Development and automation of algorithm for determining basis of nonlinear parameter functions of kinetic constants

2019 ◽  
Vol 19 (4) ◽  
pp. 252-257
Author(s):  
A. S. Ismagilova ◽  
Z. A. Khamidullina ◽  
S. I. Spivak
Keyword(s):  
Mathematical Model ◽  
Kinetic Parameters ◽  
Platinum Catalyst ◽  
Hydrogen Oxidation ◽  
Nonlinear Parameter ◽  
Kinetic Constants ◽  
Model Parameters ◽  
Functional Relations ◽  
The Mathematical Model ◽  
Theoretical Issues

Mathematical modeling of catalytic processes is necessary for the complete and accurate description, as well as for controlling the quality and physicochemical studied of catalysts. In the paper, theoretical issues of industrial catalysis are discussed. The work is devoted to theoretical graph analysis of informativity of kinetic parameters of the model of a complex chemical reaction. The aim is the development and automation of algorithm for determining basis of nonlinear parameter functions in solving inverse problems of chemical kinetics in order to define the number and form of independent combinations of rate constants of elementary stages. A program package for analysis of informativity of kinetic parameters of the mathematical model of a complex catalytic reaction is developed and described. The obtained functional relations between the kinetic parameters can be useful for experimentalists in physicochemical interpretation and analysis of mechanisms of chemical reactions. In other words, the proposed method allows independent combinations of kinetic constants to be distinguished that results in shortening the number of the model parameters and, as a consequence, enhance the accuracy of the mathematical model. The mechanism of hydrogen oxidation over a platinum catalyst is given as an example of the use of the software.

Combustion in Ni–Al system with Cu additive (powder or rod) Experiment and mathematical model

2020 ◽  
pp. 33-43
Author(s):  
O. V. Lapshin ◽  
A. M. Shul’pekov ◽  
R. M. Gabbasov ◽  
V. D. Kitler
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Relative Density ◽  
Aluminum Matrix ◽  
Kinetic Constants ◽  
Model Parameters ◽  
Nickel Aluminum ◽  
Copper Melt ◽  
Analytical Formulas ◽  
The Mathematical Model

Experimental studies were carried out with theoretical calculations of wave synthesis in the Ni–Al–Cu system were performed using the mathematical model developed. Approximate analytical formulas were obtained for synthesis performance evaluation. The inverse problem method was used to get kinetic constants that determine process dynamics based on the experimental data and analytical relationships. It is shown that the combustion front propagation velocity increases monotonically with an increase in the reaction sample relative density in the range of relative density values of 0.4 to 0.6. The depth of copper melt penetration from the center of the sample into the nickel-aluminum matrix depends on the relative density of the sample and copper wire diameter: higher densities and larger diameters lead to an increase in the liquid-phase impregnation area. The rate of nickel and aluminum powder frame wetting with copper melt is limited by the synthesis wave speed. Based on the experimental data and analytical ratios, we estimated the effective kinetic constants describing the high-temperature synthesis of the Ni + Al reaction mixture in the presence of copper additives. The thermal effect of the NiAl intermetallic formation reaction and the preexponential factor in the chemical transformation equation are calculated, the exponent value in the ratio for the mixture thermal conductivity is established; a constant determining the process of nickel-aluminum matrix impregnation with copper melt is found. The macroscopic approach used to analyze the NiAl intermetallic synthesis makes it possible to determine all the desired physicochemical characteristics and model parameters. The mathematical model is suitable for predictive estimates and experimental data analysis in the macroscopic approximation. Approximate analytical formulas are obtained for calculating the NiAl intermetallic synthesis characteristics. They allow for calculating the through channel characteristics and can be used in the design of NiAl products.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

scholarly journals A mathematical model of common-cold epidemics on Tristan da Cunha

1971 ◽  
Vol 69 (3) ◽  
pp. 423-433 ◽  
Author(s):  
B. J. Hammond ◽  
D. A. J. Tyrrell
Keyword(s):  
Mathematical Model ◽  
Common Cold ◽  
Average Duration ◽  
Model Parameters ◽  
Epidemic Threshold ◽  
Tristan Da Cunha ◽  
Simulation Techniques ◽  
Time Courses ◽  
The Mathematical Model ◽  
Computer Simulation Techniques

SUMMARYRecords of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

scholarly journals The generation of a mathematical model of the biogas production process from organic municipal solid waste

2020 ◽  
Vol 180 ◽  
pp. 02019 ◽  
Author(s):  
Marzhan Temirbekova ◽  
Madina Aliyarova ◽  
Iliya Iliev ◽  
Aliya Yelemanova ◽  
Saule Sagintayeva
Keyword(s):  
Mathematical Model ◽  
Municipal Solid Waste ◽  
Solid Waste ◽  
Anaerobic Fermentation ◽  
Biogas Production ◽  
Biogas Plant ◽  
Model Parameters ◽  
Biochemical Processes ◽  
Biogas Plants ◽  
The Mathematical Model

This paper justifies the efficiency of the biogas collection and utilization at the MSW (municipal solid waste) landfill in Almaty with the installation of several modern biogas plants. The optimal mode of processes occurring in a biogas plant is determined by computer generated simulations. Mathematical model parameters were identified to describe biochemical processes occurring in a biogas plant. Two approaches are used to resolve the mathematical model: the finite-difference method for solving the system of differential equations and simulation modeling by using the Any Logic package. A program is written in the algorithmic language C ++. Numerous calculations were carried out, the results of which are presented in curves and their qualitative picture is consistent with the ongoing processes. The created computer program allows to make a preliminary forecast of anaerobic fermentation occurring in the bioreactor depending on volume of the substrate, methane microorganisms and temperature conditions.

