scholarly journals FORECASTING THE GROUNDWATER TREATMENT PROCESS IN A BIOREACTOR USING FERROBACTERIA

2021 ◽  
pp. 22-28
Author(s):  
Oleksandr Kvartenko ◽  
Igor Prysiazhniuk
Keyword(s):  
Mathematical Model ◽  
Cauchy Problem ◽  
Mathematical Models ◽  
New Technologies ◽  
Pore Space ◽  
Multicomponent System ◽  
Operation Time ◽  
Groundwater Treatment ◽  
The Cauchy Problem ◽  
Kinetics Of

The monitoring of water quality parameters in 90 settlements of eight regions of Ukraine made it possible to state that groundwater is a complex multicomponent system. Existing deironing stations using simplified aeration-filtration technology are not able to remove Fe (II) compounds from water in the presence of humic complexes. Therefore, in modern conditions, the urgent task is to intensify their work through the introduction of new technologies, including biotechnology with the development of appropriate mathematical models. It is shown that much less attention was paid to modeling the kinetics of groundwater treatment processes in bioreactors than to traditional physicochemical methods, for which modern mathematical models were developed. The aim of the work is to develop a mathematical model of the kinetics of the process of groundwater treatment in bioreactors. The mathematical model is represented by the Cauchy problem for a nonlinear system of differential equations in partial derivatives of the first order. The system of the Cauchy problem consists of five equations with five unknown functions, which describe the distribution the concentration of ferrum cations, bacteria and the matrix structures in two phases (movable and immobilized) both in space and time. The inverse influence of the characteristics of the process, in particular, the concentration of matrix structures in the inter-pore space, as well as characteristics of the medium with the help of coefficients of mass exchange and porosity, were taken into account. The model allows determining the optimum operation time of a bioreactor between washings

scholarly journals Mathematical Modeling of the Contact Interaction of Plate and Beam in Color Noise Field

2019 ◽  
Author(s):  
Татьяна Яковлева ◽  
Tat'yana Yakovleva ◽  
Валентин Баженов ◽  
Valentin Bazhenov ◽  
Вадим Крысько ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cauchy Problem ◽  
Contact Interaction ◽  
Three Dimensional ◽  
Physical Nonlinearity ◽  
Transverse Load ◽  
Time Step ◽  
Color Noise ◽  
Material Contact ◽  
The Cauchy Problem

A mathematical model and data visualization of contact interaction between a plate and a beam under the action of external transverse load and external additive color noise is constructed. The construction is in a stationary temperature field, the effect of which is taken into account according to the theory of Duhamel Neumann by solving the three-dimensional and two-dimensional heat conduction equations by the finite difference method, the heat exchange between the plate and the beam is not taken into account. The plate is subject to the Kirchhoff model, and the beam to the Euler- Bernoulli model. The mathematical model takes into account the physical nonlinearity of the elastically deformable material. Contact interaction is taken into account according to the theory of Kantor. The system of differential equations is reduced to the Cauchy problem by the Bubnov-Galerkin method in higher approximations in spatial variables. The Cauchy problem is solved by the Runge-Kutta method of the fourth order of accuracy. To solve the physically nonlinear problem, at each time step, an Birger iterative procedure was applied. The visualization of the results of a numerical experiment was carried out using the methods of nonlinear dynamics and using wavelet analysis. The numerical results of the effect of color noise on the contact interaction between the plate and the beam are given. It has been established that red additive noise has a more significant effect on the oscillation pattern of the lamellar-beam structure in comparison with pink and white noise.

scholarly journals Mathematical modeling of cancer treatment

2020 ◽  
Vol 16 (4) ◽  
pp. 437-446
Author(s):  
Anastaciya B. Goncharova ◽  
◽  
Eugeny P. Kolpak ◽  
Madina M. Rasulova ◽  
Alina V. Abramova ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Cauchy Problem ◽  
Tumor Cells ◽  
Ovarian Neoplasms ◽  
Interference Competition ◽  
Functional Space ◽  
Survival Times ◽  
The Cauchy Problem ◽  
Mathematical Interpretation

The paper proposes mathematical models of ovarian neoplasms. The models are based on a mathematical model of interference competition. Two types of cells are involved in the competition for functional space: normal and tumor cells. The mathematical interpretation of the models is the Cauchy problem for a system of ordinary differential equations. The dynamics of tumor growth is determined on the basis of the model. A model for the distribution of conditional patients according to four stages of the disease, a model for assessing survival times for groups of conditional patients, and a chemotherapy model are also proposed.

scholarly journals Modeling of constrained motion

2021 ◽  
Vol 62 ◽  
pp. 43-49
Author(s):  
Vytautas Kleiza ◽  
Rima Šatinskaitė
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Mathematical Models ◽  
Kutta Method ◽  
Constrained Motion ◽  
Holonomic Constraints ◽  
Second Order Differential Equations ◽  
Runge Kutta Method ◽  
The Cauchy Problem ◽  
2D And 3D

This paper presents an investigation of modeling and solving of differential equations in the study of mechanical systems with holonomic constraints. The 2D and 3D mathematical models of constrained motion are made. The structure of the models consists of nonlinear first or second order differential equations. Cases of free movement and movement with resistance are investigated. Solutions of the Cauchy problem of obtained differential equations were obtained by Runge–Kutta method.

scholarly journals ON A GENERALIZED MATHEMATICAL MODEL OF MALTHUS

2019 ◽  
pp. 38-46
Author(s):  
Ф.М. Лосанова ◽  
Р.О. Кенетова
Keyword(s):  
Mathematical Model ◽  
Cauchy Problem ◽  
The Cauchy Problem

В работе рассмотрено обобщенное уравнение Мальтуса, описывающее одновидную по пуляцию. Решена задача Коши для случаев 0 1 и 1 2. The paper considers the generalized Malthus equation describing a singlespecies population. Solved the Cauchy problem for cases 0 1 and 1 2.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

A mathematical model and an algorithm for sampling sets of components on the Assembly enterprises of space technology

2018 ◽  
Vol 15 (1) ◽  
pp. 39-55
Author(s):  
V. B. Rudakov ◽  
V. M. Makarov ◽  
M. I. Makarov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Space Technology ◽  
Economic Costs ◽  
Problem Statement ◽  
Optimal Plan ◽  
Product Mix ◽  
Technical Parameters ◽  
Complex Products ◽  
Assembly Plants

The article considers the problem of determining the rational plans of the input sampling reliability and technical parameters of components of space technology, the totality of which is supplied to the Assembly plants for the manufacture of complex products of space technology. Problem statement and mathematical model based on the minimization of the economic costs of control and losses related to the risks of taking wrong decisions, are given in the article. The properties of the mathematical models are investigated, the algorithm for its optimization is developed. The result is an optimal plan for the sampling of sets of components, which includes: an optimal product mix subject to mandatory control of the aggregate and optimum risks of first and second kind, when acceptance number of statistical plan is zero. The latter circumstance is due to the high requirements of reliability and technical parameters of products of space technology.

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