Chaos, Turbulence and Fractal: Theory and Applications

Affiliation(s)

V. Laksshmikantham Institute for Advanced Studies, GVP College of Engineering J. Nehru Technical University, Kakinada, India.

V. Laksshmikantham Institute for Advanced Studies, GVP College of Engineering J. Nehru Technical University, Kakinada, India.

ABSTRACT

The paper identifies chaos, turbulence and fractal of quantum and
macro gravity and studies their behavior, properties and applications based on
the grand unified theory (GUT) and qualitative mathematics and modeling.
Applications include devising electromagnetic engines, tornado aborter and
terminator and technologies for electromagnetic treatment of genetic diseases
such as cancer, systemic lupos erythematosus, diabetes and mental disorder
without harm to normal cell and side effect. Typhoon in the Western Pacific
which is turbulence is impossible to terminate and impractical to deflect but
prediction can be improved because it follows the Northern Pacific Wind Cycle
(Southern Pacific Wind Cycle in the Southern Hemisphere) and is affected by the
temperature variation over the Philippine Deep and around Mayon Volcano. The
electromagnetic engine uses the clean, inexhaustible, free dark matter,
specifically, the energy of magnetic flux, in place of conventional fuel, e.g.,
fossil, nuclear and geothermal. The tornado aborter and terminator utilize the
gravitational flux of the Earth, its vortex flux of superstrings as a
cosmological vortex which is turbulence. The technologies for electromagnetic
treatment of genetic diseases utilize electromagnetic waves based on resonance.
All of them are GUT technologies because they are applications of GUT. Except
for the magnetic train which is in operation the rest is still at the
conceptual and research and development (R&D) phase but the theory is
complete and the strategy for R&D are laid down in detail in the cited
original papers.

Cite this paper

E. Escultura, "Chaos, Turbulence and Fractal: Theory and Applications,"*International Journal of Modern Nonlinear Theory and Application*, Vol. 2 No. 3, 2013, pp. 176-185. doi: 10.4236/ijmnta.2013.23025.

E. Escultura, "Chaos, Turbulence and Fractal: Theory and Applications,"

References

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[2] E. E. Escultura, “Earthly Turbulence,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 237-260 http://www.benthamscience.com/eBooks/9781608051786/index.htm

[3] G. A. Edgar, “Measure, Topology and Fractal Geometry,” Springer-Verlag, New York, 1990. doi:10.1007/978-1-4757-4134-6

[4] J. Gleick, “Chaos: Making a New Science,” Penguin Books, New York, 1988.

[5] C. A. Pickover, “Chaos and Fractals,” Elsevier Science, Amsterdam, 1998.

[6] 6K. J. Falconer, “The Geometry of Fractal Sets,” Cambridge University Press, Cambridge, 1986.

[7] E. E. Escultura, “The Grand Unified Theory,” Nonlinear Analysis, A-Series: TMA, Vol. 69, No. 3, 2008, pp. 823-831. doi:10.1016/j.na.2008.02.043

[8] E. E. Escultura, “Qualitative Mathematics and Modeling: Theoretical and Practical Applications,” LAP LAMBERT Academic Publishing, in press.

[9] E. E. Escultura, “The Solution of the Gravitational n-Body Problem,” Nonlinear Analysis, A-Series: TMA, Vol. 30, No. 8, 1997, pp. 5021-5032.

[10] P. C. W. Davies and J. Brown, “Superstring, A Theory of Everything,” Cambridge University Press, New York, 1988.

[11] E. E. Escultura, “The Mathematics of the Grand Unified Theory,” Nonlinear Analysis, A-Series: TMA, Vol. 71, 2009, pp. e420-e431.

[12] E. E. Escultura, “Qualitative Model of the Atom, Its Components and Origin in the Early Universe,” Nonlinear Analysis: Real World Applications, Vol. 11, 2009, pp. 29-38.

[13] E. E. Escultura, “Dynamic Modeling of Chaos and Turbulence,” Nonlinear Analysis, A-Series: TMA, Vol. 63, No. 5-7, 2005, pp. e519-e532.

[14] E. E. Escultura, “Superstring loop dynamics and applic to astronomy, biology,” Nonlinear Analysis, A-Series: TMA, Vol. 35, No. 8, 1999, pp. 259-285.

