Density functional theory investigation of the structure of SO2 and SO3 on Cu(1 1 1) and Ni(1 1 1)

Density functional theory (DFT) slab calculations, mainly using the generalised gradient approximation, have been used to investigate the minimum energy structures of molecular SO₂ and SO₃ on Cu(1 1 1) and Ni(1 1 1) surfaces. On Ni(1 1 1) the optimal local adsorption structures are in close agreement with experimental results for both molecular species obtained using the X-ray standing wavefield technique, although for adsorbed SO₂ the energetic difference between two alternative lateral positions of the lying-down molecule on the surface is marginally significant. On Cu(1 1 1) the results for adsorbed SO₂, in particular, were sensitive to the DFT functional used in the calculations, but in all cases failed to reproduce the experimentally-established preference for adsorption with the molecular plane perpendicular to the surface. This result is discussed in the context of previously published DFT results for these species adsorbed on Cu(1 0 0). The optimal geometry found for SO₃ on Cu(1 1 1) is similar to that on Ni(1 1 1), providing agreement with experiment regarding the molecular orientation but not the adsorption site.     

Acoustic anisotropy and birefringence in fibre-reinforced composite materials

All nine elastic moduli of an orthotropic composite material, namely, polypropylene reinforced with glass fiber, are determined from the measured values of the bulk acoustic wave velocities along specific directions in the planes of symmetry of the material. These data are used to calculate the angular dependences of phase velocities, polarization vectors, and directions of ray velocities of bulk waves in the composite. It is demonstrated that the difference in the velocities of shear waves polarized along and across the glass fiber gives rise to an acoustic birefringence and can lead to an elliptical polarization of waves. The measurement of the phase velocities of shear waves as functions of the wave polarization is suggested as a method for the determination of the fiber orientation in a composite material.     

Analysis of Static Simulated Annealing Algorithms

Generalized hill climbing (GHC) algorithms provide a framework for modeling local search algorithms to address intractable discrete optimization problems. This paper introduces a measure for determining the expected number of iterations to visit a predetermined objective function level, given that an inferior objective function level has been reached in a finite number of iterations. A variation of simulated annealing (SA), termed static simulated annealing (S²A), is analyzed using this measure. S²A uses a fixed cooling schedule during the algorithm execution. Though S²A is probably nonconvergent, its finite-time performance can be assessed using the finite-time performance measure defined in this paper.     

Optical spectroscopy of Yb/Er codoped NaY(WO4)2 crystal

Erbium and ytterbium codoped double tungstates NaY(WO₄)₂ crystals were prepared by using Czochralski (CZ) pulling method. The absorption spectra in the region 290-2000 nm have been recorded at room temperature. The Judd-Ofelt theory was applied to the measured values of absorption line strengths to evaluate the spontaneous emission probabilities and stimulated emission cross sections of Er³⁺ ions in NaY(WO₄)₂ crystals. Intensive green and red lights were measured when the sample were pumped by a 974 nm laser diode (LD), especially, the intensities of green upconversion luminescence are very strong. The mechanism of energy transfer from Yb³⁺ to Er³⁺ ions was analyzed. Energy transfer and nonradiative relaxation played an important role in the upconversion process. Photoexcited luminescence experiments are also fulfilled to help analyzing the transit processes of the energy levels.     

Vector-Orthogonality and Lanczos-Type Methods

A method for solving a linear system is defined. It is a Lanczos-type method, but it uses formal vector orthogonality instead of scalar orthogonality. Moreover, the dimension of vector orthogonality may vary which gives a large freedom in leading the algorithm, and controlling the numerical problems. The ideas of truncated and restarted methods are revisited. The obtained residuals are exactly orthogonal to a space of increasing dimension. Some experiments are done, the problem of finding automaticaly good directions of projection remains partly open.     

MULTI-MODE TRIMMING OF IMPERFECT THIN RINGS USING MASSES AT PRE-SELECTED LOCATIONS

This paper presents a practical method for trimming the natural frequencies of an initially imperfect ring to simultaneously eliminate certain of the frequency splits present. Compared with previous work, the novel feature of this method is that the trimming masses are positioned at pre-selected locations on the ring. The basis for the proposed method is the concept of equivalent imperfection mass, which allows any imperfect ring to be considered as a perfect ring with equivalent imperfection masses attached. By considering this trimming problem it is deduced that it is possible to trim N pairs of modes simultaneously by removing (a minimum of) 2 N trimming masses at particular locations around the ring. By positioning the trimming masses at pre-selected locations, it is shown that a simple set of trimming masses can be calculated easily, and from this set an infinite number of solution sets can be found. Methods for generating these sets are outlined for the trimming of both a single and a dual pair of modes. In practice, it is likely that the trimming masses will be spaced regularly. For this special case, it is found that it is not possible to trim all single- and dual-mode pairs with any arrangement of masses. Validation of the derived simple solution set and the proposed procedure to generate further sets is achieved by studying a number of theoretical examples.     

On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.