On the determination of quark masses from the Dalitz plot for the decay η → π+π?π0

An experimental Dalitz plot distribution for the decay η → π ⁺ π ⁻ π ⁰ is fitted by the theoretical one obtained in chiral perturbation theory with unitarity corrections taken into account. The fit shows that the difference of light-quark masses is larger than is expected from electromagnetic mass differences of neutral and charged kaons. From Yadernaya Fizika, Vol. 67, No. 2, 2004, pp. 443–445. Original English Text Copyright ? 2004 by Martemyanov, Sopov. This article was submitted by the authors in English.     

Dielectric properties of liquid crystals of the cyano derivative compounds with different fragments in the molecular core

This paper reports on the results of investigations into the influence of variations in the chemical composition of the aromatic core of cyano-containing molecules of liquid crystals on their dielectric properties in the frequency range 1–2000 MHz. It is shown that the dispersion of the longitudinal permittivity is adequately described by the sum of two Debye processes with different weighting factors and relaxation times. The frequency dependence of the transverse permittivity is well approximated by the Debye process with a continuous distribution of relaxation times in a specified range. It is established that the replacement of one benzene ring in the biphenyl core of the 5CB liquid-crystal molecule by a cyclohexane (or bicyclooctane) fragment leads to a considerable decrease in both relaxation times for the longitudinal permittivity, a change in the low-frequency limit of the relaxation time range for the transverse permittivity, and the evolution of the frequency dependence of the dielectric anisotropy.     

Elasticity and inelasticity of biomorphic silicon carbide ceramics

The effect of the vibration strain amplitude on the Young modulus and ultrasonic absorption (internal friction) in biomorphic SiC ceramics is investigated in the temperature range 116–296 K. The biomorphic SiC ceramics is prepared through pyrolysis of eucalyptus with subsequent infiltration of silicon. It is demonstrated that the vibration loading of samples in air and under vacuum is accompanied by a number of unexpected effects. The behavior of the studied ceramics is governed by at least two mechanisms, which, to a large extent, are responsible for the elastic and inelastic properties of the material. One mechanism is associated with the adsorption-desorption of environmental molecules (hypothetically, owing to the presence of pores and residual carbon), and the other mechanism involves microplastic deformation due to the motion of dislocations or other (similar) structural units.     

Spatial deterministic chaos in optical systems and methods of its modeling

The phenomenon of spatial deterministic chaos is described. A transition from an ordinary differential equation to a discrete map is justified for modeling of the chaos. Methods of studying the chaos dynamics in this model are suggested. It is established how the physical properties of a nonlinear ring interferometer influence the structure of charts of the Lyapunov exponents. The approaches developed in the present study allow an optical cryptosystem to be optimized.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 65–71, December, 2004.     

Dispersion Characteristics of Waveguide Arrays in Optical Spectrum Analyzers

Formulas for calculating the spectral characteristics of waveguide arrays, which are incorporated into waveguide spectrum analyzers based on planar waveguides, channel waveguides, and fiber optical waveguides, are derived taking into account the contribution of both the waveguide dispersion and the material dispersion to the dispersion factor. These formulas are used to study the dependence of the dispersion factor on the waveguide-system parameters for specific models of waveguide arrays. It is shown that consideration of contributions of the waveguide dispersion and material dispersion can affect profoundly the spectral characteristics of waveguide arrays.     

Theory of periodic states for feedback-controlled photorefractive nonlinear systems

Certain feedback loops can be used in photorefractive optical schemes to implement periodic states and create spatial gratings characterized by extremely high or low diffraction efficiencies. This highly nonlinear phenomenon is studied both experimentally and numerically. An analytical method is developed for analyzing periodic states with the use of symmetries of time-dependent diffraction equations and fast feedback response. The method is applied to describe the properties of periodic states, including their spatial structure, diffraction-efficiency oscillation period and amplitude, and characteristics of feedback-controlled strong phase modulation.     

Effect of lattice deformation and phase transitions on the electronic spectra of TlGaS<Subscript>2</Subscript>, TlGaSe<Subscript>2</Subscript>, and TlInS<Subscript>2</Subscript> layered semiconductors

The effect of the lattice deformation on the electronic spectra of TlGaS₂, TlGaSe₂, and TlInS₂ layered semiconductor crystals is analyzed. It is shown that changes in the band gap of these semiconductors due to thermal expansion and a change in the composition under hydrostatic or uniaxial pressure can be described within a unified model of the deformation potential. The main feature of this model is the inclusion of deformation potentials with different signs, which is characteristic of other semiconductors with a layered structure. An analysis of the lattice deformation of the studied semiconductors in terms of the proposed model of the deformation potential has revealed that, in the immediate vicinity of the phase transitions, the crystal lattice under pressure undergo an unusual deformation.     

A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).     

Interior ballistics of a single-stage plasmatron and the general features of radiative heat exchange

A mathematical model of a single-stage ballistic plasmatron for producing radiating gas is proposed. Various operating conditions are analyzed and compared with experimental data. The general features of radiative heat exchange in the device are outlined.     

Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).