[15] E. E. Escultura, “The Trajectories, Reachable Set, Minimal Levels and Chain of Trajectories of a Control System,” Ph. D. Thesis, University of Wisconsin, Madison, 1970.

[16] E. E. Escultura, “Abstracts and Summary of Publications,” The Grand Unified Theory. http://users.tpg.com.au/pidro/

[17] E. Escultura, “The Unified Theory of Evolution,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 237-260. http://www.benthamscience.com/eBooks/9781608051786/index.htm

[18] E. E. Escultura, “The Physics of Intelligence,” Journal of Education and Learning, Vol. 1, No. 12, 2012, pp. 51-64.

[19] E. E. Escultura, “Electromagnetic Treatment of Genetic Diseases,” Journal of Biomaterials and Nanobiotechnology, Vol. 3, No. 2, 2012, pp. 292-300. www.ccsenet.org doi:10.4236/jbnb.2012.322036

[20] E. E. Escultura, “The New Real Number System and Discrete Computation and Calculus,” Neural, Parallel and Scientific Computations, Vol. 17, 2009, pp. 59-84.

[21] E. E. Escultura, “Exact Solutions of Fermat’s Equation (Definitive Resolution of Fermat’s Last Theorem),” Nonlinear Studies, 1997, Vol. 5, No. 2, pp. 227-2254.

[22] E. E. Escultura, “The New Mathematics and Physics,” Journal of Applied Mathematics and Computation, Vol. 138, No. 1, 2003, pp. 127-149. doi:10.1016/S0096-3003(02)00126-1

[23] P. J. Davies, and R. Hersch, “The Mathematical Experience,” Birkhauser, Boston, 1981.

[24] E. E. Escultura, “Quantum Gravity,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 61-80. http://www.benthamscience.com/eBooks/9781608051786/index.htm

[25] E. E. Escultura, “Macro Gravity,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 87-107. http://www.benthamscience.com/eBooks/9781608051786/index.htm

[26] D. Pendick, “Fires in the Sky,” Earth, Vol. 20, 1996, pp. 62-64.

[27] V. A. Atsukovsky, “General Ether-Dynamics; Simulation of the Matter Structures and Fields on the Basis of the Ideas about the gas-Like Ether,” Energoatomizdat, Moscow, 1990.

[28] E. E. Escultura, “Extended Geometrical and Generalized Fractal, Chaos and Applications,” In: Kyle J. Brennan, Ed., Handbook on the Classification and Application of Fractals, Nova Publishers, 2011, pp. 1-39. https://www.novapublishers.com/catalog/product_infinfo.php?products_id=23231

[29] E. E. Escultura, “From Macro to Quantum Gravity,” Problems of Nonlinear Analysis in Engineering Systems, Vol. 7, No. 1, 2001, pp. 56-78.

[30] H. A. Nieper, “Revolution in Technology, Medicine, Society,” Management Interessengemeinschaft für Tachyon-Feld-Energie, Odenburg, 1984.

[31] I. L. Gerlovin, “The Foundations of United Theory of Interactions in a Substance,” Energoattomizdat, Leningrad, 1990.

[32] E. E. Escultura, “Columbia’s Disastrous Final Flight: Crossroad for Science,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 81-87. doi:10.2174/97816080527071110101

[33] E. E. Escultura, “The Pillars of the New Physics and Some Updates,” Nonlinear Studies, Vol. 14, No. 3, 2007, pp. 241-260.

[34] “Weighing in on Neutrino Mass,” Science, Vol. 280, 1997, pp. 1689-1691.

[35] “Neutrinos Weigh in,” Science, Vol. 282, No. 5397, 1998, pp. 2158-2159. doi:10.1126/science.282.5397.2158

[36] “Search for Neutrino Mass Is a Big Stretch for Three Labs,” Science, Vol. 283, No. 5405, 1999, pp. 928-929.

[37] E. Merchbacher, “Quantum Mechanics,” 2nd Edition, John Wiley & Sons, Inc., New York, 1970.

[38] “Ultra-Energetic Particles,” Science, Vol. 281, No. 5379, 1998, pp. 241-242.

[39] E. E. Escultura, “The Theory of Chaos and Turbulence,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, Sharjah, 2011, pp. 130-139. doi:10.2174/97816080527071110101

[40] A. Ganeri, “The Ocean Atlas,” Dorling Kindersley, London, 1994.

