Indeterministic
consideration of micro-world based on quantum mechanics has resulted in its
probabilistic understanding. At the same time the study of the micro-world
based on Coulomb interactions in some cases gives deterministic view of it.
However, at this way it is necessary to solve complex problems of many
particles interaction. The program Galactica have to be developed for the
numerical solution with high accuracy gravitational problems of many-bodies.
The paper considers a modification of the program algorithm for solution of
Coulomb interaction. For integrating differential equations of motion, the
initial conditions have to be given, which are deter- mined by the geometry of
the interacting particles. Since in contemporary physics the atoms geo- metry
is not specified, as an example, their axisymmetric models are studied. They
consist of positively charged nucleus and are symmetrically arranged on the
plane of the electrons. The neces- sary tasks were solved to determine
positions and velocities of particles at the initial time. Based on their
results, the program in environment MathCad for creation of a file of inital
conditions is developed. Using the modified program Galactica, the motion of
particles in an axisymmetric structure with eight peripheral electrons is
researched. It has appeared that they are unstable. For comparison, a similar
problem was studied with the gravitational interaction. It also proved to be
unstable. So more detailed studies of the problem of stability of axisymmetric
structures were made. They showed that the stability of the structure increases
with the decrease of the interac- tion parameters. Such stable structure with
eight peripheral bodies is considered for gravitational interaction. The paper
also considers an example of a helium atom at axisymmetric interaction with two
peripheral electrons. This structure is also unstable. At the same time
two-particle inte- raction on the example of the hydrogen atom, considered
using the Galactica, is stable and the re- sults of numerical solutions
coincide with the exact analytical solution. The studies showed that the
program Galactica can be used to research the Coulomb interactions. The paper
shows that axially symmetric structure of the atom can be used to create his
other geometries. The developed methods and programs may be used in these
studies. In the future, they will increase the degree of determinateness of
micro-world. This
paper, as well as the book, will be useful to physicists, students, senior pupils
and everything who are interested in the scientific worldview. The programs are the free access (http://www.ikz.ru/~smulski/GalactcW/) and can be used for student projects.
Cite this paper
Smulsky, J. J. (2014). Axisymmetric Coulomb Interaction and Research of Its Stability by System Galactica. Open Access Library Journal, 1, e773. doi: http://dx.doi.org/10.4236/oalib.1100773.
Smulsky, J.J. (2012) The System of Free Access Galactica to Compute Interactions of N-Bodies. International Journal of Modern Education and Computer Science, 4, 1-20.
http://www.mecs-press.org
http://dx.doi.org/10.5815/ijmecs.2012.11.01
Канарёв, Ф.М. Закон формирования спектров атомов и ионов.
http://www.sciteclibrary.ru/rus/catalog/pages/12586.html
http://www.micro-world.su/index.php/2010-12-22-11-46-00/784-2013-01-16-02-03-51
Gryziński, M. (1987) Spin-Dynamical Theory of the Wave-Corpuscular Duality. International Journal of Theoretical Physics, 26, 967-980.
http://dx.doi.org/10.1007/BF00670821
Gryziński, M. (1965) Classical Theory of Atomic Collisions. I. Theory of Inelastic Collisions. Physical Review A, 138, 336-358. http://dx.doi.org/10.1103/PhysRev.138.A336
Gryziński, M. (1970) Ramsauer Effect as a Result of the Dynamic Structure of the Atomic Shell. Physical Review Letters, 24, 45-47.
http://dx.doi.org/10.1103/PhysRevLett.24.45
Gryziński, M. (1959) Classical Theory of Electronic and Ionic Inelastic Collisions. Physical Review, 115, 374-383.
http://dx.doi.org/10.1103/PhysRev.115.374
Gryziński, M. (1957) Stopping Power of a Medium for Heavy, Charged Particles. Physical Review A, 107, 1471-1475.
http://dx.doi.org/10.1103/PhysRev.107.1471
Яворский, Б.М. and Детлаф А.А. (1968) Справочник по физике. Для инженеров и студентов вузов. Издание четвертое, переработанное. Москва: Издательство 《Наука》. Главная редакция физико-математической литературы, 940 p.
Смульский, И.И. (2003) Осесимметричная задача гравитационного взаимодействия N-тел//Математическое моделирование, т. 15, 27-36.
http://www.smul1.newmail.ru/Russian1/IntSunSyst/Osvnb4.doc
Смульский, И.И. (2008) Численное моделирование эволюции спутника вращающегося тела/В сб. Теорети- ческие и прикладные задачи нелинейного анализа. Российская Академия Наук: ВЦ им. А.А. Дородницына. М.: ВЦ РАН А.А. Дородницына. 100-118.
http://www.ikz.ru/~smulski/Papers/ModSun07c.pdf
Мельников, В.П. and Смульский, И.И. (2009) Астрономическая теория ледниковых периодов: Новые приближения. Решенные и нерешенные проблемы. Новосибирск: Академическое изд-во 《Гео》, 2009. 98 с. Книга на двух языках. С обратной стороны: Melnikov V.P., Smulsky J.J. Astronomical Theory of Ice Ages: New Approximations. Solutions and Challenges. Novosibirsk: Academic Publishing House “GEO”, 84 p.
http://www.ikz.ru/~smulski/Papers/AsThAnR.pdf
Мельников, В. П., Смульский, И.И. and Смульский, Я.И. (2008) Составная модель вращения Земли и возможный механизм взаимодействия континентов. Геология и Геофизика, 1129-1138.
http://www.ikz.ru/~smulski/Papers/RGGRu190.pdf
Smulsky, J.J. (2009) Gravitation, Field and Rotation of Mercury Perihelion. Proceedings of the 15th Annual Conference, Natural Philosophy Alliance, Albuquuerque, 7-11 April 2008, 254-260.
http://www.ikz.ru/~smulski/Papers/08Smulsky2c.pdf
http://www.ikz.ru/~smulski/Papers/ModSun04.pdf
Smulsky, J.J. (2012) Letter to the Antirelativists. Proceedings of the 19th Annual Conference, Natural Philosophy Alliance, Albuquerque, 25-28 July 2012, 567-568.
http://www.worldsci.org/pdf/abstracts/abstracts_6667.pdf
http://www.ikz.ru/~smulski/Papers/LettAntrlR.pdf
Смульский, И.И. (1995) Траектории при взаимодействии двух тел, зависящем от относительного расстояния и скорости. Математическое Моделирование, 7, 117-126.
http://www.smul1.newmail.ru/Russian1/FounPhisics/TrV2tl.pdf
Smulsky, J.J. (2002) The New Fundamental Trajectories: Part 1. Hyperbolic/Elliptic Trajectories. Galilcan Electrodynamics, 13, 23-28.
http://www.smul1.newmail.ru/English1/FounPhisics/NFT.pdf
Smulsky, J.J. (2002) The New Fundamental Trajectories: Part 2. Parabolic/Elliptic Trajectories. Galilcan Electrodynamics, 13, 47-51.
http://www.smul1.newmail.ru/English1/FounPhisics/NFT.pdf