SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

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.

scholarly journals Sensitivity analysis of the mathematical model of catalytic reforming of gasoline

2019 ◽  
Vol 3 (2) ◽  
pp. 43-53
Author(s):  
L. F. Safiullina ◽  
◽  
I. M. Gubaydullin ◽  
K. F. Koledina ◽  
R. Z. Zaynullin ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Catalytic Reforming ◽  
The Mathematical Model

scholarly journals SIMULATION AND SENSITIVITY ANALYSIS ON THE PARAMETER OF NON-TARGETED IRRADIATION EFFECTS MODEL

2018 ◽  
Vol 81 (1) ◽  
Author(s):  
Muhamad Hanis Nasir ◽  
Fuaada Mohd Siam
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Real Life ◽  
Double Strand Breaks ◽  
Signal Molecules ◽  
Danger Signal ◽  
Survival Fraction ◽  
Strand Breaks ◽  
Radiation Induced ◽  
The Mathematical Model

Real-life situations showed damage effects on non-targeted cells located in the vicinity of an irradiation region, due to danger signal molecules released by the targeted cells. This effect is widely known as radiation-induced bystander effects (RIBE). The purpose of this paper is to model the interaction of non-targeted cells towards bystander factors released by the irradiated cells by using a system of structured ordinary differential equations. The mathematical model and its simulations are presented in this paper. In the model, the cells are grouped based on the number of double-strand breaks (DSBs) and mis-repair DSBs because the DSBs are formed in non-targeted cells. After performing the model's simulations, the analysis continued with sensitivity analysis. Sensitivity analysis will determine which parameter in the model is the most sensitive to the survival fraction of non-targeted cells. The proposed mathematical model can explain the survival fraction of non-targeted cells affected by the bystander factors.

scholarly journals Eigenvalue Elasticity and Sensitivity Analyses of the Transmission Dynamic Model of Corruption

2019 ◽  
pp. 30-34
Author(s):  
Adeyemi Olukayode Binuyo
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Dynamic Model ◽  
Transmission Dynamics ◽  
Sensitivity Analyses ◽  
Contact Rate ◽  
Transmission Dynamic ◽  
Effective Contact ◽  
The Government ◽  
The Mathematical Model

In this paper, the eigenvalue elasticity and sensitivity values of the mathematical model of transmission dynamics of corruption were obtained and presented using the eigenvalue elasticity and sensitivity analysis methods. The parameter with the greatest impact on the mathematical model was determined using the methods. This parameter will assist the government on how to reduce and provide measures to eradicate corrupt practices among the populace. From the mathematical model of corruption presented, it was obtained that the effective contact rate of corruption has the highest value when using the eigenvalue elasticity and sensitivity analysis.

scholarly journals О постановках обратных задач

2020 ◽  
pp. 203-206
Author(s):  
Yurii Menshikov
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Approximate Solution ◽  
Inverse Problems ◽  
Solution Algorithms ◽  
The Mathematical Model

Some possible options for the formulation of inverse problems are considered. The ultimate research goals in these cases determine the algorithms for the approximate solution of the inverse problem and allow one to correctly interpret these solutions. Two main statements of inverse problems considered: inverse problems of synthesis and inverse problems of measurement. It is shown that in inverse synthesis problems one should not take into account the error of the mathematical model. In addition, it is possible in these cases to synthesize approximate solution algorithms that do not have a regularizing property. Examples of practical problems considered.

scholarly journals Drying kinetics of Chinese garlic (Allium tuberosum) and its effect on color

2020 ◽  
Vol 42 ◽  
pp. e8
Author(s):  
Paula De Almeida Rios ◽  
Ednilton Tavares De Andrade ◽  
Kátia Soares Moreira ◽  
Filipe Da Silva De Oliveira ◽  
Bárbara Lemes Outeiro Araújo
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Air Temperature ◽  
Linear Regression Analysis ◽  
Drying Kinetics ◽  
Allium Tuberosum ◽  
Thin Slices ◽  
The Mathematical Model ◽  
Quasi Newton ◽  
Kinetics Of

Dehydrated garlic is an important component both for culinary and medicinal purposes. However, there is a scarcity of studies that characterizes its drying kinetics. Thus, the objective of this work was to study the drying kinetics of Chinese garlic (Allium tuberosum), as well as to analyze the color effect resulting from each treatment. The garlic bulbs were cut into thin slices with a width of 2 and 3 mm, subjected to the drying air temperature of 35, 45, 55 and 70 °C in a mechanical dryer of a fixed layer with forced convection. Was performed a non-linear regression analysis by the Quasi-Newton method, for adjustment to 11 mathematical models to the experimental data of drying. The Midilli equation was the mathematical model that best characterized all the drying temperatures, for the experimental data. The diffusion coefficient presented values between 1.46 x 10-11 and 7.32 x 10-11 m2.s-1. The increase of the drying air temperature caused the dimming of the samples with a reduction of the L* coordinate and reduction of the yellow of the samples according to the coordinate results h*. The temperature of 70 °C was detrimental to the maintenance of the Chinese garlic coloration. 

scholarly journals МАТЕМАТИЧЕСКАЯ МОДЕЛЬ И МЕТОД РАСЧЕТА ДИНАМИКИ СУШКИ И ТЕРМОДЕСТРУКЦИИ БИОМАССЫ

2018 ◽  
Vol 82 (1) ◽  
Author(s):  
Наталья Николаевна Сороковая ◽  
Дмитрий Николаевич Коринчук
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Thermal Decomposition ◽  
Numerical Method ◽  
Heat And Mass Transfer ◽  
The Body ◽  
Physical Factors ◽  
Deformation Equation ◽  
The Mathematical Model ◽  
Kinetics Of