[41] “The Earth Atlas,” Dorling Kindersley, London, 1994, pp. 138-139.

[42] E. E. Escultura, “The Big Bang and What It Was,” In: J. R. O'Connell and A. L. Hale, Eds., The Big Bang: Theory, Assumptions and Problems, 2012. https://www.novapublishers.com/catalog/product_info.php?products_id=21109

[43] G. Schilling, “Watching the Universe’s Second Biggest Bang,” Science, Vol. 283, No. 5410, 1999, pp. 2013-2014. doi:10.1126/science.283.5410.2003

[44] “The Quasars and Early Galaxies,” Scientific American, April 1983, pp. 708-745.

[45] A. Hellemans, “Galaxy’s Oldest Stars Shed Light on Big Bang,” Science, Vol. 282, No. 5382, 1998, pp. 1428-1429. doi:10.1126/science.281.5382.1428b

[46] E. E. Escultura, “GUT Technology,” In: E. E. Escultura, Ed, Scientific Natural Philosophy, Bentham Science Publishers, Sharjah, 2011, pp. 147-148. http://www.benthamscience.com/ebooks/9781608051786/index.htm.

[47] E. E. Escultura, “Creative Mathematics Education,” Creative Education, Vol. 3, No. 1, 2012, pp. 45-54. http://www.scirp.org/journal/PaperInformation.aspx?paperID=17266; doi:10.4236/ce.2012.31008

[48] E. E. Escultura, “A Novel Creative Approach to Mathematics-Science Education,” In: E. E. Escultura, Ed., Qualitative Math. Modeling: Theoretical and Practical Applications, in Press, LAP LAMBERT Academic Publishing, pp. 229-241. www.lap-publishing.com

[49] E. E. Escultura, “Qualitative Modeling for Complex Systems,” Problems of Nonlinear Analysis in Engineering Systems (International IFNA-ANS scientific Journal, Vol. 2, No. 36, 2011, pp. 79-85), Vol. 17, No. 36, 2011, pp. 79-85.

[50] E. E. Escultura, Sustainable Development of the Third World: Focus on the Philippines,” Accepted, International Transactions in Operational Research. http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1475-3995/issues

[51] E. E. Escultura, “The Origin and Evolution of Biological Species,” Journal of Science of Healing Outcomes, No. 6-7, 2010, pp. 17-27.

[52] G. S. Osipenko, A. N. Pokrovsky, B. V. Krylov and V. B. Plakhova, “Mathematical Modeling of Pain Sensation,” Proceedings of the Second International Conference on Mathematical Modeling, St. Petersburg, 2000.

[53] V. B. Krylov and B. F. Shehegelov, “Mathematical Methods in the Physiology of Sensory Systems,” Second International Conference on Tools for Mathematical Modeling, St. Petersburg, June 1999, pp. 14-19.

[54] E. E. Escultura, “Genetic Alteration, Modification and Sterilization with Applications to the Treatment of Genetic Diseases,” The Journal of the Science of Healing Outcomes, No. 8-10, 2011, pp. 30-45.

[1] E. E. Escultura, “Turbulence: Theory, Verification and Applications,” Nonlinear Analysis, A-Series: Theory, Methods and Applications (TMA), Vol. 47, No. 8, 2001, pp. 5955-5966.

[2] E. E. Escultura, “Earthly Turbulence,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 237-260 http://www.benthamscience.com/eBooks/9781608051786/index.htm

[3] G. A. Edgar, “Measure, Topology and Fractal Geometry,” Springer-Verlag, New York, 1990. doi:10.1007/978-1-4757-4134-6

[4] J. Gleick, “Chaos: Making a New Science,” Penguin Books, New York, 1988.

[5] C. A. Pickover, “Chaos and Fractals,” Elsevier Science, Amsterdam, 1998.

[6] 6K. J. Falconer, “The Geometry of Fractal Sets,” Cambridge University Press, Cambridge, 1986.

[7] E. E. Escultura, “The Grand Unified Theory,” Nonlinear Analysis, A-Series: TMA, Vol. 69, No. 3, 2008, pp. 823-831. doi:10.1016/j.na.2008.02.043

[8] E. E. Escultura, “Qualitative Mathematics and Modeling: Theoretical and Practical Applications,” LAP LAMBERT Academic Publishing, in press.

