A global Lipschitz continuity result for a domain-dependent Neumann eigenvalue problem for the Laplace operator

Let Ω be an open connected subset of Rⁿ of finite measure for which the Poincaré-Wirtinger inequality holds. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset φ(Ω) of Rⁿ, where φ is a locally Lipschitz continuous homeomorphism of Ω onto φ(Ω). Then, we show Lipschitz-type inequalities for the reciprocals of the eigenvalues delivered by the Rayleigh quotient. Then, we further assume that the imbedding of the Sobolev space W^1,2(Ω) into the space L²(Ω) is compact, and we prove the same type of inequalities for the projections onto the eigenspaces upon variation of φ.     

Ti location in the MFI framework of Ti-Silicalite-1: a neutron powder diffraction study.

The first direct evidence that Ti atoms are not equally distributed in the 12 crystallographically independent T sites of the MFI framework is presented on the basis of neutron diffraction data collected at the HRPD instrument of the ISIS pulsed neutron source. We found strong evidence indicating that T6, T7, and T11 are the most populated sites and weak evidence that Ti may be hosted in T10. Ti occupancy can be excluded for sites T1, T2, T4, T5, T9, and T12. The occupancy of the remaining sites is doubtful. Since defective silicalite has been shown to exhibit the same preferential sites (T6, T7, T11, and T10) for Si vacancies, it may be suggested that the incorporation mechanism of the Ti atoms in the MFI framework occurs via the insertion of titanium in the defective sites. This hypothesis implies that titanium has a mineralizing effect on the MFI framework, and it is supported by independent spectroscopic data on both TS-1 and defective silicalite. The results are discussed in comparison with the known substitution mechanisms in the T-sites of MFI-type structures.     

Influence of growth parameters on the interface abruptness in CBE-grown InGaAs/InP QWs and SLs

A simple thermodynamic model for As and P incorporation at the CBE-grown InGaAs/InP and InP/InGaAs interfaces has been developed. This model agrees with the X-ray diffraction and the photoluminescence features experimentally obtained from high-quality single quantum wells (SQWs) and multi-quantum wells (MQWs). Our experimental results compare well with the best published data and clearly show that monolayer interfaces can be obtained in this material system only by chosing the proper growth interruption (GI) conditions and accepting a strong mismatch at each interface. This effect could become dramatic in superlattice structures in which the QW period is smaller than 5 nm and the resulting strain could lead to poor crystal quality and optical properties.     

Spectral stability of general non-negative self-adjoint operators with applications to Neumann-type operators

We prove a stability theorem for the eigenvalues of general non-negative self-adjoint linear operators with compact resolvents and by applying it we prove a sharp stability result for the dependence of the eigenvalues of second order uniformly elliptic linear operators with homogeneous Neumann boundary conditions upon domain perturbation.     

Template burning inside TS-1 and Fe-MFI molecular sieves: an in situ XRPD study

The high X-ray flux available at the European Synchrotron Radiation Facility (ESRF), combined with the use of a suitably designed area detector setup, allowed us to follow in real time the structural changes occurring during the template burning processes inside TS-1 and Fe-silicalite MFI zeolites with a X-ray powder diffraction technique (XRPD). Rietveld analysis of the XRPD patterns collected in the 350-1000 K interval, integrated each 15 K, yields to the determination of the template overall occupancy factor versus T with an accuracy comparable with that obtained by thermogravimetric measurements, routinely employed for this purpose. The evolution of the structural parameters (V, a, b, c, site occupancy factor of the template molecule) vs T has been obtained. These data allow us to have, for the first time, a complete view of the structural rearrangements induced by the template burning process on the zeolitic framework. The differences caused by the different heteroatom inserted in the MFI lattice (Ti or Fe) are discussed. For both TS-1 and Fe-MFI, the kinetics of the reaction were investigated, to obtain the activation energy of the calcinations process employing the nonisothermal data according to the theory recently proposed by Kennedy and Clark [Thermochim. Acta, 1997, 307, 27-35]. For TS-1 only, the time-resolved template burning experiment has been repeated in isothermal conditions at four different temperatures, to obtain the activation energy from isothermal data, according to the standard procedure. Comparison between Arrhenius plots obtained from isothermal and nonisothermal data demonstrates that the Kennedy and Clark method can be also applied to complex materials such as the MFI zeolites. This approach, when applied to time-resolved XRPD studies, is much less time consuming (requesting, in principle, one single nonisothermal run) with respect to the classic approach, which requests at least three isothermal runs. Moreover, it allows a remarkably lower associated error (151 +/- 11 versus 146 +/- 30 kJ mol(-)(1)) due to the much higher number of experimental points employed to perform the linear fit.     

Two-dimensional modelling of multifrequency piezocomposites

The multifrequency composites of 2-2 connectivity modelled in this work are made with groups of piezoelectric elements of different lateral dimensions, periodically reproduced in the structure. These composites have potential to improve the performances of standard piezoelectric composites with the same materials and ceramic fraction, on account that they have different resonators coupled mechanically along the structure. A one-dimensional model was developed to study their performances in a first approximation. In order to obtain a design model, a two-dimensional model, previously used to describe multielement array transducers, has been extended to the case of 2-2 polymer-piezoceramic composites. Several composite samples, having piezoceramic strips with different width-to-thickness ratios, have been built, and their resonance behaviour compared with the model prediction. Finally, the model has been extended to the case of 2-2 multifrequency composites. For multifrequency composites having in the same composite structure two or three piezoceramic strips with different lateral dimensions, the comparison between experimental and predicted results shows good agreement. The model has been used to optimise a double composite in comparison with a standard one with the same volume fraction and constituents.     

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