**Mathematical modeling of the processes of dynamic discharge visualization liquid-phase objects**

Krizhanovsky E., Korotkina S.

KTI Association

The problem of revealing the peculiarities of physical and chemical properties of liquids, the analysis of their stability, dynamics, ability to self-organizing and the fore-cast of behavior in open systems at various external influences is actual for medicine, physics, chemistry, biology and cosmetology.

Many of the known traditional physical and chemical methods of the analysis hav-ing high accuracy for definition of physical and chemical properties of water systems, have own limitations at research of liquids with close chemical compound or physical characteristics.

Thus, gas chromatography, having high accuracy in definition of a chemical com-pound of researched substance is not capable to reveal distinctions at such liquids, as natural oils and their synthetic counterparts, and also high dilution of water and alcohol solutions. Moreover, many physical and chemical methods demand the big operational and time expenses.

The results of last years researches have shown, that the method of dynamic gas discharge visualization (GDV) is capable to reveal weak changes of physical and chem-ical properties in liquid-phase objects. This method is also appeared as not labour-consuming method [1].

The essence of dynamic GDV-graphy method is in study of time series of charac-teristics of the gas discharge, induced from the object, placed in strong electromagnetic field (EMF) during exposure time. Thus characteristics of the gas discharge are reflects both internal properties of researched objects, and properties of an environment and an EMF.

For practical application of GDV-graphy method the numerical characteristics of the GDV image (GDV-gram) and the mathematical models describing the processes of dynamic GDV of objects have been developed.

On the basis of the advanced mathematical models and methods the techniques and algorithms for the automatized system of registration and the analysis of dynamics of the gas discharge around liquid-phase objects was developed.

Mathematical models can be divided into three classes:

1. Mathematical models of the statistical analysis of time series of characteristics of GDV-gram.

2. Mathematical models of the analysis of fractal dimensions and cumulative entropy of time series of characteristics of GDV-gram.

3. Mathematical models of the physical processes expressed by the features of time series of characteristics of GDV-grams.

For automatized system the algorithms of analysis of characteristics of GDV-gram by the methods of the spectral analysis and the analysis singular spectra (the modified analysis of principal component) have been developed. For definition of fractal dimen-sion of time series Higuchi algorithm have been used.

Essentially new mathematical model was developed based on presentation of gas discharge as a fractal cluster. It has allowed describing physical meaning of directions of the trends of time series of GDV-gram characteristics due to transition from physics of cluster to kinetic of ionization.

An expression for an electromagnetic field of fractal cluster has been deduced

, (1)

where q – propagation vector; i – frequency of ionization, frequency of diffusion losses , D-coefficient of diffusion, w – frequency of electromagnetic wave.

Thus, it is shown, that EMF of radiating cluster is a function from frequencies of ionization and diffusion losses, and also fractal dimension of cluster.

Whence follows, that at trends in expression (1) will increasing, at trends will decreasing, and in a case trends will have periodic, quasistationary type.

As follows from (1), the changing of fractal dimension of a gas discharge glow can change a direction of a trend.

Expression (1) for EMF near to a drop of a liquid has shown high reliability at the analysis of experimental data as time series of GDV parameters of images in view of known physical properties of investigated liquids.

On the basis of the conducted work the following results have been achieved.

• The mathematical models are developed, allowing to predict the behavior of liquids of the certain class under influence of a strong EMF.

• Techniques and algorithms for the automatized system of registration and the analysis of dynamics of the gas discharge glow around liquid-phase objects was devel-oped on the basis of the advanced mathematical models and methods.

• The opportunity of application of a method of dynamic GDV for revealing dis-tinctions of natural and synthetic oils with an identical chemical compound was proved.

Reference

1. K. Korotkov, E. Krizhanovsky, M. Borisova, D. Korotkin et.al. Time dynamics of the gas discharge around drops of liquids, J.Appl.Phys., 95, 3334-3338, (2004)

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