mathematical model
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Sneha Dey ◽  
A. Ghorai ◽  

Exploration of dynamics of raindrops is one of the simple yet most complicated mechanical problems. Mass accretion from moist air during the motion of raindrop through resistive medium holds an arbitrary power law equation. Its integral part is the change of shape, terminal motions and terminal solutions, etc. Classical Newtonian formalism is used to formulate a mathematical model of generalized first order differential equation. We have discussed about the terminal velocity of raindrop and its variation with the extensive use of python program and library. It is found that terminal velocity 𝐯𝐓𝐜𝛂𝛃 is achieved within 20 seconds where 𝛂=, 𝛃=(𝟎,𝟏) and 𝐧=𝟎,𝟏,𝟐,𝟑,𝟒,…. Its variations due to mass accretion roughly follows the earlier predicted range 𝐠/𝟕 to 𝐠/𝟑.

Mikhail Andreev ◽  
Alexey Suvorov ◽  
Alisher Askarov ◽  
Vladimir Rudnik ◽  
Bhavesh R. Bhalja

Fuel ◽  
2022 ◽  
Vol 309 ◽  
pp. 122133
Xiwei Ke ◽  
Markus Engblom ◽  
Hairui Yang ◽  
Anders Brink ◽  
JunFu Lyu ◽  

2022 ◽  
Vol 1 (1) ◽  
pp. 63-71
Vladimir Pryadkin ◽  
Artem Artemov ◽  
Pavel Kolyadin ◽  
A. Kolcov

The article presents a mathematical model of the destructive effect of a wide-profile tire on the roadway. The mathematical model makes it possible to adequately reproduce the effect of a wide-profile tire on the road surface, taking into account the load and parameters of the tire, as well as the structure of the road surface and the temperature state.

2022 ◽  
Vol 24 (4) ◽  
pp. 72-80
Ivan S. Polyanskii ◽  
Inna V. Polyanskaya ◽  
Kirill O. Loginov

In the article, to solve the problem of assessing the information impact on the electorate during election campaigns, algorithmic solutions, including a mathematical model, a numerical scheme and algorithmic implementations, are formed. This assessment is reduced to determining the instantaneous values of the number of voters who prefer a candidate (party), taking into account: the positive or negative stochastic nature of the impact of mass media; interpersonal interaction; two-step assimilation of information; the presence of a variety of mass media, social groups and a list of candidates. The mathematical model is based on a generalized model of information confrontation in a structured society and, with the introduction of stochastic components in the intensity of agitation, it is reduced to solving the FokkerPlanckKolmogorov equation. For its study in the formulation of the Galerkin method, a numerical scheme is proposed and the order of its convergence is determined. In relation to the basic procedures of the numerical scheme, the features of the algorithmic implementation are clarified.

Energies ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 608
Lukasz Szablowski ◽  
Olaf Dybinski ◽  
Arkadiusz Szczesniak ◽  
Jaroslaw Milewski

The paper presents a mathematical model of a molten carbonate fuel cell with a catalyst in the anode channel. The modeled system is fueled by methane. The system includes a model of the steam reforming process occurring in the anode channel of the MCFC fuel cell and the model of the cell itself. A reduced order model was used to describe the operation of the molten carbonate fuel cell, whereas a kinetic model describes the methane steam reforming. The calculations of the reforming were done in Aspen HYSYS software. Four values of the steam-to-carbon ratio (2.0, 2.5, 3.0, and 3.5) were used to analyze the performance of the reforming process. In the first phase, the reaction kinetics model was based on data from the literature.

M.V. Zalesov ◽  
V.A. Grigoreva ◽  
V.S. Trubilov ◽  
A.Ya. Boduen

It is important for mining dump trucks to minimize the weight of the carrier and the load platform while maintaining a sufficient level of their rigidness and strength. This requirement significantly affects the weight of the transported material, the cost of transportation and, consequently, the economic efficiency of mining operations. Processes of loading and dumping of bulk loads, which is transported by dump trucks, make a significant contribution to reducing the service life of the carrier. Therefore, proper consideration of the bulk load dynamics is an important and relevant task. Contemporary systems for calculating the dynamics of solids allow for joint modeling with applications designed to calculate the dispersed body dynamics. This approach helps to obtain adequate loads in the pivots and force links of the model, to analyze the loading of the load platform, to asses the durability of the dump truck elements, to define the geometry of the load platform. In order to perform the simulation, it is required to develop a mathematical model of a dump truck, including all its key elements and subsystems, a model of the bulk load, and a model of the load platform. The purpose of the study is to develop a mathematical model of a mine dump truck to determine the loads in the pivots and force links connected to the carrier and the load platform for the strength calculations and durability analysis. The calculations are made with the combined use of the solids dynamics calculation system and the application to calculate the dynamics of dispersed bodies.

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