Dynamic modeling of chaos and turbulence

Abstract

The series, Diophantus: Introduction to Mathematical Philosophy, Kalikasan, Manila, 1993; Nonlinear Anal. 30 (8) (1997) 5021–5032; Nonlinear Stud. 5 (2) (1998) 227–254; Nonlinear Anal., 35 (8) (1999) 259–285; Proc. Second Int. Conf. Tool. Math. Model., St. Petersburg, 4 (1999) 74–89; Proceedings of Third International Conference on Differential Equations, St. Petersburg, 2000 pp. 71–86; Probl. Nonlinear Anal. Eng. Syst. 7 (1) (2001) 56–78; Proceedings of Third International Conference on Dynamic Systems and Applications, Atlanta, 2001 pp. 201–208; Nonlinear Anal. 47 (2001) 5955–5966; Probl. Nonlinear Anal. Eng. Syst. 7 (2) (2001) 30–44; Indian J. Pure Appl. Math. 32 (10) (2001) 1539–1551; Appl. Math. Comput. 130 (1) (2001) 145–169; Indian J. Pure Appl. Math. 33 (1) (2003) 111–129; Appl. Math. Comput. 138 (2003) 127–149; Appl. Math. Comput. 139 (1) (2003) 23–36; Recent results, new inventions and new cosmology, accepted, Probl. Nonlinear Anal. Eng. Syst.; The new nonstandard analysis and intuitive calculus, submitted for publication; The philosophical and mathematical foundations of FLT's resolution, rectification and extension of underlying fields and applications, accepted, Int. J. Nonlinear Differential Equations; Extending the reach of computation, submitted for publication; The theory of learning: implications for math–science education and research, submitted for publications; Columbia: The crossroads for science, accepted, Int. J. Nonlinear Differential Equations; Dynamic modeling and applications, Proceedings of Fourth International Conference on Tools for Mathematical Modeling, 2003, St. Petersburg State Technical University; Nonlinear Anal. Phenomena, 1 (1) (2004) 1–23 and Nonlinear Anal. Phenomena, 2 (1) (2005) 15–30 introduced, embellished, developed, and elaborated dynamic modeling and its principal mathematical component—qualitative mathematics—and used it to resolve long-standing unsolved problems of mathematics and physics such as Fermat's last theorem, the gravitational n-body problem, Goldbach's Conjecture and the search for the basic constituent of matter. Among its major achievements is the development of the flux theory of gravitation (FTG) anchored on 42 laws of nature. The paper considers the questions of chaos and turbulence and shows that gravity is turbulence, specifically, the dynamics of vortex flux of dark matter consisting of its basic constituent, the superstring. FTG explains our universe as a super...super galaxy comprised of nested fractal sequences of vortices from our universe down through galaxy clusters, galaxies, stars, planets, moons and cosmic dust. As vortex, each term is self-similar to our universe. Beyond the cosmic dust is the domain of quantum gravity, forming nested fractal sequences of vortices each starting from a molecule, e.g., protein, down to the atom and primum. Crossing the boundary of visible matter we enter dark matter and find its basic constituent of nested fractal sequence of superstrings. The paper notes three new laws of nature discovered in the course of resolving the puzzles surrounding the disastrous final flight of the Columbia Space Shuttle (Int. J. Nonlinear Diff. Equations, Accepted). Finally using Hubble's law and guided by FTG, the rate of expansion of our universe and its acceleration are computed.