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y^K 52-337
FRACTAL STRUCTURE GENESIS OF ELECTRON-OPTICAL MOIRE
ON SMALL EXTENSION MAGNETIC DISPERSION FIELDS
V.M. Ivanov1, A.V. Lanovaya2, E.A. Pechagin1,
E.B. Vinokurov1, A.A. Lozenkov1
Department «Electrical Equipment and Automation», (1),
«HigherMathematics» »2), TSTU
Represented by a Member of the Editorial Board Professor V.F. Kalinin
Key words and phrases: electromagnetic field; field distortion by defects; moire.
Abstract: Information criteria for small volume non-uniform magnetic field evaluation as the factor of moire pattern and fractal dimension asymmetry were suggested. Dependence of these criteria on crack edge length in flat current conductor was found. It was shown that alteration of moire pattern asymmetry round hole-type distortions and edge cracks are similar to known electromagnetic energy distribution in these regions. This fact can serve as grade dimension of energy concentration round non-conducting distortions.
Fractal theory is very often applied in cases when we need to describe different objects, structures and phenomena characterized with self-similarity. According to Benua Mandelbrot assumption, integrity development cycles of hierarchically organized structures are fractal and concerned with self-organization processes. Different fractal types have one feature in common - the existence of recessive generation procedure based on self-completion or self-organization mechanisms. This process is accompanied with the appearance of a host of similar structures and pictures based on one and the same physical phenomenon.
On one hand physical affects connected with field asymmetry are fractal but violation of symmetry with preserved periodicity leads to alteration of fractal dimension. On the other hand fractal presentation of physical phenomenon by computer visualization enables to identify and recognize different mathematic and natural forms, ex. One can carry the direct observation of local magnetic field alternations round energized conductor imperfections (natural form) together with analytic description of electromagnetic energy concentration on imperfections of these conductors (mathematical form). Here fractal serves as an instrument of quantity invariant search and interpretation which are connected with magnetic measurement tasks.
The investigation of magnetic field through changing topology of electron-optical moire patterns resulted in finding out some regularities connected with distortions and richness of moire pattern, field location and intensity which appear on conductors with various imperfection geometry [1].
The fact that moire pattern is connected with moire fringe periodicity alternation and is determined by the extent of fringe richness in a moire pattern, enables us to judge upon electron-optical moire pattern fractal structure genesis on a magnetic field of conductors with structure imperfections. This kind of development was to a first approximation detected experimentally by counting sets of black and white pixels after moire pattern filtration in the information-measuring system [2]. In this case two
variable quantities were analyzed - fractal dimension df and geometric imperfection parameters. It is obviously easy to connect df with magnetic field value generated by imperfection in an energized conductor.
One should take into account the interdependence of imperfection parameters and field intensity, which in its turn is found on electron-optical moire pattern with the help of the following technique.
1. Moire patterns are filtrated in order to find sets of black and white pixels R.
2. Alternating flat set M(R) is detected topographically and corresponds to the number of black pixels after filtration.
3. Fractal dimension df is found through the correlation
d s
M(R) = R f.
4. The degree of magnetic field distortion is evaluated through df alteration.
Investigating moire fractal one can find self-similarity of its structure on various
steps of moire structure genesis. The uniform algorithm of moire periodicity realization is observed on different levels of moire generating. Undoubtedly this is the effect of a local magnetic field which unites pattern elementary formations varying their spacing and leaving the structure unchanged. That is why the development of electron-optical moire is connected with equal fragment alternating structure formation where dark and light bands are interchanging and due to the field under investigation can be either symmetric or asymmetric. As it was pointed out the last can characterize the field distortion degree revealing the existence of various conductor structure imperfections.
In other words one can not take away from the general moire pattern one of its fragment repeating self-similar structure without destroying the pattern integrity.
Thus fractal structure genesis of electron-optical moire pattern on small volume dispersion magnetic fields depends on object geometry, location dimensions of witness net and accelerating potential of an electron gun. The pattern distortion degree can be determined by alteration of fractal dimension df, which in its turn is the assessment criterion of the field distortion degree on conductor imperfections.
