Radiospectroscopic and dielectric spectra of nanomaterials

The shape of lines in the radiospectroscopic (NMR and EPR) and dielectric spectra of materials formed by nanoparticles (hereafter, nanomaterials) is analyzed theoretically. The theory is developed in the framework of the core and shell model according to which a nanoparticle consists of two regions whose properties are affected and unaffected by the surface, respectively. The changes in the resonance frequency, the relaxation time, and the static permittivity due to the surface tension are taken into account, and the Gaussian and Lorentzian shapes of homogeneously broadened lines are considered. The inhomogeneous broadening of the spectral lines is examined for several types of nanoparticle size distributions. It is demonstrated that the splitting of the initial lines in the spectra of bulk systems into pairs of lines with a decrease in the particle size is a specific feature of the spectra of nanoparticles. The intensities and half-widths of the lines are investigated as functions of the parameters of the size distribution of nanoparticles. The results of theoretical calculations are compared with recent experimental data on the ¹⁷O and ²⁵Mg NMR spectra of nanocrystalline MgO. The theoretical dependences of the intensity, the resonance frequency, and the half-width of the spectral lines are in good agreement with the experimental data. The proposed theory offers a satisfactory explanation of the behavior of the static permittivity in BaTiO₃ ceramic materials with nanometer-sized grains.     

A priori estimates for quasilinear degenerate parabolic equations

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

     

Numerical determination of the density profile of an inhomogeneous membrane: solution of the inverse vibration problem

Given one or more vibrational modes of a membrane, the free vibration equation can be applied to infer the mass surface density. This paper considers determining the surface density of an inhomogeneous membrane from digitized holographic projections (interferograms) of the modeshapes. Spatially discrete numerical models of the membrane surface are presented, which can be used to solve both forward and inverse vibration problems. The accuracy of the discrete models is examined for exactly solvable free vibration problems involving inhomogeneous membranes. For the solution of the inverse problem, error estimates are given for the mass surface density deduced from modeshape interferograms. The practicability of the method is investigated using simulated experimental data for membranes with composite and continuously inhomogeneous density profiles. Strategies are discussed for reducing errors in the reconstructed densities.     

A microspectroscopic study of the electronic homogeneity of ordered and disordered Sr2FeMoO6

Disordered Sr₂FeMoO₆ shows a drastic reduction in saturation magnetization compared to highly ordered samples, moreover magnetization as a function of the temperature for different disordered samples shows qualitatively different behaviours. We investigate the origin of such diversity by performing spatially resolved photoemission spectroscopy on various disordered samples. Our results establish that e_xtensive electronic inhomogeneity, arising most probably from an underlying chemical inhomogeneity in disordered samples, is responsible for the observed magnetic inhomogeneity. It is further pointed out that these inhomogeneities are connected with composition fluctuations of the type Sr₂Fe_1+x Mo_1-x O₆ with Fe-rich (x > 0) and Mo-rich (x < 0) regions. Dedicated to Prof J Gopalakrishnan on his 62nd birthday.     

Statistical Analysis of the Effect of Mineral Admixtures on the Strength of the Interfacial Transition Zone

Microscopic evidence indicates that the thickness of the interfacial transition zone (ITZ) between the aggregate and the cement paste is modified when mineral admixtures partially replace portland cement. Unfortunately, there is limited information on the significance of these microscopic modifications to the mechanical properties of the ITZ. This research reports experimental results on the shear and tensile strength of the ITZ as affected by the addition of the following mineral admixtures: silica fume, fly ash, and natural pozzolan. Statistical analysis was used to identify the significant parameters affecting the tensile and shear strength of the ITZ. Experimental results indicate that not only does the incorporation of silica fume and fly ash increase the strength of the ITZ, these mineral admixtures have a greater influence on the strength increase of the ITZ than in the strength increase of the cement paste.     

Determining radii of meromorphy via orthogonal polynomials on the unit circle

Using a convergence theorem for Fourier–Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard's theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szeg functions.     

Stress monitoring in a Guinness 10-day scuba dive

Nowadays, there is high demand for sensitive gas sensors both for human and environmental monitoring. This paper deals with a high-resolution (0.2 ppb) laser-based photoacoustic spectroscopic system realized at ENEA Frascati, Italy, applied for monitoring stress in scuba divers during sustained immersion by analyzing breath samples. Blood tests and psychometric tests for scuba divers were performed at Catholic University in Rome. Results will be reported and discussed.     

Electro-absorption and refraction in Fabry-Perot quantum well modulators: a general discussion

Fabry-Perot resonators have long been advocated to improve the limited contrast ratio of multiple quantum well optical modulators used in photonic switches based on self electrooptic effect devices (SEEDs) and in other array based optical interconnection schemes. Using data on field dependent GaAs/AlGaAs quantum well absorption and refraction, we have modelled the reflectivity, modulation depth and contrast ratio of resonant modulators. Our results are generally valid for any quantum well modulator and demonstrate 23the important role played by electro-refraction even in regions of strong absorption. Resonators give large contrast ratios but there are trade-offs in the maximum reflectivity change achievable with Fabry-Perot resonators compared to simple modulators. The model gives the optimum number of quantum wells and reflectivity values required to make a resonator at any wavelength for a given quantum well structure. Understanding the limits of Fabry-Perot quantum well modulator performance is important for their application in symmetric self electrooptic effectiveness for photonic switching where modulation and detection properties are both used and for optical interconnection systems.     

Synchronization through system interconnections

An interconnection strategy with built-in adaptive controllersis presented which achieves synchronization of scalar linearsystems: the closed-loop network forces all outputs to followthe same signal asymptotically while maintaining the open-loopcharacteristics. In the design of the output feedback controllers,no knowledge of system parameters is assumed, but each systemmust have the same poles and be high-gain-stable. The proofof the main theorem relies critically on derived systems-theoreticresults and the special system topology as a network of interconnectedsystems. The topology is explained by first solving the simplerproblem of signal synchronization.