scholarly journals Mathematical Modelling of a Specialized Vehicle Caterpillar Mover Dynamic Processes Under Condition of the Distributing the Parameters of the Caterpillar

2018 ◽  
Vol 7 (4.3) ◽  
pp. 40 ◽  
Author(s):  
Serhii Strutynskyi ◽  
Volodymyr Kravchu ◽  
Roman Semenchuk
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Modelling ◽  
Mass Concentration ◽  
Forced Oscillations ◽  
Dynamic Processes ◽  
Random Loads ◽  
Distributed Parameters ◽  
The Mathematical Model ◽  
Transverse Oscillations

Features of a specialized vehicle caterpillar mover are considered. A dynamic model of caterpillar transverse oscillations as a system with distributed parameters is proposed. The differential equation in partial derivatives is obtained and its connection in the form of a decomposition by normal oscillation types is found. The analysis of frequencies and the type of caterpillar oscillations has been made. Inertial loads have been found. The mathematical model of forced oscillations of a caterpillar under the influence of random loads is developed and the mathematical modelling is executed. An analysis of the vibration movements and vibration velocities of the intersections of the caterpillar is carried out. The mathematical modeling of the caterpillar oscillations caused by stochastic discrete loads was carried out. A model of random discrete loads has been developed, calculations of the realization of random loads are performed. It was established that the transverse discrete loads occur in points of mass concentration on the caterpillar surface. 

scholarly journals Development of a subsystem for automatic protection of submersible pumps based on mathematical modeling

2018 ◽  
Vol 226 ◽  
pp. 04028
Author(s):  
Alexander V. Pilipenko ◽  
Andrei A. Tashev ◽  
Nail K. Sharifov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Modelling ◽  
Protection System ◽  
Piston Pump ◽  
The Mathematical Model

In this paper, the authors produce a mathematical modelling of a piston pump, develop algorithms for the operation of a protection system, taking into account the results of mathematical modelling. The authors test the mathematical model on the operation of real equipment and analyze its accuracy.

scholarly journals Measurement and improvement of efficiency of Library by mathematical modelling and finding reliability

2021 ◽  
Vol 7 (2) ◽  
pp. 1-5
Author(s):  
Yakshi Bahl ◽  
Tarun Kumar Garg
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Mathematical Modelling ◽  
Exponential Distribution ◽  
Death Process ◽  
Library System ◽  
The Mathematical Model ◽  
Server System ◽  
Birth Death

Here in this paper we have developed  the mathematical model of the library server using  Markov birth – death process assuming that library system server system is based on exponential distribution. The model so developed by victimisation Chapman Kolmogorov differential equation and is solved by using Mathematica. The solution so obtained is analysed for various rates of failures and repair. The finding so obtained are discussed with the concerned authorities of the library to boost the efficiency of the library.

scholarly journals Conceptual and Mathematical Modeling of a Coastal Aquifer in Eastern Delta of R. Nestos (N. Greece)

Hydrology ◽  
2021 ◽  
Vol 8 (1) ◽  
pp. 23
Author(s):  
Ioannis Gkiougkis ◽  
Christos Pouliaris ◽  
Fotios-Konstantinos Pliakas ◽  
Ioannis Diamantis ◽  
Andreas Kallioras
Keyword(s):  
Mathematical Modeling ◽  
Groundwater Flow ◽  
Coastal Aquifer ◽  
Flow Model ◽  
Meteorological Data ◽  
Field Measurements ◽  
Groundwater Flow Model ◽  
Aquifer System ◽  
Geophysical Surveys ◽  
The Mathematical Model

In this paper, the development of the conceptual and groundwater flow model for the coastal aquifer system of the alluvial plain of River Nestos (N. Greece), that suffers from seawater intrusion due to over-pumping for irrigation, is analyzed. The study area is a typical semi-arid hydrogeologic environment, composed of a multi-layer granular aquifers that covers the eastern coastal delta system of R. Nestos. This study demonstrates the results of a series of field measurements (such as geophysical surveys, hydrochemical and isotopical measurements, hydro-meteorological data, land use, irrigation schemes) that were conducted during the period 2009 to 2014. The synthesis of the above resulted in the development of the conceptual model for this aquifer system, that formed the basis for the application of the mathematical model for simulating groundwater flow. The mathematical modeling was achieved using the finite difference method after the application of the USGS code MODFLOW-2005.

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

A New Method and Applications of the Boundary Value Problem of Differential Equation

2014 ◽  
Vol 937 ◽  
pp. 695-699
Author(s):  
Hong E Li ◽  
Xiao Xu Dong ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Cong Yin Fan
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Kernel Function ◽  
Boundary Value ◽  
Outer Boundary ◽  
Seepage Flow ◽  
Petroleum Engineering ◽  
Constructive Method ◽  
Linear Homogeneous Differential Equation ◽  
The Mathematical Model

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.

Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid

2016 ◽  
Vol 693 ◽  
pp. 837-842
Author(s):  
Fu Yi Xia ◽  
Li Ming Xu ◽  
De Jin Hu
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Abrasive Particle ◽  
Influence Factors ◽  
Machining Process ◽  
Quadric Surface ◽  
Precision Grinding ◽  
Cup Wheel ◽  
The Mathematical Model ◽  
Trajectory Equation

A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

The Description of a Distributed Parameter Process through a Finite Discrete Dimensional System

2014 ◽  
Vol 657 ◽  
pp. 874-878
Author(s):  
Sever Şerban ◽  
Doina Corina Şerban
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Industrial Process ◽  
Time Discretization ◽  
Distributed Parameter ◽  
Geometrical Parameters ◽  
Dimensional System ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Distributed Parameters

This article analyses the process of warming a metal by using a walking beam furnace. This process is meant to offer the technologist objective information that may allow him to produce eventual modifications of the temperature references from the furnaces zones. Thus making the metals temperature at the furnaces exit to have an imposed distribution, within precise limits, according to the technological requests. This industrial process has a geometrical parameters distribution, more precisely it can be described through a partial differential equation, by being attached to dynamic infinite dimensional systems (or with distributed parameters). Using a procedure called geometric-time discretization (in the condition of the solutions convergence), we have managed to obtain a representation under the form of a finite discrete dimensional linear system for a process with distributed parameters.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

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