[9] E. E. Escultura, “The Solution of the Gravitational n-Body Problem,” Nonlinear Analysis, A-Series: TMA, Vol. 30, No. 8, 1997, pp. 5021-5032.

[10] P. C. W. Davies and J. Brown, “Superstring, A Theory of Everything,” Cambridge University Press, New York, 1988.

[11] E. E. Escultura, “The Mathematics of the Grand Unified Theory,” Nonlinear Analysis, A-Series: TMA, Vol. 71, 2009, pp. e420-e431.

[12] E. E. Escultura, “Qualitative Model of the Atom, Its Components and Origin in the Early Universe,” Nonlinear Analysis: Real World Applications, Vol. 11, 2009, pp. 29-38.

[13] E. E. Escultura, “Dynamic Modeling of Chaos and Turbulence,” Nonlinear Analysis, A-Series: TMA, Vol. 63, No. 5-7, 2005, pp. e519-e532.

[14] E. E. Escultura, “Superstring loop dynamics and applic to astronomy, biology,” Nonlinear Analysis, A-Series: TMA, Vol. 35, No. 8, 1999, pp. 259-285.

[15] E. E. Escultura, “The Trajectories, Reachable Set, Minimal Levels and Chain of Trajectories of a Control System,” Ph. D. Thesis, University of Wisconsin, Madison, 1970.

[16] E. E. Escultura, “Abstracts and Summary of Publications,” The Grand Unified Theory. http://users.tpg.com.au/pidro/

[17] E. Escultura, “The Unified Theory of Evolution,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 237-260. http://www.benthamscience.com/eBooks/9781608051786/index.htm

[18] E. E. Escultura, “The Physics of Intelligence,” Journal of Education and Learning, Vol. 1, No. 12, 2012, pp. 51-64.

[19] E. E. Escultura, “Electromagnetic Treatment of Genetic Diseases,” Journal of Biomaterials and Nanobiotechnology, Vol. 3, No. 2, 2012, pp. 292-300. www.ccsenet.org doi:10.4236/jbnb.2012.322036

[20] E. E. Escultura, “The New Real Number System and Discrete Computation and Calculus,” Neural, Parallel and Scientific Computations, Vol. 17, 2009, pp. 59-84.

[21] E. E. Escultura, “Exact Solutions of Fermat’s Equation (Definitive Resolution of Fermat’s Last Theorem),” Nonlinear Studies, 1997, Vol. 5, No. 2, pp. 227-2254.

[22] E. E. Escultura, “The New Mathematics and Physics,” Journal of Applied Mathematics and Computation, Vol. 138, No. 1, 2003, pp. 127-149. doi:10.1016/S0096-3003(02)00126-1

[23] P. J. Davies, and R. Hersch, “The Mathematical Experience,” Birkhauser, Boston, 1981.

[24] E. E. Escultura, “Quantum Gravity,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 61-80. http://www.benthamscience.com/eBooks/9781608051786/index.htm

[25] E. E. Escultura, “Macro Gravity,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 87-107. http://www.benthamscience.com/eBooks/9781608051786/index.htm

[26] D. Pendick, “Fires in the Sky,” Earth, Vol. 20, 1996, pp. 62-64.

[27] V. A. Atsukovsky, “General Ether-Dynamics; Simulation of the Matter Structures and Fields on the Basis of the Ideas about the gas-Like Ether,” Energoatomizdat, Moscow, 1990.

[28] E. E. Escultura, “Extended Geometrical and Generalized Fractal, Chaos and Applications,” In: Kyle J. Brennan, Ed., Handbook on the Classification and Application of Fractals, Nova Publishers, 2011, pp. 1-39. https://www.novapublishers.com/catalog/product_infinfo.php?products_id=23231

[29] E. E. Escultura, “From Macro to Quantum Gravity,” Problems of Nonlinear Analysis in Engineering Systems, Vol. 7, No. 1, 2001, pp. 56-78.

[30] H. A. Nieper, “Revolution in Technology, Medicine, Society,” Management Interessengemeinschaft für Tachyon-Feld-Energie, Odenburg, 1984.

[31] I. L. Gerlovin, “The Foundations of United Theory of Interactions in a Substance,” Energoattomizdat, Leningrad, 1990.

