mathematical modeling

Modeling the dynamics of a capsule-type locomotion system actuated by an imbalanced rotor under the action of dry anisotropic friction

Mobile robotic systems with vibratory drives are becoming increasingly popular in various fields of industry and medicine.  This article is dedicated to the study of the dynamic behavior of a mobile capsule-type robot equipped with an imbalanced vibration exciter.  The research methodology involves constructing a simplified dynamic diagram of the robot's mechanical system, using Lagrange's equations of the second kind to describe its motion, and solving the obtained system of differential equations using numerical methods integrated into the Wolfram Mathematica software

DESIGN OF A VIBRATING MACHINE FOR DRY CLEANING OF ROOT VEGETABLES USING NONLINEAR MATHEMATICAL AND THREE-DIMENSIONAL MODELING

The design of a highly efficient vibrating machine for dry cleaning root vegetables of various types, shapes, and sizes has been developed. First, a schematic diagram of the machine was built, containing all the future machine's main components. A nonlinear mathematical model was constructed to describe its dynamics during its operation to determine the future machine's optimal geometric, kinematic, and power parameters. The mathematical model is based on the apparatus of asymptotic methods of nonlinear mechanics and Lagrange's equations.

An Influence of the Time and Spatial Harmonics on an Electromagnetic Torque of a Symmetrical Six-Phase Induction Machine With a Six-Step Inverter Supply Under Open Phase Circuit Fault

Six-phase induction machines offer several advantages over traditional three-phase machines, including higher levels of electromechanical compatibility with loads, energy efficiency, and fault tolerance.

This article presents an analysis of the impact of harmonics in the winding distribution function in the stator slots and the harmonics of the machine’s supply on its electromechanical compatibility with the load during a single-phase failure.

Energy-efficient Control of Electric Vehicle Heating, Ventilation, and Air Conditioning System – Performance Optimization and Energy Consumption Reduction

The article addresses the challenge of improving the energy efficiency of the heating, ventilation, and air conditioning (HVAC) system in electric vehicles. Due to the absence of an internal combustion engine in electric vehicles, there is no additional heat source, meaning that HVAC systems consume a significant portion of the battery energy, thereby reducing the vehicle’s range. The aim of this study is to develop an energy-efficient control algorithm for the HVAC system that minimizes energy consumption while maintaining adequate comfort levels for passengers.

Modeling the Block Formation Process in Blockchain and Its Impact on Scalability

The article investigates the process of block formation in blockchain networks and the impact of node network architecture and consensus algorithms on their scalability and performance. Analysis of blockchain system scalability is important due to problems that arise when network load increases, particularly the increase in the number of block forks and transaction confirmation times. The research focuses on studying the impact of network delays and the choice of consensus algorithm on the performance and scalability of blockchain networks.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. II

Modeling of the impurity diffusion process in a layer under the action of a system of random point sources is carried out.  Mass sources of different power are uniformly distributed in a certain internal interval, that may also coincide with the entire region of the layer.  The statistics of random sources is given.  The solution of the initial-boundary value problem is found as the sum of the homogeneous problem solution and the convolution of the Green's function with the system of the random point sources.  Averaging of the solution is performed on the internal subinterval and in the ent

Algorithm for determining inclusion parameters in solving inverse problems of geoelectrical exploration using the profiling method

The paper aims to develop an algorithm for recognizing the physical and geometric parameters of inclusion, using indirect methods of boundary, near-boundary, and partially-boundary elements based on the data of the potential field. Methodology. The direct and inverse two-dimensional problems of the potential theory concerning geophysics were solved when modeling the earth's crust with a piecewise-homogeneous half-plane composed of a containing medium and inclusion that are an ideal contact.

Spatiotemporal dynamics of RNA viruses in the presence of immunity and treatment: case of SARS-CoV-2

In this paper, we develop a mathematical model using partial differential equations to investigate the behavior of RNA viruses in the presence of antiviral treatment.  The developed model includes both cell-to-cell and virus-to-cell modes of transmission.  Initially, we establish the well-posedness of the model by demonstrating the existence and uniqueness of solutions, as well as their positivity and boundedness.  Additionally, we identify and analyze the stable equilibrium states, their global stability depending on specific threshold parameters, using Lyapunov functi

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. I

The model of the impurity diffusion process in the layer where a system of random point mass sources acts, is proposed.  Mass sources of various power are uniformly distributed in a certain internal interval of the body.  Statistics of random sources are given.  The solution of the initial-boundary value problem is constructed as a sum of the homogeneous problem solution and the convolution of the Green's function and the system of the random point mass sources.  The solution is averaged over both certain internal subinterval and the entire body region.  Simulation unit