gamma-CD. XRD study reveals that the cationic [Ta6Br12(H2O)(6)](2+) ion is closely embedded within two gamma-CD units to give a supramolecular ditopic cation, suitable to be used as a linker within extended structure. Solution study demonstrates clearly that pre-associations exist in solution, for which binding constants and thermodynamic parameters have been determined, giving preliminary arguments about the chaotropic nature of the inorganic ions. Finally, both building blocks, i.e., the ditopic supramolecular cation {[Ta6Br12(H2O)(6)]@2CD}(2+) and the Dawson-type anion, react together to give a three-component, well-ordered hybrid material derived either as a supramolecular hydrogel or single crystals. The solid-state structure shows an unprecedented helicoidal tubular chain resulting from the periodic alternation of POM and supramolecular cation, featuring short hydrogen-bonding contacts between the electron-poor POM and electron-rich cluster. The 1D tubular ionic polymer observed in the single crystals should make it possible to understand the long-range ordering observed within the hydrogel hybrid material. The supramolecular chemical complementarities between the gamma-CD-based ditopic cation and POM open a wide scope for the design of hybrid materials that accumulate synergistic functionalities

Much recent attention has been devoted towards unraveling the microscopic optoelectronic properties of hybrid organic-inorganic perovskites. Here we investigate by coherent inelastic neutron scattering spectroscopy and Brillouin light scattering, low frequency acoustic phonons in four different hybrid perovskite single crystals: MAPbBr_{3}, FAPbBr_{3}, MAPbI_{3}, and α-FAPbI_{3} (MA: methylammonium, FA: formamidinium). We report a complete set of elastic constants characterized by a very soft shear modulus C_{44}. Further, a tendency towards an incipient ferroelastic transition is observed in FAPbBr_{3}. We observe a systematic lower sound group velocity in the technologically important iodide-based compounds compared to the bromide-based ones. The findings suggest that low thermal conductivity and hot phonon bottleneck phenomena are expected to be enhanced by low elastic stiffness, particularly in the case of the ultrasoft α-FAPbI_{3}.

No abstract

Numerous codes are being developed to solve Shallow Water equations. Because there are used in hydraulic and environmental studies, their capability to simulate properly flow dynamics is critical to guarantee infrastructure and human safety. While validating these codes is an important issue, code validations are currently restricted because analytic solutions to the Shallow Water equations are rare and have been published on an individual basis over a period of more than five decades. This article aims at making analytic solutions to the Shallow Water equations easily available to code developers and users. It compiles a significant number of analytic solutions to the Shallow Water equations that are currently scattered through the literature of various scientific disciplines. The analytic solutions are described in a unified formalism to make a consistent set of test cases. These analytic solutions encompass a wide variety of flow conditions (supercritical, subcritical, shock, etc.), in 1 or 2 space dimensions, with or without rain and soil friction, for transitory flow or steady state. The corresponding source codes are made available to the community (http://www.univ-orleans.fr/mapmo/soft/SWASHES), so that users of Shallow Water-based models can easily find an adaptable benchmark library to validate their numerical methods.

In this paper, we are concerned with models for sedimentation transport consisting of a shallow water system coupled with a so called Exner equation that described the evolution of the topography. We show that, for some model of the bedload transport rate including the well-known Meyer-Peter and Müller model, the system is hyperbolic and, thus, linearly stable, only under some constraint on the velocity. In practical situations, this condition is hopefully fulfilled. The numerical approximations of such system are often based on a splitting method, solving first shallow water equation on a time step and, after updating the topography. It is proved that this strategy can create spurious/unphysical oscillations which are related to the study of hyperbolicity e.g. the sign of some eigenvalue of the coupled system differs from the splitting one. Some numerical results are given to illustrate these problems and the way to overcome them in some cases using an stronger C.F.L. condition.

Cs2Mo6Br14 (1) and Cs2Mo6I14 (2) have been synthesized by solid state chemistry techniques and structurally characterized by single crystal X‐ray diffraction. They crystallize in the P3¯1c space group (Nr. 163) with the following lattice parameters: a = 10.1925(1) Å, c = 15.0690(3) Å, Z = 2 for 1; a = 10.804(5) Å, c = 16.258(5) Å, Z = 2 for 2. These clusters halides, whose structures are related to that of Cs2Mo6Cl8Br6, are built up from discrete [(Mo6Xi8)Xa6]2‐ anionic units (X = Br, I) stacked according to an hexagonal close‐packing arrangement. In the present work, the influence of the halogen on the cesium sites will be evidenced and discussed. Furthermore, a simple high yield preparation method of (TBA)2Mo6Xi8Xa6 will be proposed starting from Cs2Mo6X14.

Much research has been devoted to molybdenum octahedral clusters Mo 6 since the discovery of the A x Mo 6 Y 8 solidstate series (Y = S, Se, Te) in the early 1970s.[1] Indeed, their interesting physical properties and potential applicationse.g., superconductivity at high critical field, thermoelectric, catalysis, or redox intercalation processes -have stimulated the research of many groups. [2] (Fig. 1). The physical properties of Mo 6 solid-state compounds are related to the number of electrons available for metal-metal bonding within the cluster (valence electron count, VEC) and to the strength of interaction between the units. Mo-centered electrons are located on twelve metal-metal bonding molecular orbitals of the molecular orbital diagram. Their full occupation leads to a closed-shell configuration with a VEC of 24.[ [8,9] that can be used for the formation and organization of supramolecular assemblies as well as hybrid materials. Hybrids can be synthesized either by the grafting of functional donor ligands in apical position or through the association of anionic cluster units with organic or organometallic cations by cation metathesis or electrochemical techniques.[10]The large emission region of the [Mo 6 X 14 ] 2-anion in the red and near infrared (580-900 nm) is particularly interesting for biotechnology applications as it is selectively transmitted through tissues owing to the relatively low absorption at these wavelengths.[11] Anionic Mo 6 cluster units are usually associated with alkali counter cations within inorganic solids. Indeed, the use of inorganic cluster compounds as luminescent dyes, for instance in bio-imaging strategies, presupposes that both clusters and counter cations are embedded in an inert matrix in order to avoid ionic diffusion, oxidization of the cluster, or apical ligand exchanges in aqueous media, which will precipitate the cluster as a hydroxo species.