Extension of the analytical kinetics of micellar relaxation: improving a relation between the Becker-Doring difference equations and their Fokker-Planck approximation

Результат исследований: Научные публикации в периодических изданияхстатья

3 Цитирования (Scopus)

Выдержка

Relaxation of micellar systems can be described with the help of the Becker- D¨oring kinetic difference equations for aggregate concentrations. Passing in these equations to continual description, when the aggregation number is considered as continuous variable and the concentration difference is replaced by the concentration differential, allows one to find analytically the eigenvalues (to whom the inverse times of micellar relaxation are related) and eigenfunctions (or the modes of fast relaxation) of the linearized differential operator of the kinetic equation corresponding to the Fokker-Planck approximation. At this the spectrum of eigenvalues appears to be degenerated at some surfactant concentrations. However, as has been recently found by us, there is no such a degeneracy at numerical determination of the eigenvalues of the matrix of coefficients for the linearized difference Becker-D¨oring equations. It is shown in this work in the frameworks of the perturbation theory, that taking into account the co
Язык оригиналаанглийский
Страницы (с-по)551–562
ЖурналPhysica A: Statistical Mechanics and its Applications
Том479
DOI
СостояниеОпубликовано - 2017
Опубликовано для внешнего пользованияДа

Отпечаток

Fokker-Planck
difference equations
Difference equation
eigenvalues
Kinetics
Eigenvalue
kinetics
Approximation
approximation
differential operators
Continuous Variables
Kinetic Equation
Degeneracy
Perturbation Theory
Eigenfunctions
Differential operator
Aggregation
eigenvectors
perturbation theory
matrices

Цитировать

@article{0b79e40467684b5ea7a5b587484a2356,
title = "Extension of the analytical kinetics of micellar relaxation: improving a relation between the Becker-Doring difference equations and their Fokker-Planck approximation",
abstract = "Relaxation of micellar systems can be described with the help of the Becker- D¨oring kinetic difference equations for aggregate concentrations. Passing in these equations to continual description, when the aggregation number is considered as continuous variable and the concentration difference is replaced by the concentration differential, allows one to find analytically the eigenvalues (to whom the inverse times of micellar relaxation are related) and eigenfunctions (or the modes of fast relaxation) of the linearized differential operator of the kinetic equation corresponding to the Fokker-Planck approximation. At this the spectrum of eigenvalues appears to be degenerated at some surfactant concentrations. However, as has been recently found by us, there is no such a degeneracy at numerical determination of the eigenvalues of the matrix of coefficients for the linearized difference Becker-D¨oring equations. It is shown in this work in the frameworks of the perturbation theory, that taking into account the co",
keywords = "Micelles, Kinetic equation, Fast relaxation, Perturbation theory",
author = "Babintsev, {I. A.} and Adzhemyan, {L. Ts.} and Shchekin, {A. K.}",
year = "2017",
doi = "10.1016/j.physa.2017.03.028",
language = "English",
volume = "479",
pages = "551–562",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",

}

Extension of the analytical kinetics of micellar relaxation: improving a relation between the Becker-Doring difference equations and their Fokker-Planck approximation. / Babintsev, I. A.; Adzhemyan, L. Ts.; Shchekin, A. K.

В: Physica A: Statistical Mechanics and its Applications, Том 479, 2017, стр. 551–562.

Результат исследований: Научные публикации в периодических изданияхстатья

TY - JOUR

T1 - Extension of the analytical kinetics of micellar relaxation: improving a relation between the Becker-Doring difference equations and their Fokker-Planck approximation

AU - Babintsev, I. A.

AU - Adzhemyan, L. Ts.

AU - Shchekin, A. K.

PY - 2017

Y1 - 2017

N2 - Relaxation of micellar systems can be described with the help of the Becker- D¨oring kinetic difference equations for aggregate concentrations. Passing in these equations to continual description, when the aggregation number is considered as continuous variable and the concentration difference is replaced by the concentration differential, allows one to find analytically the eigenvalues (to whom the inverse times of micellar relaxation are related) and eigenfunctions (or the modes of fast relaxation) of the linearized differential operator of the kinetic equation corresponding to the Fokker-Planck approximation. At this the spectrum of eigenvalues appears to be degenerated at some surfactant concentrations. However, as has been recently found by us, there is no such a degeneracy at numerical determination of the eigenvalues of the matrix of coefficients for the linearized difference Becker-D¨oring equations. It is shown in this work in the frameworks of the perturbation theory, that taking into account the co

AB - Relaxation of micellar systems can be described with the help of the Becker- D¨oring kinetic difference equations for aggregate concentrations. Passing in these equations to continual description, when the aggregation number is considered as continuous variable and the concentration difference is replaced by the concentration differential, allows one to find analytically the eigenvalues (to whom the inverse times of micellar relaxation are related) and eigenfunctions (or the modes of fast relaxation) of the linearized differential operator of the kinetic equation corresponding to the Fokker-Planck approximation. At this the spectrum of eigenvalues appears to be degenerated at some surfactant concentrations. However, as has been recently found by us, there is no such a degeneracy at numerical determination of the eigenvalues of the matrix of coefficients for the linearized difference Becker-D¨oring equations. It is shown in this work in the frameworks of the perturbation theory, that taking into account the co

KW - Micelles

KW - Kinetic equation

KW - Fast relaxation

KW - Perturbation theory

U2 - 10.1016/j.physa.2017.03.028

DO - 10.1016/j.physa.2017.03.028

M3 - Article

VL - 479

SP - 551

EP - 562

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -