Expressions of dissipated powers and stored energies in poroelastic media modeled by {u,U} and {u,P} formulations

This paper is devoted to the rigorous obtention of the energy balance in porous materials. The wave propagation in the porous media is described by Biot-Allard's {u,U} and {u,P} formulations. The paper derives the expressions for stored kinetic and strain energies together with dissipated energies. It is shown that, in the case of mixed formulations, these expressions do not correspond to the real and imaginary parts of the variational formulations. A quantitative convergence analysis of finite element scheme is then undertaken with the help of these indicators. It is shown that the order of convergence of these indicators for linear finite-element is one and that they are then well fitted to check the validity of finite-element models.     

Ionic conduction and thermal properties of poly(ethylene oxide) - Er (CF3SO3)3 films

Measurements of electrical conductivity and thermal behaviour have been carried out on polymer electrolyte films obtained by the addition of erbium triflate to poly(ethylene oxide), PEO. Homogeneous electrolyte samples were prepared by using solvent casting and hot-pressing techniques to produce films with a composition defined by the general formula (EO)_nEr(CF₃SO₃)₃, where n lies between 3 and 150. This electrolyte system was found to behave in a manner broadly similar to other trivalent salt containing polymer electrolytes, however, in contrast to previously studied lanthanide systems, a salt - polymer complex crystallized after prolonged annealing of salt rich compositions at room temperature. Paper presented at the 2nd Euroconference on Solid State Ionics, Funchal, Madeira, Portugal, Sept. 10 – 16, 1995     

WDS versus silicon drift detector EDS: a case report for the comparison of quantitative chemical analyses of natural silicate minerals

Electron probe microanalysis (EPMA) is an essential analytical approach to determine elemental concentrations of various solid specimens quantitatively in mineralogical, petrological and materials research. Either wavelength dispersive X-ray (WDS) or energy dispersive X-ray (EDS) spectrometric techniques can collect the characteristic X-rays generated from each element in the specimen by an incident electron beam in order to define chemical constituents. Although WDS has been the preferred technique because of its higher spectral resolution and ability to detect trace elements, new generation EDS systems with silicon drift detectors (SDD), equipped with thin windows and integrated digital processing electronics, are claimed to approach the WDS throughput. In this study, we compared the analytical capability of a SDD EDS system with respect to WDS equipped systems on natural silicate minerals. For this purpose, natural rock samples, in which the silicate minerals present had already been analysed by various WDS systems, were chosen to compare these results with the ones acquired with a SDD EDS system. SDD EDS yielded satisfactory results for major elements (Na, Mg, Al, Si, K, Ca, Ti, Mn and Fe) compared with the results of the same minerals obtained by various WDS systems.     

Robust transport barriers resulting from strong Kolmogorov-Arnold-Moser stability

Hamiltonian systems that locally violate the twist condition arise in many applications. Numerical simulations reveal that, when systems of this type are perturbed, the degenerate or nontwist tori are remarkably stable. This phenomenon, which we refer to as strong Kolmogorov-Arnold-Moser (KAM) stability, is shown to be linked to very small resonance widths near degenerate tori. Quantitative estimates of degenerate resonance widths are derived and bifurcations of degenerate resonances are described. Strong KAM stability leads to robust transport barriers, which are important in all of the many applications in which Hamilitonians with the nontwist property arise.     

Assessment of the nature of interactions of cations with cycloheptatriene derivatives using change in the aromaticity: Comparison with electron density and NBO results

ABSTRACT

Interactions of cycloheptatriene derivatives, C₇H₆X, (X?=?NH, PH, AsH, O, S, Se) with the cations H⁺, CH₃⁺, Cu⁺, Al⁺, Li⁺, Na⁺, and K⁺ are studied using B3LYP functional and 6-311++G(d,p) basis set. The calculated gas-phase cation affinities (CA) and cation basicities (CB) for all molecules decrease as H⁺ > CH₃⁺ > Cu⁺ > Al⁺ > Li⁺ > Na⁺ > K⁺. We used the induced aromaticity in the 7-membered ring of C₇H₆X upon interaction with the cations, M⁺, as a measure of C₇H₆X/M⁺ interaction. Nucleus-independent chemical shift (NICS) and harmonic oscillator model of aromaticity (HOMA) were used as two indices of aromaticity. The highest and lowest induced aromaticities were observed for interactions of H⁺ and K⁺, respectively. Also, the aromaticity induced by interaction with a cation in C₇H₆AsH and C₇H₆PH was larger than that in C₇H₆NH and C₇H₆O. Hence, the aromaticity was considered as a measure of covalency for the C₇H₆X/M⁺ interactions showing a rational dependence on both the molecule and cation. The nature of the interactions was also assessed using electron density, charge distribution analysis and NBO calculations. The results of the aromaticity indices, NICS and HOMA, were compared with the electron density and NBO results.