scholarly journals Simulation of the process of water purification in multilayered micro porous media

2019 ◽  
pp. 61-63
Author(s):  
Olena Prysiazhniuk ◽  
Andrii Safonyk ◽  
Anna Terebus
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Boundary Value Problem ◽  
Water Purification ◽  
Asymptotic Approximation ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
The Mathematical Model ◽  
Purification Of Water

The mathematical model of the process of adsorption purification of water from impurities in multilayer microporous filters is formulated. An algorithm for numerically-asymptotic approximation of solution of the corresponding nonlinear singularly perturbed boundary value problem is developed. The developed model allows to investigate the distribution of concentration of pollutant inside the filer.

scholarly journals The Mathematical Modeling of Metals Mass Transfer in Three Layer Peat Blocks

2015 ◽  
Vol 1 ◽  
pp. 87
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Mathematical Models ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Difference Methods ◽  
The Mathematical Model

The mathematical model for calculation of concentration of metals for 3 layers peat blocks is developed due to solving the 3-D boundary-value problem in multilayered domain-averaging and finite difference methods are considered. As an example, mathematical models for calculation of Fe and Ca concentrations have been analyzed.

scholarly journals Mathematical Modelling of Mass Transfer in Zones of Complete and Incomplete Saturation under the Action of Systematic Combined Drainage

2019 ◽  
pp. 86-87
Author(s):  
Anatolii Vlasyuk ◽  
Tatiana Tsvietkova
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Porous Media ◽  
Boundary Value Problem ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Finite Differences ◽  
Unsaturated Porous Media ◽  
Vertical Drains ◽  
The Mathematical Model

The mathematical model of a processes mass transfer in saturated and unsaturated porous media to the filtertrap in isothermal conditions to the system of vertical drains is presented. The numerical solution of the respective boundary value problem was obtained by the method of finite differences using the numerical method of conformal mappings in an inverse statement.

scholarly journals MATHEMATICAL SIMULATION OF THE SYSTEM SEISMIC FLUCTUATIONS, WHICH CONSISTS OF THE TAILINGS DUMP EMBANKMENT DAM, THE MATERIAL OF DEPOSIT (TAILS) AND UNDER BOTTOM GROUND LAYERS

2016 ◽  
Author(s):  
И.Д. Музаев
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Seismic Wave Propagation ◽  
Contact Boundary ◽  
Embankment Dam ◽  
Seismic Vibrations ◽  
Contact Surfaces ◽  
The Mathematical Model

Разработана математическая модель совместных сейсмических колебаний системы, состоящей из дамбы обвалования хвостохранилища, материала отложения (хвосты) и подподошвенных слоев грунтового массива. Модель представляет собой контактную краевую задачу для дифференциального уравнения сдвигово-вязких поперечных колебаний тела дамбы с материалами отложений, а также для дифференциальных уравнений сдвигово-вязких поперечных колебаний слоев массива грунта. Эти уравнения взаимосвязаны через граничные условия на контактных поверхностях. Краевая задача решена аналитически. Получены расчетные формулы для вычисления перемещений, скорости и ускорения тела дамбы при распространении падающей на систему сейсмической волны в слоях грунта и в теле дамбы The mathematical model of the system seismic vibrations, which consists of the tailings dump embankment dam, the material of deposit (tails) and under botto ground layers is developed. Model is contact boundary-value problem for the differentialequation of the dam body shift- viscous lateral oscillations with the materials of deposits, and also for the differential equations of the shift- viscous lateraloscillations of the ground layers. These equations are interconnected through the boundary conditions on the contact surfaces. Boundary-value problem is solved analytically. Calculation formulas for enumerating of displacements, velocity and acceleration calculation of the dam body with the seismic wave propagation in the ground layers and into in the dam body.

scholarly journals Boundary Value Problem of an Infinite Array of Loaded Apertures

2015 ◽  
Vol 3 ◽  
pp. 11-15
Author(s):  
Luis Alejandro Iturri-Hinojosa ◽  
Alexander E. Martynyuk ◽  
Mohamed Badaoui
Keyword(s):  
Mathematical Model ◽  
Reflection Coefficient ◽  
Plane Wave ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Incident Plane Wave ◽  
Incident Plane ◽  
Infinite Array ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model of the scattering by a periodically arranged apertures in conducting plates is presented. The boundary value problem of an infinite array of loaded apertures is formulated for an arbitrary incident plane wave. The reflection coefficient for some array geometries is obtained and the calculated values are in good agreement with the measurements in a previously published researches. All the rectangular apertures in the array are assumed to be identical and infinitesimally thin. The mathematical model is based on Floquet’s theorem that specifies the requirement of periodicity by the electromagnetic fields.

THE STABILITY AND FREE VIBRATIONS OF A COLUMN SUBJECTED TO A CONSERVATIVE LOAD GENERATED BY A HEAD WITH A PARABOLIC CONTOUR

2013 ◽  
Vol 13 (07) ◽  
pp. 1340012
Author(s):  
LECH TOMSKI ◽  
SEBASTIAN UZNY
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Free Vibrations ◽  
Specific Load ◽  
Kinetic Criterion ◽  
The Stability ◽  
The Mathematical Model ◽  
First Time ◽  
Roller Radius

The boundary value problem concerning the free vibrations of a slender system subjected to a specific load has been formulated and solved in this work. Heads with parabolic contour have been used to realize the specific load for the first time. The boundary value problem has been formulated using Hamilton's principle. The critical load and the characteristic curves in the plane load–natural frequency have been determined on the basis of the kinetic criterion of stability. Numerical calculations have been assigned to different values of the parameters of the considered system for which the parabolic parameter and the parameter of the roller radius are ranked. The roller is the head of the receiving load. The accuracy of the mathematical model was confirmed on the basis of experimental research based on frequency and modal analysis.

scholarly journals Research of a mathematical model of low-concentrated aqueous polymer solutions

2006 ◽  
Vol 2006 ◽  
pp. 1-27 ◽  
Author(s):  
Mikhail V. Turbin
Keyword(s):  
Mathematical Model ◽  
Weak Solution ◽  
Boundary Value Problem ◽  
Polymer Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Aqueous Polymer ◽  
Initial Boundary Value ◽  
The Mathematical Model

The initial-boundary value problem for the mathematical model of low-concentrated aqueous polymer solutions is considered. For this initial-boundary value problem a concept of a weak solution is introduced and the existence theorem for such solutions is proved.

scholarly journals Regularized Asymptotics of the Solution of the Singularly Perturbed First Boundary Value Problem on the Semiaxis for a Parabolic Equation with a Rational “Simple” Turning Point

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 405
Author(s):  
Alexander Yeliseev ◽  
Tatiana Ratnikova ◽  
Daria Shaposhnikova
Keyword(s):  
Parabolic Equation ◽  
Maximum Principle ◽  
Boundary Value Problem ◽  
Regularization Method ◽  
Turning Point ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Asymptotic Convergence ◽  
The Maximum Principle ◽  
Regularized Asymptotics

The aim of this study is to develop a regularization method for boundary value problems for a parabolic equation. A singularly perturbed boundary value problem on the semiaxis is considered in the case of a “simple” rational turning point. To prove the asymptotic convergence of the series, the maximum principle is used.

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