Mathematical modeling of water purification in a bioplato filter

2021 ◽  
pp. 56-57
Author(s):  
Ivanchuk Natalya ◽  
Sergiy Kunytskyi
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Water Purification ◽  
Dynamic Change ◽  
Filtration Coefficient ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Filter System ◽  
Physical Effects ◽  
Change Of Porosity

A mathematical model of filtration taking into account clogging and suffusion in the bioplato filter system in the two-dimensional case was built. The constructed mathematical model takes into account the physical effects of the dynamic change of porosity and the dependence of the filtration coefficient on the concentration of contaminants, which is not in the known analogues

scholarly journals MODELING OF WASTEWATER TREATMENT

2021 ◽  
Author(s):  
Yu.S. Chirikanova ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Wastewater Treatment ◽  
Activated Sludge ◽  
Water Purification ◽  
Software Package ◽  
Biological Treatment ◽  
Aeration Tank ◽  
Biological Wastewater Treatment ◽  
Biological Treatment System

The paper deals with the problem of mathematical modeling of biological wastewater treatment. The peculiarity of the biological treatment system is that a block with activated sludge, called an aeration tank, is used for water purification. To describe the process of biological wastewater treatment in aeration tanksa mathematical model developed in the GPS-X software package is proposed.

scholarly journals Mathematical modeling of a self-propelled scraper at the beginning of soil set

2021 ◽  
Vol 1 (92) ◽  
pp. 154
Author(s):  
Sergii Kovalevskyi
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Dynamic Change ◽  
Vertical Force ◽  
Horizontal Force ◽  
Small Influence ◽  
Rate Of Increase ◽  
Draw Conclusion ◽  
External Forces

The process of filling of scoop of dragshovel consists of a few operations which periodically repeat oneself in the working loop. Each of these stages is accompanied the different moving of dragshovel and his separate knots, conditioned actions of external forces, at cutting and load of soil in a scoop, that needs separate consideration of the tense state of dragshovel equipment in a few calculation positions. The analysis of the modes of ladening of metallokonstrukcii of dragshovel during implementation of basic operations of digging allows to define the rational modes of operations of machine. For the decision of the put tasks the calculation chart of self-propelled dragshovel was developed in the process of zaglubleniya of knife in soil, on the basis of which taking into account the grounded limitations and scope terms, a twomass mathematical model, having degrees of freedom in horizontal and vertical directions, is created. With the purpose of simplification of mathematical model the angular vibrations of tractor and dragshovel were not taken into account, in connection with their small influence on the operating loadings at zaglublenii of scoop. Realization of mathematical model allowed to get the charts of dynamic change of horizontal and vertical force, operating in the hinges of hauling frame. Swaying character of loadings rotined that maximal values were arrived at almost for the identical interval of time in the first semiperiod, and horizontal and vertical efforts increase with the increase of intensity of resistance digging. The results of researches rotined that forces operating in the front hinge of hauling frame grow with the increase of intensity of resistance digging, arriving at the maximal values of 195 and 78 kN. Horizontal efforts to a great extent exceed vertical and increased with growth of intensity of resistance digging. The rate of increase of maximums of horizontal force can be considered even, because at megascopic intensities from 150 to 250 kN/m, most values grow approximately on 32 %, that enables to draw conclusion about expedience of work with the less rates of movement of dragshovel, taking into account loading of metallokonstrukcii. The rate of growth of maximums of vertical force can be considered even, approximately on 7 %, with the increase of rate of climb of knife of dragshovel, that far fewer as compared to growth of efforts, operating in horizontal direction. Therefore diminishing of speed of zaglubleniya will not result in the substantial diminishing of loading on the hauling frame of dragshovel.

scholarly journals Specific features of mathematical modeling of flows with detonation waves on unstructured computational grids

2017 ◽  
pp. 348-358
Author(s):  
А.И. Лопато ◽  
П.С. Уткин
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Algorithm ◽  
Plane Channel ◽  
Second Order ◽  
Computational Grids ◽  
Detonation Waves ◽  
Two Dimensional ◽  
Cellular Detonation ◽  
Two Dimensional Flows

Представлены математическая модель и вычислительный алгоритм для математического моделирования двумерных течений с волнами детонации на полностью неструктурированных расчетных сетках с треугольными ячейками. Рассмотрена задача о формировании ячеистой детонации в плоском канале для случая устойчивой детонации при различном сеточном разрешении и с использованием схем первого и второго порядков аппроксимации. A mathematical model and a numerical algorithm for the mathematical modeling of two-dimensional flows with detonation waves on fully unstructured computational grids with triangular cells are proposed. The problem concerning the formation of cellular detonation in a plane channel in the case of stable detonation for different grid resolutions and with the use of first and second order schemes is considered.

Two Dimensional Unsteady State Mathematical Model for dispersion of Chlorine in Water in a Channel

2011 ◽  
Vol 3 (8) ◽  
pp. 503-505
Author(s):  
Jaipal Jaipal ◽  
◽  
Rakesh Chandra Bhadula ◽  
V. N Kala V. N Kala
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Unsteady State

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

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