Comparison results for oscillation of nonlinear differential equations

((without abstract.))     

Electronic perturbation in a molecular nanowire of [IrCl5(NO)]- units

The nitrosyl in [IrCl5(NO)]- is probably the most electrophilic known to date. This fact is reflected by its extremely high IR frequency in the solid state, electrochemical behavior, and remarkable reactivity in solution. PPh4[IrCl5(NO)] forms a crystal in which the [IrCl5(NO)]- anions are in a curious wire-like linear arrangement, in which the distance between the N--O moiety of one anion and the trans chloride of the upper one nearby is only 2.8 A. For the same complex [IrCl5(NO)]- but with a different counterion, Na[IrCl5(NO)], the anions are stacked one over the other in a side-by-side arrangement. In this case the electronic distribution can be depicted as the closed-shell electronic structure Ir III-NO+, as expected for any d(6) third-row transition metal complex. However, in PPh4[IrCl5(NO)] an unprecedented electronic perturbation takes place, probably due to NO*-Cl- acceptor-donor interactions among a large number of [IrCl5(NO)]- units, favoring a different electronic distribution, namely the open-shell electronic structure Ir IV-NO*. This conclusion is based on XANES experimental evidence, which demonstrates that the formal oxidation state for iridium in PPh4[IrCl5(NO)] is +4, as compared with +3 in K[IrCl5(NO)]. In agreement, solid-state DFT calculations show that the ground state for [IrCl5(NO)]- in the PPh4+ salt comprises an open-shell singlet with an electronic structure which encompasses half of the spin density mainly localized on a metal-centered orbital, and the other half on an NO-based orbital. The electronic perturbation could be seen as an electron promotion from a metal-chloride to a metal-NO orbital, due to the small HOMO-LUMO gap in PPh4[IrCl5(NO)]. This is probably induced by electrostatic interactions acting as a result of the closeness and wire-like spatial arrangement of the Ir metal centers, imposed by lattice forces due to pi-pi stacking interactions among the phenyl rings in PPh4+. Experimental and theoretical data indicate that in PPh4[IrCl5(NO)] the Ir-N-O moiety is partially bent and tilted.     

Discrete and continuous models for in plane loaded random elastic brickwork

The aim of this paper is to study non-periodic masonries – typical of historical buildings – by means of a perturbation approach and to evaluate the effect of a random perturbation on the elastic response of a periodic masonry wall. The random masonry is obtained starting from a periodic running bond pattern. A random perturbation on the horizontal positions of the vertical interfaces between the blocks which form the masonry wall is introduced. In this way, the height of the blocks is uniform, while their width in the horizontal direction is random. The perturbation is limited such as each block has still exactly 6 neighboring blocks. In a first discrete model, the blocks are modeled as rigid bodies connected by elastic interfaces (mortar thin joints). In other words, masonry is seen as a “skeleton” in which the interactions between the rigid blocks are represented by forces and moments which depend on their relative displacements and rotations. A second continuous model is based on the homogenization of the discrete model. Explicit upper and lower bounds on the effective elastic moduli of the homogenized continuous model are obtained and compared to the well-known effective elastic moduli of the regular periodic masonry. It is found that the effective moduli are not very sensitive to the random perturbation (less than 10%). At the end, the Monte Carlo simulation method is used to compare the discrete random model and the continuous model at the structural level (a panel undergoing in plane actions). The randomness of the geometry requires the generation of several samples of size L of the discrete masonry. For a sample of size L, the structural discrete problem is solved using the same numerical procedure adopted in [Cecchi, A., Sab, K., 2004. A comparison between a 3D discrete model and two homogenized plate models for periodic elastic brickwork, International Journal of Solids Structures 41 (9–10), 2259–2276] and the average solution over the samples gives an estimation which depends on L. As L increases, an asymptotic limit is reached. One issue is to find the minimum size for L and to compare the asymptotic average solution to the one obtained from the continuous homogenized model.     

A collocation method to fit geophysical survey data

A self adaptive collocation method has been applied to the quantitative interpretation of geophysical survey data. Examples of interpretation of vertical electrical soundings (VES) and magneto-telluric soundings (MTS) have been chosen for this work due to the high nonlinearity of the response functions and to the high degree of correlation of the parameters involved. In both cases horizontally isotropic multi-layered models have been adopted.For comparison two different computing algorithms have been considered. In the first, using a generalized inverse formulation a new different decomposition into characteristic values has been used. In the second the Marquardt procedure has been modified in an original way to give a faster convergence using a strategy based on the contemporary adjustment of the step length and the direction of the regression. The confidence limits of the results have been evaluated.Results are given for interpretation of both MTS and VES curves using the two different algorithms. Model data and field data have been considered for an effective comparison of speed of convergence and accuracy.     

On oscillatory solutions of quasilinear differential equations

Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second-order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zero-counting function.     

On oscillation and nonoscillation properties of Emden-Fowler difference equations

A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation

Compatible model for herringbone bond masonry: Linear elastic homogenization,failure surfaces and structural implementation

A simplified kinematic procedure at a cell level is proposed to obtain in-plane elastic moduli and macroscopic masonry strength domains in the case of herringbone masonry. The model is constituted by two central bricks interacting with their neighbors by means of either elastic or rigid-plastic interfaces with friction, representing mortar joints. The herringbone pattern is geometrically described and the internal law of composition of the periodic cell is defined.A sub-class of possible elementary deformations is a-priori chosen to describe joints cracking under in-plane loads. Suitable internal macroscopic actions are applied on the Representative Element of Volume (REV) and the power expended within the 3D bricks assemblage is equated to that expended in the macroscopic 2D Cauchy continuum. The elastic and limit analysis problem at a cell level are solved by means of a quadratic and linear programming approach, respectively.To assess elastic results, a standard FEM homogenization is also performed and a sensitivity analysis regarding two different orientations of the pattern, the thickness of the mortar joints and the ratio between block and mortar Young moduli is conducted. In this way, the reliability of the numerical model is critically evaluated under service loads.When dealing with the limit analysis approach, several computations are performed investigating the role played by (1) the direction of the load with respect to herringbone bond orientation, (2) masonry texture and (3) mechanical properties adopted for joints.At a structural level, a FE homogenized limit analysis is performed on a masonry dome built in herringbone bond. In order to assess limit analysis results, additional non-linear FE analyses are performed, including a full 3D numerical expensive heterogeneous approach and models where masonry is substituted with an equivalent macroscopic material with orthotropic behavior and possible softening. Reliable predictions of collapse loads and failure mechanisms are obtained, meaning that the approach proposed may be used by practitioners for a fast evaluation of the effectiveness of herringbone bond orientation.     

An equivalence theorem on properties A, B for third order differential equations

Differential equations are often classified according to oscillatory/nonoscillatory properties of their solutions as equations having property A or property B. The aim of the paper is to state an equivalence theorem between property A and property B for third order differential equations. Some applications, to linear as well as to nonlinear equations, are given too. Particularly, we give integral criteria ensuring property A or B for nonlinear equations. Our only assumption on nonlinearity is its superlinearity in neighbourhood of infinity, hence our results apply also to Emden-Fowler type equations.The second author wishes to thank C.N.R. of Italy and Grant Agency of Czech Republic (grant 201/96/0410) which made this research possible.