Mathematical Modeling of Layered Nanocomposite of Fractal Structure

Mathematical Modeling of Dielectric Permeability and Volt-Ampere Characteristics of a Semiconductor Nanocomposite Conglomerate

Mathematical computer models of the permittivity of silicon-based nanostructures upon interaction with electromagnetic radiation in a wide frequency range have been developed. To implement computer models for studying the electrophysical properties of the structures under study, algorithms and a set of programs have been developed. The results of the study of materials will not only provide fundamental information about the physical effects occurring in composite nanostructures but will also be useful for solving problems related to calculations for given electrophysical problems. For a nanocomposite based on ceramics and semiconductor oxides of zinc grains, resonant bursts of permittivity are observed within a wavelength of 300–400 nm; it has been found that this is due to the presence of electronic polarization of the nanocomposite core. The paper presents the results of modeling the current-voltage characteristics of a nanocomposite based on ceramics and semiconductor grains of zinc oxide. The obtained results show that the geometrical parameters, such as the number of layers and sample width, affect the CVC of the nanocomposite, and the operating point of the CVC shifts. This may be of interest in the development of materials with desired electrical characteristics for the creation of varistors.

Transformation Method for Solving System of Boolean Algebraic Equations

In recent years, various methods and directions for solving a system of Boolean algebraic equations have been invented, and now they are being very actively investigated. One of these directions is the method of transforming a system of Boolean algebraic equations, given over a ring of Boolean polynomials, into systems of equations over a field of real numbers, and various optimization methods can be applied to these systems. In this paper, we propose a new transformation method for Solving Systems of Boolean Algebraic Equations (SBAE). The essence of the proposed method is that firstly, SBAE written with logical operations are transformed (approximated) in a system of harmonic-polynomial equations in the unit n-dimensional cube Kn  with the usual operations of addition and multiplication of numbers. Secondly, a transformed (approximated) system in Kn  is solved by using the optimization method. We substantiated the correctness and the right to exist of the proposed method with reliable evidence. Based on this work, plans for further research to improve the proposed method are outlined.

Mathematical Modeling of the Electrophysical Properties of a Layered Nanocomposite Based on Silicon with an Ordered Structure

The authors carried out modeling of the electrophysical properties of composite media. The frequency dependences of the dielectric constant on the type of inclusions in the composite are investigated. On the basis of the nanocomposite considered in the work, based on Si, B, and SiO2, the authors model a reflecting screen, the lattice elements of which have a layered hierarchically constructed structure similar to a fractal formation. The influence of the level of fractality on the optical properties of the object was also investigated, and it was found that the proposed structure makes it possible to increase the operating frequency range of the reflecting screen and the efficiency, in comparison with reflecting screens that have a lattice of traditional structure. The results obtained can be of practical interest for broadband and nonlinear radar devices, localization devices and mobile objects, microelectronics, as well as intelligent applications in the field of information security.

Parallel Computational Algorithm for Object-Oriented Modeling of Manipulation Robots

An algorithm for parallel calculations in a dynamic model of manipulation robots obtained by the Lagrange–Euler method is developed. Independent components were identified in the structure of the dynamic model by its decomposition. Using the technology of object-oriented programming, classes corresponding to the structures of the selected components of the dynamic model were described. The algorithmization of parallel computing is based on the independence of the calculation of objects of individual classes and the sequence of matrix operations. The estimation of the execution time of parallel algorithms, the resulting acceleration, and the efficiency of using processors is given.

Mathematics Model for 6-DOF Joints Manipulation Robots

A universal solution to an applied problem related to the study of deviations occurring in the joints of manipulation robots, for example, due to elastic deformations or gaps in them, is proposed. A mathematical (dynamic) model obtained by the Lagrange–Euler method is presented, making it possible to investigate such deviations. Six generalized coordinates, three linear and three angulars, were used to describe the variations of each joint in the dynamic model. This made it possible to introduce into consideration joints with six degrees of freedom (6-DOF joints). In addition, mathematical models for external forces acting on the links of manipulation robots are presented. When composing matrices of coefficients of equations of motion, elements identically equal to zero were excluded, which significantly increased the computational efficiency of these equations. The dynamic model based on the obtained equations can be used in the computer simulation of manipulation robots.