Aperiodic multilayer structures: Properties and applications

Based on the calculation of characteristics of aperiodic multilayer structures, proposals on their applications in laser mirrors, optical switches (logic gates), and phase modulators are formulated. These proposals are based on multiparametric optimization of properties of aperiodic structures and take into account modern technological capabilities of their fabrication, which also include the possibilities of nanotechnologies.     

Quadratic algebras related to elliptic curves

We construct quadratic finite-dimensional Poisson algebras corresponding to a rank-N degree-one vector bundle over an elliptic curve with n marked points and also construct the quantum version of the algebras. The algebras are parameterized by the moduli of curves. For N = 2 and n = 1, they coincide with Sklyanin algebras. We prove that the Poisson structure is compatible with the Lie-Poisson structure defined on the direct sum of n copies of sl(N). The origin of the algebras is related to the Poisson reduction of canonical brackets on an affine space over the bundle cotangent to automorphism groups of vector bundles. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 163–183, August, 2008.     

Simulation of a functional solution to the acoustic tomography problem for data from quasi-point transducers

Two variants of a functional-analytical algorithm intended for solving inverse tomography problems are discussed and numerically carried out. The acoustic fields that are transmitted and received by transducers, which are equivalent to point ones, serve as experimental data. These data are used to calculate the classical or generalized scattering amplitude, and the scatterer characteristics are then reconstructed. The algorithm requires neither model linearization, no iterations for refining the estimates of scatterers, thus making it attractive for solving acoustic-tomography problems in different applications. The results of the numerical reconstruction of inhomogeneities in the sound velocity and absorption in a medium are presented.     

Quadratic algebras based on $$SL(NM)$$ elliptic quantum $$R$$ -matrices

Theoretical and Mathematical Physics - We construct a quadratic quantum algebra based on the dynamical $$RLL$$ -relation for the quantum $$R$$ -matrix related to $$SL(NM)$$ -bundles with a...     

The state of Al(III) in alcohol solutions of aluminum alkoxide as probed by <Superscript>27</Superscript>Al and <Superscript>13</Superscript>C NMR and small-angle X-ray scattering

Solutions of aluminum alkoxides obtained by interaction of aluminum metal with methyl, ethyl, and isopropyl alcohols were studied by ²⁷Al and ¹³C NMR and small-angle X-ray scattering. Alkoxides with a tetrahedral environment of aluminum prevail in methanol solutions, and those with an octahedral environment of aluminum predominate in ethanol solutions. In isopropyl alcohol at 293 K, polynuclear alkoxides with tetrahedral, octahedral, and pentacoordinated aluminum environments coexist. The structure of polynuclear complexes was refined by comparison of their calculated dimensions with small-angle X-ray scattering data.     

Scaling in the Optical Characteristics of Aperiodic Structures with Self-Similarity Symmetry

The properties of diffraction gratings and multilayered systems constructed using 1D models of quasicrystals are considered based on numerical simulation. It is shown that there is a direct relationship between the self-similarity symmetry of quasicrystals and scaling in the characteristics of the above-mentioned optical devices. The degree of structural correspondence between the graphical representations of the geometric properties of crystals, light diffraction patterns of gratings, and the transmission spectra of multilayered systems is estimated. It is shown that certain types of self-similarity symmetry make the characteristics of aperiodic diffraction gratings highly stable to a change in the size ratio of forming elements.