This can be exemplified by experimental data obtained through investigation of dispersion field distortions of multi-channel magnetic heads. The investigation was carried out in order to detect rejects. The latter was assessed by alteration of fractal dimension of perfect and rejected items by the suggested technique (Fig. 1).
b)
Fig. 1. Electron-optical moire pattern of magnetic head dispersion field:
a - perfect; b - rejected
Fig. 2. Dependence of fractal dimension on magnetic field distortion degree
It turned out that there exists specific df (Fig. 2) which can serve as original rejecting criterion in information-measuring system for magnetic head quality control [3]. This dramatically simplifies measuring system algorithm and structure as well as increases magnetic head quality control precision and speed.
Thus peculiar characteristic of small volume magnetic field moire pattern lies in the fact that one can define the limits of its divisibility and growth, i.e. it is not infinite like many other physical phenomena in nature. Fractal structure genesis is based on recursion that is topology of fractal pattern is generated by recursion algorithm. At the same time fractal dimensions appear to be the obvious measure of magnetic field distortion of energized objects.
References
1. Иванов, В.М. Исследование концентрации энергии в области непроводящих включений плоского проводника с током средствами электронной микроскопии / В.М. Иванов, Е.А. Печагин, А.Н. Уваров // Электрика. - 2003. - № 7. -С. 34-37.
2. Фильтрация изображений муаровых картин, полученных на основе электронно-оптических эффектов / В.М. Иванов [и др.] // Повышение эффективности средств обработки информации на базе математического моделирования : материалы докл. VII Всерос. науч.-техн. конф. - Тамбов, 2004. - Ч. 1. - С. 46-51.
3. Критерии разбраковки измерительно-вычислительной системы контроля качества магнитных систем / В.Ф. Калинин [и др.] // Вестник Тамб. гос. техн. унта. - 2004. - Т. 10, № 4А. - С. 961-67.
Фрактальный структурогенез электронно-оптического муара на магнитных полях рассеяния малой протяженности
В.М. Иванов1, А.В. Лановая2, Е.А. Печагин1, Е.Б. Винокуров1, А.А. Лозенков1
Кафедры: Электрооборудование и автоматизация» (1),
«Высшая математика» (2), ГОУ ВПО «ТГТУ»
Ключевые слова и фразы: искажение полей дефектами; муар; электромагнитное поле.
Аннотация: Предложены информационные критерии оценки неоднородных магнитных полей в малых объемах в виде коэффициента асимметрии муарового узора и фрактальной размерности. Найдены зависимости этих критериев от
длины краевой трещины в плоском проводнике с током. Показано, что изменение коэффициента асимметрии муарового узора вокруг дефектов типа отверстия и краевой трещины аналогично известному распределению электромагнитной энергии в этих областях, что может служить мерой оценки концентрации этой энергии вокруг непроводящих дефектов.
Fraktalische Strukturgynese des elektronenoptischen Moires auf den magnetischen Feldern des Zerstreuens der kleinen Ausdehnung
Zusammenfassung: Es sind die informativen Kriterien der Einschatzung der ungleichartigen magnetischen Felder in den kleinen Umfangen als der Koeffizient der Asymmetrie des geflammten Musters und der Fraktaldimension angeboten. Es sind die Abhangigkeiten dieser Kriterien von der Lange des Ortsrisses im flachen Schaffner mit dem Strom gefunden. Es ist aufgezeigt, dafl die Veranderung des Koeffizienten der Asymmetrie des geflammten Musters um die Defekte als die Offnung und des Ortsrisses der bekannten Verteilung der elektromagnetischen Energie auf diesen Gebieten ahnlich ist. Das kann zum Mafl der Einschatzung der Konzentration dieser Energie um die nichtleitenden Defekte dienen.
Structurogenese fractal de la moire electronique et optique sur les champs magnetiques de la dispersion de la petite surface
Resume: Sont proposes les criteres informatiques de revaluation des champs magnetiques non-heterogenes dans de petits volumes en vue du coefficient de l’asymetrie du dessin de moire et de la dimension fractale. Sont trouvees les dependances de ces criteres de la longueur de la fissure de limite dans un conducteur plat avec le courant. Est montre que la mesure du coefficient de l’asymetrie du dessin de moire autour des defauts du type de l’ouverture et de la fissure de limite est analogue a la repartition connue de l’energie electromagnetique dans ces domaines ce qui pourrait servir de la mesure de revaluation du coefficient de cette energie autour des defauts non-conduisants.
