International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

Modern intensification of materials processing technology leads to an increase in the role of non-stationary interconnected exchange processes compared to stationary unconnected interconnected exchange processes compared to stationary unconnected. This fact is still insufficiently reflected in the field of solving energy and mass transfer problems (EMT) at small Fourier numbers (Fourier numbers ≤0.1) at short-term phase contact (SPC). In this article, a generalized mathematical model of interconnected non-stationary irregular energy and mass transfer mode at short-term contact across a boundary with selective permeability of phases is formalized. In vector-matrix form, a conjugate mixed boundary value problem is solved with excitation in each of the phases of flows of substances absent in the other phase. By analogy with heat exchange and mass exchange, matrices of potential assimilation of phases and a contact matrix are introduced, which allows obtaining a uniform solution for a number of special cases and especially simplified the entry for the vector of interphase flow densities. The mathematical notation of the solutions of the considered parabolic system of partial differential equations of the second order for intensive irreversible processes (Fourier numbers ≤0.1) are written in vector-matrix form and are close to the scalar Higbee theory for mass transfer.

A group of numerical methods suitable for describing the propagation of light in a Photonic Crystal Fiber (PCF) are discussed. PCFs can be classified according to the mechanism of light propagation. The methodology of the analysis is briefly reviewed to understand how changing the different physical parameters of the fiber and the design affects its optical properties. By analyzing the systematic studies presented, a design with the desired optical fiber properties can be realized.
PCFs can be made from just one material with two-dimensional photonic crystals or periodic arrays of air holes parallel to the fiber axis to form a shell and core shape. Several types of PCFs have been considered. The mechanism for trapping light in the fiber core is explained. The use of the wave methods for electromagnetic field analysis is discussed. The application of variation principles and weighted residual methods is shown. The advantages of the finite element method (FEM) are indicated. The vector FEM for obtaining the modes in photonic crystal fibers is considered.