Nonlinear Mathematical Models of Metamaterials Defined as “Mass-in-Mass” and “Damper-in-Mass” Chains

To describe dynamic processes in an acoustic (mechanical) metamaterial, there are proposed models that are a one-dimensional chain containing the same masses connected by linearly elastic (or nonlinearly elastic) elements (springs) with the same stiffness. In this case, it is assumed that each mass contains inside itself a series connection of another mass and an elastic element or viscous element (damper).

Asymptotic Properties of One Mathematical Model in Food Engineering under Stochastic Perturbations

For the example of one nonlinear mathematical model in food engineering with several equilibria and stochastic perturbations, a simple criterion for determining a stable or unstable equilibrium is reported. The obtained analytical results are illustrated by detailed numerical simulations of solutions of the considered Ito stochastic differential equations. The proposed criterion can be used for a wide class of nonlinear mathematical models in different applications.

STRUCTURE AND REQUIREMENTS FOR A UNIVERSAL TRAINING DEVICE FOR UNMANNED AIRCRAFT COMPLEXES

The problems of personnel training for the operation of unmanned aerial vehicles have been updated. The differences between the skills and abilities of personnel for manned and unmanned aircraft are highlighted. The widespread types of flight simulators are considered, their features are given. The basic schemes of application of linear and nonlinear mathematical models of formation (formalization) of knowledge, abilities and skills of the personnel taking into account absence / presence of updating of the information in the course of training are substantiated.The basic modes of operation of USL, the universal simulator for training are specified. Emphasis is placed on the fact that USL is a partial case of an automated training management system (ACS), and a block diagram of training with it is given. The tasks that can be solved on a universal simulator and the requirements for software and hardware, automated workplace, digital sound, general software, peripherals, data exchange, digital video, user interface and webbased automated instructions are discussed in detail. The functions and structure of the universal simulator for training unmanned aircraft complex are presented.

Analytical method for nonlinear mathematical models with Atangana conformable derivative

In this study, we investigate the analytical solutions of the modified Benjamin Bona Mahony and Sharma-Tosso-Olver equations, which are defined with Atangana conformable fractional derivative, using the modified exponential function method. Analytical solutions of the modified Benjamin Bona Mahony and Sharma-Tosso-Olver equations were obtained by using the modified exponential function method. Two, three-dimensional and contour graphics are used to understand the physical interpretations of the resulting analytical solutions to the mathematical model. When all these results and graphs are analzyed, it has been shown that the modified exponential function method is an effective method for obtaining analytical solutions for all other nonlinear fractional partial differential equations containing conformable fractional derivatives of Atangana.

Optimal Capacity And Flow Assignment For Self-Healing ATM Networks Based On Path Restoration: Nonlinear Models

This thesis addresses the design of self-healing Asynchronous Transfer Mode (ATM) networks which is a special aspect of a more general problem, referred to as capacity and flow assignment (CFA) problem in self-healing ATM networks. We have proposed two nonlinear mathematical models for global reconfiguration strategy and failure-oriented reconfiguration strategy in our thesis. Our restoration strategies aim to minimize the capacity installation cost and the routing cost when a single link failure occurs in the network. A special case of the augmented Lagrangian method so-called Separable Augmented Lagrangian Algorithm (SALA) is proposed for solving the proposed nonlinear mathematical models. Numerical results are presented comparing the two restoration strategies in terms of five performance metrics which are capacity installation cost, total required capacity, routing cost, total network cost and required CPU time for convergence of the algorithms. Our results show that the global reconfiguration strategy has always performed better than the failure-oriented reconfiguration strategy for all the network scenarios, topologies and bandwidth requirements.

Optimal Capacity And Flow Assignment For Self-Healing ATM Networks Based On Path Restoration: Nonlinear Models

This thesis addresses the design of self-healing Asynchronous Transfer Mode (ATM) networks which is a special aspect of a more general problem, referred to as capacity and flow assignment (CFA) problem in self-healing ATM networks. We have proposed two nonlinear mathematical models for global reconfiguration strategy and failure-oriented reconfiguration strategy in our thesis. Our restoration strategies aim to minimize the capacity installation cost and the routing cost when a single link failure occurs in the network. A special case of the augmented Lagrangian method so-called Separable Augmented Lagrangian Algorithm (SALA) is proposed for solving the proposed nonlinear mathematical models. Numerical results are presented comparing the two restoration strategies in terms of five performance metrics which are capacity installation cost, total required capacity, routing cost, total network cost and required CPU time for convergence of the algorithms. Our results show that the global reconfiguration strategy has always performed better than the failure-oriented reconfiguration strategy for all the network scenarios, topologies and bandwidth requirements.

Hardening Cement Conglomerates by Mining Industries Waste

About 3.5 billion tons of mining waste is generated annually in Russia. The task of their utilization is urgent in connection with the accumulation of large-tonnage waste of simultaneously mined rocks, enrichment waste and crushing screenings. The problem can be solved by using these wastes as mineral additives to artificial cement-based conglomerates. According to the study results it was found, that the compressive strength of hardened cement paste increased during all hardening periods, when finely dispersed mining wastes were introduced. In the early stages of hardening, limestone had a predominant effect. Introduction of diopside led to the greatest hardening together with the hardening period increase. Linear and nonlinear mathematical models, describing the dependence of cement strength on the type and amount of mineral additives, were constructed. The highest strength values of hardened cement paste, both after hardening under normal conditions for 28 days, and after heat and moisture treatment could be achieved with 7% dispersed diopside. At the same time, the hardening effect (increase in the strength of cement by 35–40%) was retained when 1/3 of the diopside in the complex additive was replaced by dispersed limestone. An increase in the content of limestone in the complex additive composition over 1/3 was impractical.