Разработана математическая модель и численный метод расчета динамики тепломассопереноса, фазовых превращений и усадки при сушке коллоидных капиллярно-пористых тел цилиндрической формы в условиях равномерного обдува теплоносителем. Математическая модель строилась на базе дифференциального уравнения переноса субстанции (энергии, массы, импульса) в деформируемых системах. Проведены экспериментальные исследования кинетики обезвоживания частиц энергетической вербы в потоке воздуха с целью верификации математической модели. Обоснована возможность ее использования для расчета совместных процессов сушки и начального этапа термического разложения биомассы. С использованием ранее полученных данных по значениям энергии активации Аэф(Т) для различных видов биомассы проведено математическое моделирование динамики и кинетики высокотемпературной сушки в потоке дымовых газов энергетической вербы, которая сопровождается термодеструкцией гемиоцеллюлозы. Результаты численных экспериментов свидетельствуют об адекватности предложенного подхода, эффективности математической модели и метода ее реализации. На их основе возможно проводить исследование динамики тепломассопереноса при сушке частиц различных видов измельченной биомассы; определение температуры начала и окончания первой стадии термического разложения; момента достижения равновесного влагосодержания в зависимости от свойств материала и сушильного агента. Эти данные позволяют выбирать оптимальные с точки зрения сохранения энергии и качества высушиваемого продукта  режимные параметры процесса.         A mathematical model and a numerical method for calculating the dynamics of heat and mass transfer, phase transformations and shrinkage during the drying of colloidal capillary-porous cylindrical bodies under conditions of equitable winding by a coolant are developed. The mathematical model was based on the differential equation of substance (energy, mass, impulse) transfer in deformable systems. It includes the equations diffusion-filtration transfer of energy for the system as a whole, and the mass transfer of the liquid, vapor and air phases in the pores of the body. Expressions for the intensity of evaporation of a liquid, capillary pressure, and the diffusion coefficients are presented. The relative volume strain was found by means of an analytical solution of the thermoconcentration deformation equation. Based on the explicit three-layer counting difference scheme and the procedure splitting of algorithm  by physical factors, a numerical method for realizing this mathematical model is developed.Experimental studies of the kinetics of dehydration of energy willow particles in the airflow were carried out to verify the mathematical model. Its applicability for calculating combined processes of drying and of the initial stage of thermal decomposition of biomass is substantiated. Using the previously obtained data on the activation energy values for various types of biomass, a mathematical simulation of the dynamics and kinetics of high-temperature drying in the flue gas flow of energy willow was carried out, which is accompanied by thermal destruction of hemiocellulose. The results of numerical experiments indicate the adequacy of the proposed approach, the effectiveness of the mathematical model and the method of its implementation. On their basis, it is possible to study the dynamics of heat and mass transfer when drying particles of different types of ground biomass; determination of the temperature of the beginning and ending of the first stage of thermal decomposition; the moment when the equilibrium moisture content is reached, depending on the properties of the material and the drying agent. These data allow choosing the process parameters that are optimal in terms of energy saving and quality of the dried product.

scholarly journals In vivo imaging of the kinetics of microglial self-renewal and maturation in the adult visual cortex

2020 ◽  
Author(s):  
Monique S. Mendes ◽  
Jason Atlas ◽  
Zachary Brehm ◽  
Antonio Ladron-de-Guevara ◽  
Matthew N. McCall ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Visual Cortex ◽  
Adult Brain ◽  
Self Renewal ◽  
Two Photon ◽  
And Migration ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
The Brain

AbstractMicroglia are the resident immune cells in the brain with the capacity to autonomously self-renew. Under basal conditions, microglial self-renewal appears to be slow and stochastic, although microglia have the ability to proliferate very rapidly following depletion or in response to injury. Because microglial self-renewal has largely been studied using static tools, the mechanisms and kinetics by which microglia renew and acquire mature characteristics in the adult brain are not well understood. Using chronic in vivo two-photon imaging in awake mice and PLX5622 (Colony stimulating factor 1 receptor (CSF1R) inhibitor) to deplete microglia, we set out to understand the dynamic self-organization and maturation of microglia following depletion in the visual cortex. We confirm that under basal conditions, cortical microglia show limited turnover and migration. Following depletion, however, microglial repopulation is remarkably rapid and is sustained by the dynamic division of the remaining microglia in a manner that is largely independent of signaling through the P2Y12 receptor. Mathematical modeling of microglial division demonstrates that the observed division rates can account for the rapid repopulation observed in vivo. Additionally, newly-born microglia resemble mature microglia, in terms of their morphology, dynamics and ability to respond to injury, within days of repopulation. Our work suggests that microglia rapidly self-renew locally, without the involvement of a special progenitor cell, and that newly born microglia do not recapitulate a slow developmental maturation but instead quickly take on mature roles in the nervous system.Graphical Abstract(a) Microglial dynamics during control condition. Cartoon depiction of the heterogenous microglia in the visual cortex equally spaced. (b) During the early stages of repopulation, microglia are irregularly spaced and sparse. (c) During the later stages of repopulation, the number of microglia and the spatial distribution return to baseline. (d-f) We then created and ran a mathematical model that sampled the number of microglia, (d) the persistent doublets, (e) the rapid divisions of microglia and (f) the secondary divisions of microglia during the peak of repopulation day 2-day 3. The mathematical model suggested that residual microglia can account for the rapid repopulation we observed in vivo.

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