Mathematical model of the process of homogenization of dairy products of high fat content on the basis of the Markov chain

Хвостов, А. А.; Битюков, В. К.; Хвостова, М. А.; Полищук, К. В.

doi:10.20914/2310-1202-2016-4-61-66

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…При этом вероятность перехода в новое состояние (молекулярно-массовое распределение (ММР) полимера) зависит только от состояния, из которого совершается переход и не зависит от всей предыстории процесса. Для описания такого рода процессов может использоваться математический аппарат теории цепей Маркова [2,3].…”

Section: Introductionunclassified

Matrix-graph model of the polymer materials destruction process

Хвостов

Тихомиров

Хаустов

et al. 2018

Vestn. Voronež. gos. univ. inž. tehnol.

Self Cite

View full text Add to dashboard Cite

The paper deals with the problem of mathematical modeling of the process of thermochemical destruction using the theory of graphs. To synthesize a mathematical model, the Markov chain is used. For the formalization of the model a matrix-graph method of coding is used. It is proposed to consider the process of destruction as a random process, under which the state of the system changes, characterized by the proportion of macromolecules in each fraction of the molecular mass distribution. The intensities of transitions from state to state characterize the corresponding rates of destruction processes for each fraction of the molecular weight distribution (MWD). The processes of crosslinking and polymerization in this work have been neglected, and it is accepted that there is a probability of transition from any state with a lower order index (corresponding to fractions with higher molecular weights) to any state with a higher index (corresponding fractions with lower molecular weights). A computational formula is presented for estimating the number of arcs and model parameters from a given number of fractions of the molecular weight distribution of the polymer. An example of coding in a matrix form of a graph model of the process of degradation of polybutadiene in solution for the case of six fractions of the molecular weight distribution is shown. As the simulation environment, the interactive graphical simulation environment of MathWorks Simulink is used. To evaluate the parameters of the mathematical model, experimental studies of the degradation of polybutadiene in solution were carried out. The chromatography of the polybutadiene solution was used as the initial data for the estimation of the MWD polymer. The considered matrix-graph representation of the structure of the mathematical model of the polymer destruction process makes it possible to simplify the compilation of the model and its software implementation in the case of a large number of vertices of the graph describing the process of destruction

show abstract

Section: Introductionunclassified