Coarsening kinetics with elastic effects

We discuss the coarsening process of melt inclusions inside a solid phase. Elastic effects lead to an oblate shape of the particles, resulting in a system with strong diffusional and elastic interactions between inclusions. The usual mean-field approximation breaks down and several independent length scales have to be taken into account. In a system of parallel oriented particles we find scaling laws for the coarsening of the different length scales involved. In particular, the lateral size of the particles obeys a nontrivial growth law, R approximately t(5/12).     

IAE-3 and IAE-6 high resolution photographic materials for recording laser radiation in the IR-region

New photographic materials for recording the radiation of injection lasers (λ=840 nm) with a sensitivity of ?10^-4 J/sm² and a resolution of 4300 lines/mm, and photographic materials for recording the radiation in the region of 1060 nm with a sensitivity of ?10^-4 J/sm² and a resolution of 1000 lines/mm are described.     

Temperature Dependence of Selective Emission Intensity of the R1 Line upon Laser–Thermal Heating of Ruby

Optics and Spectroscopy - The temperature dependence of the selective emission intensity of the R1 line upon laser-thermal heating of ruby is studied and explained by competition of radiative and...     

Diagnostics of the Phase Composition of Lead-Zirconate-Titanate Films according to Raman Spectra: Phase Identification

The problem concerning the diagnostics of the phase composition of lead-zirconate-titanate (PZT) films under conditions of overlapping Raman spectra is solved via applied mathematical statistics. The proposed phase-identification method based on reference spectra is implemented using different Raman-spectrum regions measured on the surface of multiphase PZT films. It is demonstrated that the identification of phases, as well as determination of their concentration, must be performed using the spectral range in which the calculated first principal components of the set of Raman spectra differ to the greatest extent from each other.     

Gap solitons in an anharmonic diatomic lattice

Localized stationary modes with frequency in the forbidden region of the elastic vibrations of a diatomic anharmonic lattice are studied by the coupled-wave method. The mechanisms responsible for the brightening of the lattice in the cases of narrow and wide forbidden frequency bands are determined and an analytical expression is found for the stationary gap solitons. Fiz. Tverd. Tela (St. Petersburg) 39, 158–162 (January 1997)     

Discretization of the dynamic problem of elasticity theory with a discontinuous solution

A discretization algorithm for initial boundary-value problems is developed for systems of two linear equations of hyperbolic type with discontinuous solutions. A Crank—Nicholson scheme is constructed for discretization of the Cauchy problem and error bounds are obtained for the approximate solution. A model example is solved.Institute of Cybernetics of the Ukrainian Academy of Sciences. Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 75–83, 1991.     

Direct central impact of different elastic bodies of rotation

A direct central collision of two bodies of revolution is studied. A nonstationary mixed boundary-value problem with an unknown moving boundary is formulated. Its solution is represented by a series in term of Bessel functions. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying the boundary conditions. The basic characteristics of the collision process are determined depending on the physic-mechanical properties of the bodies. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Automatic generation of linear programming problems for computer aided instruction

The paper presents a method for generating random linear programming problems with a previously selected type of solution. The user can choose a problem whose solution is unbounded, bounded for minima, maxima or both, unique or multiple, with given structure, at wish. Initially, the feasible solution of the LPP is generated as the sum of a linear space, a cone, and a polytope, depending on the desired properties of the solution. With the aim of obtaining a simple set of constraints, the generators of these three structures are selected as random vectors with integer simple components, the range of which can be given. Next, an objective function that satisfies the required conditions, i.e. leads to a solution of the desired type, is obtained. The generating algorithms have been implemented in Mathematica and some illustrative examples are given to clarify the generation process. With this tool, a LPP can be generated, according to the instructor requirements, where this is a human or an expert system. They can control student progress and generate a sequence of problems covering all possible cases, in steps of increasing difficulty. Combining this tool with another (also produced by the same authors) that solves the problems and explains the whole process, step by step, a computer aided module for learning LPP, which is completely autonomous, can be easily obtained.     

Study of temperature fields in a rectangular plate with a temperature-dependent internal source with the aid of fast expansions

The approximate analytic solution of the problem of temperature field in a rectangular plate with an internal temperature- dependent source is obtained by the method of fast expansions. The critical value of a parameter characterizing heat release, which fundamentally affects the analytic solution form, is found. The maximum solution error is shown to amount to 0.02 at the consideration of the first three terms of the Fourier series in fast expansion. Temperature fields are presented, and an analysis of the influence of the plate sizes and the heat release magnitude on their formation is given. Recommendations on the plate shape choice are given.