[32] E. E. Escultura, “Columbia’s Disastrous Final Flight: Crossroad for Science,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, 2011, pp. 81-87. doi:10.2174/97816080527071110101

[33] E. E. Escultura, “The Pillars of the New Physics and Some Updates,” Nonlinear Studies, Vol. 14, No. 3, 2007, pp. 241-260.

[34] “Weighing in on Neutrino Mass,” Science, Vol. 280, 1997, pp. 1689-1691.

[35] “Neutrinos Weigh in,” Science, Vol. 282, No. 5397, 1998, pp. 2158-2159. doi:10.1126/science.282.5397.2158

[36] “Search for Neutrino Mass Is a Big Stretch for Three Labs,” Science, Vol. 283, No. 5405, 1999, pp. 928-929.

[37] E. Merchbacher, “Quantum Mechanics,” 2nd Edition, John Wiley & Sons, Inc., New York, 1970.

[38] “Ultra-Energetic Particles,” Science, Vol. 281, No. 5379, 1998, pp. 241-242.

[39] E. E. Escultura, “The Theory of Chaos and Turbulence,” In: E. E. Escultura, Ed., Scientific Natural Philosophy, Bentham Science Publishers, Sharjah, 2011, pp. 130-139. doi:10.2174/97816080527071110101

[40] A. Ganeri, “The Ocean Atlas,” Dorling Kindersley, London, 1994.

[41] “The Earth Atlas,” Dorling Kindersley, London, 1994, pp. 138-139.

[42] E. E. Escultura, “The Big Bang and What It Was,” In: J. R. O'Connell and A. L. Hale, Eds., The Big Bang: Theory, Assumptions and Problems, 2012. https://www.novapublishers.com/catalog/product_info.php?products_id=21109

[43] G. Schilling, “Watching the Universe’s Second Biggest Bang,” Science, Vol. 283, No. 5410, 1999, pp. 2013-2014. doi:10.1126/science.283.5410.2003

[44] “The Quasars and Early Galaxies,” Scientific American, April 1983, pp. 708-745.

[45] A. Hellemans, “Galaxy’s Oldest Stars Shed Light on Big Bang,” Science, Vol. 282, No. 5382, 1998, pp. 1428-1429. doi:10.1126/science.281.5382.1428b

[46] E. E. Escultura, “GUT Technology,” In: E. E. Escultura, Ed, Scientific Natural Philosophy, Bentham Science Publishers, Sharjah, 2011, pp. 147-148. http://www.benthamscience.com/ebooks/9781608051786/index.htm.

[47] E. E. Escultura, “Creative Mathematics Education,” Creative Education, Vol. 3, No. 1, 2012, pp. 45-54. http://www.scirp.org/journal/PaperInformation.aspx?paperID=17266; doi:10.4236/ce.2012.31008

[48] E. E. Escultura, “A Novel Creative Approach to Mathematics-Science Education,” In: E. E. Escultura, Ed., Qualitative Math. Modeling: Theoretical and Practical Applications, in Press, LAP LAMBERT Academic Publishing, pp. 229-241. www.lap-publishing.com

[49] E. E. Escultura, “Qualitative Modeling for Complex Systems,” Problems of Nonlinear Analysis in Engineering Systems (International IFNA-ANS scientific Journal, Vol. 2, No. 36, 2011, pp. 79-85), Vol. 17, No. 36, 2011, pp. 79-85.

[50] E. E. Escultura, Sustainable Development of the Third World: Focus on the Philippines,” Accepted, International Transactions in Operational Research. http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1475-3995/issues

[51] E. E. Escultura, “The Origin and Evolution of Biological Species,” Journal of Science of Healing Outcomes, No. 6-7, 2010, pp. 17-27.

[52] G. S. Osipenko, A. N. Pokrovsky, B. V. Krylov and V. B. Plakhova, “Mathematical Modeling of Pain Sensation,” Proceedings of the Second International Conference on Mathematical Modeling, St. Petersburg, 2000.

[53] V. B. Krylov and B. F. Shehegelov, “Mathematical Methods in the Physiology of Sensory Systems,” Second International Conference on Tools for Mathematical Modeling, St. Petersburg, June 1999, pp. 14-19.

[54] E. E. Escultura, “Genetic Alteration, Modification and Sterilization with Applications to the Treatment of Genetic Diseases,” The Journal of the Science of Healing Outcomes, No. 8-10, 2011, pp. 30-45.