Study on the Dynamic Models of Systems Biology from the View of Engineering

2012 ◽  
Vol 220-223 ◽  
pp. 952-957
Author(s):  
Chen Liu ◽  
Xiao Yan Liu
Keyword(s):  
Mathematical Model ◽  
Systems Biology ◽  
Dynamic Process ◽  
Biological System ◽  
Dynamic Models ◽  
Model Parameters ◽  
State Variables ◽  
Biochemical Pathway ◽  
The Right ◽  
The Mathematical Model

From the view of engineering, based on expatiating the features of systems biology, the paper discusses the workflows and the research emphasis of systems biology. It also explains how to model and analyze the dynamic process of signal transmitting network for a biological system by an example. Based on the complexity and uncertainty of the mathematical model, the right methods are chosen to realize the effective estimation of state variables and model parameters for the biochemical pathway.

Drying of solids; estimation of the mathematical model parameters

2010 ◽  
pp. n/a-n/a ◽  
Author(s):  
Aleksandra Sander ◽  
Jasna Prlić Kardum ◽  
Antun Glasnović
Keyword(s):  
Mathematical Model ◽  
Model Parameters ◽  
The Mathematical Model

Research on the Simulation of the Charge Mathematical Model of the Vehicle Starting Battery

2013 ◽  
Vol 680 ◽  
pp. 479-483
Author(s):  
Pei Ying Li ◽  
Yu Tian Pan
Keyword(s):  
Mathematical Model ◽  
Battery Life ◽  
Model Parameters ◽  
Analysis Method ◽  
Lead Acid Battery ◽  
Battery Charge ◽  
Charge Model ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Lead Acid

In order to meet the demands of practical, convenient and quick charge requirements, a mathematical model of a certain type of vehicle starting lead-acid battery is established. Using the method of circuit analysis, the model parameters are identified by the known test data. In addition, battery charge model is simulated in each charge stage using the intelligent three-stage charge method, simulation waveform and test waveform fit very well, absolute errors between them reach to 10-6. Simulation results show that the mathematical model and its analysis method is proper for the charge characteristics of vehicle starting lead-acid battery. This has a good guidance to design intelligent charger and extend the battery life.

scholarly journals Experimental studies of iron transformations kinetics and autocatalysis during its physicochemical removal from underground water

2021 ◽  
Author(s):  
S. Yu Martynov ◽  
V. L. Poliakov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Experimental Studies ◽  
Underground Water ◽  
Model Parameters ◽  
Kinetic Coefficients ◽  
Transfer Equations ◽  
The Mathematical Model ◽  
Autocatalytic Effect ◽  
Forms Of Iron

Abstract The mathematical model of physicochemical iron removal from groundwater was developed. It consists of three interrelated compartments. The results of the experimental research provide information in support of the first two compartments of the mathematical model. The dependencies for the concentrations of the adsorbed ferrous iron and deposited hydroxide concentrations are obtained as a result of the exact solution of the system of the mass transfer equations for two forms of iron in relation to the inlet surface of the bed. An analysis of the experimental data of the dynamics of the deposit accumulation in a small bed sample was made, using a special application that allowed to select the values of the kinetic coefficients and other model parameters based on these dependencies. We evaluated the autocatalytic effect on the dynamics of iron ferrous and ferric forms. The verification of the mathematical model was carried out involving the experimental data obtained under laboratory and industrial conditions.

scholarly journals Uptake of cadmium by Pseudokirchneriella supcapitata

2005 ◽  
Vol 48 (6) ◽  
pp. 1027-1034 ◽  
Author(s):  
Magela Paula Casiraghi ◽  
Samuel Luporini ◽  
Eduardo Mendes da Silva
Keyword(s):  
Mathematical Model ◽  
Metal Ions ◽  
Simulation Model ◽  
Kinetic Parameters ◽  
Cellular Membrane ◽  
Surface Absorption ◽  
Fast Absorption ◽  
Passive Adsorption ◽  
Two Stages ◽  
The Mathematical Model

In this work the microalgae Pseudokirchneriella supcapitata was used for the removal of the cadmium in liquids. The accumulations of metal ions by the alga occur in two stages: a very fast absorption (passive adsorption) proceeded by a slower absorption (activate absorption). A mathematical model based on the surface absorption and on the transport into the interior of the cellular membrane was developed. The simulation model kinetic parameters were experimentally obtained. Through the results observed, the mathematical model was shown to be suitable when compared to the experimental results, confirming the validation of the mathematical model.

scholarly journals Discovery of the spatial pattern of prickles on the stem of the rose and the mathematical model of the pattern

2019 ◽  
Author(s):  
Kazuaki Amikura ◽  
Hiroshi Ito
Keyword(s):  
Mathematical Model ◽  
Spatial Pattern ◽  
Plant Species ◽  
Statistical Data ◽  
Model Parameters ◽  
Developmental Patterns ◽  
The Mathematical Model ◽  
The Rose

Reproducible pattern is a key characteristic of organisms. Many developmental patterns are known that it is orchestrated by diffusion of the factors. Herein, we reported a novel patterning that seems to be controlled by diffusion factors. Although it looks like the prickles randomly emerge on the stem of rose, we deciphered patterns for the position of prickles with statistical data and proposed a mathematical model to explain the process via which the pattern emerged. By changing the model parameters, we reproduce another pattern on other plant species. This finding indicates that the patterns between many species are organized by similar systems. Moreover, although the pattern of organisms is often linked to its function, we consider the spatial pattern of prickles may have a function to play the role of prickles effectively. Further studies will clarify the role of prickles and reveal the entity of diffusive factors.

Sign in / Sign up

Export Citation Format

Share Document