Discrete Velocity Models Without Nonphysical Invariants

Models for mixtures of discrete velocity gases have been recently introduced by the authors and have produced unexpected results, particularly with regard to the possible existence of nonphysical collision invariants. Here we discuss a method to construct models without spurious invariants. The method can be extended to very general models, including polyatomic gases, chemical reactions, etc.     

Evolution of two concentrated vortices in a two-dimensional bounded domain

We prove that two initially concentrated vortices with opposite vorticity of an incompressible ideal fluid moving in a two-dimensional bounded domain, remain concentrated during the time. The motion of their centers converges to the solution of the point vortex model with the corresponding initial conditions.     

Redox Potential and Crystal Chemistry of Hexanuclear Cluster Compounds

Most of TM₆-cluster compounds (TM = transition metal) are soluble in polar solvents, in which the cluster units commonly remain intact, preserving the same atomic arrangement as in solids. Consequently, the redox potential is often used to characterize structural and electronic features of respective solids. Although a high lability and variety of ligands allow for tuning of redox potential and of the related spectroscopic properties in wide ranges, the mechanism of this tuning is still unclear. Crystal chemistry approach was applied for the first time to clarify this mechanism. It was shown that there are two factors affecting redox potential of a given metal couple: Lever’s electrochemical parameters of the ligands and the effective ionic charge of TM, which in cluster compounds differs effectively from the formal value due to the bond strains around TM atoms. Calculations of the effective ionic charge of TMs were performed in the framework of bond valence model, which relates the valence of a bond to its length by simple Pauling relationship. It was also shown that due to the bond strains the charge depends mainly on the atomic size of the inner ligands.     

Space-time perturbation modes for non-linear dynamic analysis of beams

In this work an attempt is made at bridging the powerful perturbation methods of analytical dynamics to the versatile finite element techniques which can readily handle arbitrarily complex structures. The proposed analysis methodology has two distinguishing features. First, a space-time finite element formulation is used, and hence the concept of modes is here naturally extended to that of space-time modes, where the time dependency is implied in the assumed modes. As a result, the partial differential equations of motion are directly reduced to purely algebraic non-linear simultaneous equations. Second, perturbation modes, rather than the usual vibration mode shapes are used and shown to be an appropriate basis for non-linear dynamic analysis. These modes bring information about the non-linearities of the system through the higher order derivatives of the strain and kinetic energies. The procedure is illustrated on non-linear beam problems and the results are compared with those of a full finite element model, i.e., when all the degrees of freedom are considered, as well as with analytical results, when available.     

X-ray absorption spectroscopies: useful tools to understand metallorganic frameworks structure and reactivity

The large unit cells, the enormous flexibility and variation in structural motifs of MOFs represent a big challenge in the characterization of MOF materials, particularly in cases where single crystal diffraction data are not available. In this critical review it is shown that in cases where only powder diffraction data are available additional structural information, particularly regarding local coordination within the inorganic cluster, are often mandatory in order to solve the structure. There are also cases where the inorganic cluster does not follow the symmetry of the overall structure. In such cases diffraction techniques will just "see" an average structure, missing the local structure: a lack that may be critical for understanding the specific properties of the material. In both cases, EXAFS spectroscopy is the tool that provides complementary structural information on the inorganic cluster and the way it binds to the ligand. Selected examples will show how EXAFS will be relevant in: (i) confirming the structure obtained from diffraction refinements; (ii) highlighting that the inorganic cornerstone has a lower symmetry with respect to that of the organic framework; (iii) obtaining the local structure of the inorganic cluster in the desolvated material when desolvation causes a partial loss of long range order; (iv) obtaining the local structure of the inorganic cluster in the desolvated material after coordination of a probe (or reactant) molecule, including cluster deformation upon molecule coordination and metal-molecule binding distance; (v) evidencing the presence of impurities in the form of amorphous extra-phases (339 references).