A New Theoretical Approach to the Description of Physico-Chemical Reaction Dynamics With Chaotic Behavior

Gontar, V.

doi:10.1142/9789814354745_0008

Cited by 11 publications

(15 citation statements)

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“…Classic methods elaborated by Flory for linear macromolecules [6] are not applicable, in most cases, to branched, especially crosslinked structures [7]. Moreover, if systems of branched crosslinked polymers are in non-equilibrium, their description is impossible without combination of special statistical methods [8,9] and non-linear dynamics of chaos [10].…”

Section: Statistical Polymer Method Main Notions Definitions and Eqmentioning

confidence: 99%

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Simulation of Hardening Processes, in Silicate Systems

Kudryavtsev

Figovsky²

2015

ILCPA

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In this paper we consider the Quasi-homogeneous Approximation to Describe the Properties of Disperse Systems. We have used the statistical polymer method is based on the consideration of averaged structures of all possible macromolecules of the same weight. One has derived equations allowing evaluation of all additive parameters of macromolecules and their systems. The statistical polymer method allows modeling of branched crosslinked macromolecules and their systems in equilibrium or non-equilibrium. The fractal consideration of statistical polymer allows modeling of all kinds of random fractal and other objects studied by fractal theory. The statistical polymer method is applicable not only to polymers but also to composites, gels, associates in polar liquids and other aggregates. In this paper Description of the state of colloidal solutions of silicon oxide from the viewpoint of statistical physics is based on the idea lies in the fact that a colloidal solution of silicasilica sol consists of a very large number of interacting with each other particles that are in continuous motion. It is devoted to the study of an idealized system of colliding, but non-interacting particles of sol. Analysis was conducted of the behavior of silica sol, in terms of Maxwell-Boltzmann distribution and was calculated the mean free path of the colloidal particles. Based on these data, it was calculated the number of particles capable to overcome the potential barrier in a collision. To modeling of the solgel transition kinetics had considered various approaches.

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Section: Statistical Polymer Method Main Notions Definitions and Eqmentioning

confidence: 99%

“…Description of non-linear situations can be carried out in the same style, using methods of dynamic of chaos [10].…”

Section: Thermodynamic Functions Of Non-crosslinked Statistical Polimmentioning

confidence: 99%

Simulation of Hardening Processes, in Silicate Systems

Kudryavtsev

Figovsky²

2015

ILCPA

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“…Description of non-linear situations can be carried out in the same style, using methods of dynamic of chaos [5].…”

Section: Statistical Polymer Methods 205mentioning

confidence: 99%

“…Classic methods elaborated by Flory for linear macromolecules [1] are not applicable, in most cases, to branched, especially crosslinked structures [2]. Moreover, if systems of branched crosslinked polymers are in non-equilibrium, their description is impossible without combination of special statistical methods [3,4] and non-linear dynamics of chaos [5].…”

Section: Introductionmentioning

confidence: 99%

Statistical polymer method: Modeling of macromolecules and aggregates with branching and crosslinking, formed in random processes

Romm

Figovsky²

1998

Discrete Dynamics in Nature and Society

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The statistical polymer method is based on the consideration of averaged structures of all possible macromolecules of the same weight. One has derived equations allowing evaluation of all additive parameters of macromolecules and their systems. The statistical polymer method allows modeling of branched crosslinked macromolecules and their systems in equilibrium or non-equilibrium. The fractal consideration of statistical polymer allows modeling of all kinds of random fractal and other objects studied by fractal theory. The statistical polymer method is applicable not only to polymers but also to composites, gels, associates in polar liquids and other aggregates.

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“…Furthermore will be shown the feasibility of these models for mathematical description of pulse propagation in cardio-vascular system, that may be considered as complex self-organization process determined by interaction of blood flow dynamics with input impedance of arteries and vessels (see (Westerhof, 1995)). On the other hand, at recent years the new discrete dynamics of complex and living systems are developing (Gontar and Ilin, 1991; Gontar, 1993;Gontar, 1997). From our point of view, it is possible to implement the common background that is based on applications of the continual conservation laws and discrete methods for investigation of selforganization in active media.…”

Section: Introduction: Nonlinear Diffusion-reaction Systems and Self-mentioning

confidence: 99%

A structural approach to control of transitional waves of nonlinear diffusion‐reaction systems: Theory and possible applications to bio‐medicine

Kardashov

Einav

2001

Discrete Dynamics in Nature and Society

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This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions)

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A New Theoretical Approach to the Description of Physico-Chemical Reaction Dynamics With Chaotic Behavior

Cited by 11 publications

References 0 publications

Simulation of Hardening Processes, in Silicate Systems

Simulation of Hardening Processes, in Silicate Systems

Statistical polymer method: Modeling of macromolecules and aggregates with branching and crosslinking, formed in random processes

A structural approach to control of transitional waves of nonlinear diffusion‐reaction systems: Theory and possible applications to bio‐medicine

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