Том 27, № 1 (2018)

For the 2D Ising model, we analyzed dependences of thermodynamic characteristics on number of spins by means of computer simulations. We compared experimental data obtained using the Fisher-Kasteleyn algorithm on a square lattice with N = l × l spins and the asymptotic Onsager solution (N → ∞). We derived empirical expressions for critical parameters as functions of N and generalized the Onsager solution on the case of a finite-size lattice. Our analytical expressions for the free energy and its derivatives (the internal energy, the energy dispersion and the heat capacity) describe accurately the results of computer simulations. We showed that when N increased the heat capacity in the critical point increased as lnN. We specified restrictions on the accuracy of the critical temperature due to finite size of our system. Also in the finite-dimensional case, we obtained expressions describing temperature dependences of the magnetization and the correlation length. They are in a good qualitative agreement with the results of computer simulations by means of the dynamic Metropolis Monte Carlo method.

A comparative analysis of methods for calculating digital holograms based on discrete transformations for various types of objects is presented. Qualitative results of synthesis and reconstruction of holograms are obtained, as well as examples of the realization of some of the types of holograms considered. The quality of digital hologram recovery is estimated by calculation of signal-tonoise ratio (SNR) and root-mean-square error (RMSE).

Presents the results of the spectral analysis using the method of Raman scattering spectroscopy (RS) of dura mater (DM) samples, manufactured by technology “Lioplast” practised in the clinic in the area of atrophic processes at multiple gum recessions. The method of Fourier deconvolution and selection of the spectral profile by the method of least squares is used to increase the resolution and informativity of the spectrum. With the help of mathematical methods of separation of overlapping spectral contours, the main bands corresponding to the main components of the implants were found: amides, proteins, glycosaminoglycans, DNA/RNA. On the basis of the two-dimensional spectral analysis, the coefficients reflecting the composition of the dura mater with different methods of its treatment were introduced. It has been established that Raman spectroscopy can be used to evaluate implants from the dura mater.

It has been determined the influence of the substrate from the float-glass parties on the composites with the bilateral nano film main optical characteristics (the refractive index and the reflectivity coefficient) and the nano film thickness as the nano photonics element. The composites and the nano films these characteristics dependences on the parties of the float-glass substrate (gas and tin) on which one or double-layers film was drawn at the speed values of 3.8, 5.8 and 17.3 mm/s have been studied. These studies show that the composites properties and the nano films thickness were sensitive both to the film drawing speed and to the float-glass parties (gas or tin) on which these nano films were drawn. These properties of the composites with the nano films drawn from the nitrate and chloride sols are different from each other.