Localization of light energy on the nanometer scale in a silicon cone

The spatial structure of light fields in a metallized cone filled with a medium with complex dielectric function was studied on the basis of the exact solution of the eigenwave problem. It is suggested that silicon can be used as a core of optical probe in the visible spectral region. It is shown that the density of light energy at the output of optical probe can be drastically increased if silicon is used instead of glass fiber.     

Correlations in the director-orientation fluctuations in the presence of microscopic impurities in a nematic liquid crystal

The model of a spatially restricted liquid-crystal system with microscopic impurities homogeneously distributed in the system is considered. The thermodynamic correlations of the director-orientation fluctuations and the correlations of the scalar order parameter characterizing impurities in the system are investigated for this system. It is shown that the impurity correlations are weaker than in a pure isotropic liquid. The correlations in the director deviations depend essentially on the wavevector and can be substantially weakened in the presence of impurities.     

WITCH: A Penning Trap Retardation Spectrometer Combination for Precision Studies of the Weak Interaction

We present data from three seasons of experimental field work designed to recreate ancient Andean coastal ceramic firing techniques. Based on the recent discovery of two different archaeological ceramic production sites in the La Leche river valley of northern coastal Peru, the opportunity arose to apply Mössbauer spectroscopy and other analytical methods to reconstruct ancient firing procedures. Two sets of firings took place in 1993 and 1997 in Batán Grande using a partially restored Formative kiln from about 800 BC, local hardwood and cow dung as fuel. A third experiment followed in 2000 after the discovery of a Middle Sicán ceramics workshop in use between ca. AD 950 and 1050 at Huaca Sialupe, where an exact replica of an ancient kiln was built from local clay, and fired with local wood and cow dung. Additionally, inverted urns found at Huaca Sialupe were tested for their potential use as furnaces for metal working. Mössbauer spectroscopy was used to compare the physical and chemical state of specimens produced in the field experiments with ancient ceramics and with specimens produced in controlled laboratory experiments.     

Functional analysis proofs of Abel's theorems

We give alternative proofs to the classical theorems of Abel, using the concept of Berezin symbol.

     

Asymptotic Regimes of Magnetic Bianchi Cosmologies

We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII₀, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII₀ cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII₀ cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime.     

Spectrophotometric Study of Interaction of Comenic Acid with Cetylpyridinium Chloride

The interaction of comenic acid with cetylpyridinium chloride in aqueous solutions was studied by spectrophotometry. Compositions of ionic associates formed depending on cetylpyridinum chloride concentration were found, and logarithms of equilibrium constants of corresponding association reactions were determined.     

Classical Limit of Expectation Values in a Wave Packet Involving Few Stationary States

Expectation values of physical quantities in a wave packet involving few stationary states in an infinite square well are calculated. Explicit results show that the expectation values in the classical limit go over to the corresponding classical quantity in the form of the arithmetic mean (in mathematical term, the Fejér's average) of the partial Fourier series converging to the classical quantity. The number of the stationary states is that of the partial Fourer series in the Fejér's average. The quantum uncertainty is then demonstrated to have a classical counterpart.