Mathematical Modeling
Vol. 5 (2021), Issue 4

Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

    • Formulation of axisymmetric boundary value problems of the linear theory of elasticity for canonical bodies in harmonic potentials

      pg(s) 116-119

      The paper is based on the representation of the fundamental solution of the linear elasticity theory of the mechanics of a deformable solid in the J. Dougall’s form through spatial harmonic functions. The axisymmetric problem of the elasticity theory in a cylindrical coordinate system for bodies bounded by a canonical surface is formulated. As a case, the boundary value problem of pure torsion is formulated and the elastic characteristics and structure of the corresponding external loads on the side surface of a given isotropic elastic body in the above-mentioned harmonic potentials are presented. This approach makes it possible to obtain and extend the set of exact analytical solutions of boundary value problems of the spatial elasticity theory and is the theoretical basis for calculating the strength parameters of mechanical systems.

    • Consistent Presentation of the Beam Deflection Theory Including Shear Correction

      pg(s) 120-123

      This article explains a mathematically consistent approach for solving the equations of Timoshenko’s beam theory for statically loaded beams. Theoretic sections 3.4 – 3.5 give a good description of the shear deformation and the primary approach for calculating deflections of beams under bending, taking into account both causes for deflection: bending moment and shear force. Values for the shear correction factor are discussed in section 4. This work was started to check the validity of an equation for deflection of a symmetrically loaded short rectangular beam with span/height ratio = 3 under four-point bending with upper-span/span ratio = 1/3. The exact solution is not presented here, but we can confirm that the presented theory, when applied for the mentioned loading scheme, leads to thi s equation using a shear correction factor k = 5/6.

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

  • MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

    • Application of artificial neural networks for prediction of business indicators

      pg(s) 141-144

      This paper examines the applicability of the neural networks in developing predictive models. A predictive model based on artificial neural networks has been proposed and training has been simulated by applying the Long Short-Term Memory Neural Network module and the time series method. Python programming language to simulate the neural network was used. The model uses the stochastic gradient descent and optimizes the mean square error. Business indicators for forecasting the results of the activity and the risk of bankruptcy of a company are forecasted and a comparison of the obtained forecast values with the actual ones is performed in order to assess the accuracy of the forecast of the developed model. As a result, it can be noted that business indicators can be successfully predicted through the Long Short-Term Memory Neural Network and the forecasted values are close to the actual ones.

    • Decarbonizing Russia: leapfrogging from fossil fuel to hydrogen

      pg(s) 145-147

      We examine a different approach to complete decarbonization of the Russian economy, in a world where climate policy is increasingly requiring radical reduction of emissions wherever possible. We propose an energy system that can supply solar, and wind generated electricity to fulfill all demand and which accounts for intermittency problems. This is instead of a more usual approach of planning for expensive carbon capture and storage, and a massive increase in energy efficiency and therefore a drastic reduction in energy use per unit Gross Domestic Product (GDP). Coupled with this massive increase in alternative energy, we also propose using excess electricity to generate green hydrogen. Hydrogen is a known technology that can function as storage for future electricity needs or for potential fuel use. Importantly, green hydrogen can be used as a re-placement export for Russia’s current fossil fuel exports and will likely provide higher revenues. The analysis was carried out using the highly detailed modeling framework, the High-Resolution Renewable Energy System for Russia (HIRES-RUS) representative energy system. The modeling showed that there are a number of feasible combinations of wind and solar power generation coupled with green hydrogen production to achieve 100% decarbonization of the Russian economy.