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Evolution and Development of the Universe. 8 - 9 October 2008, Paris, France. ARE PARTICLES. SOS. ?. SELF-ORGANIZED SYSTEMS. Vladimir A. Manasson. Sierra Nevada Corporation Irvine, California vmanasson@earthlink.net. Dynamical feedback. ARE PARTICLES. SOS. ?. SELF-ORGANIZED SYSTEMS.

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  1. Evolution and Development of the Universe 8 - 9 October 2008, Paris, France ARE PARTICLES SOS ? SELF-ORGANIZED SYSTEMS Vladimir A. Manasson Sierra Nevada Corporation Irvine, California vmanasson@earthlink.net

  2. Dynamical feedback ARE PARTICLES SOS ? SELF-ORGANIZED SYSTEMS Self-organized systems are complex systems that acquire stability of their dynamical variables through dynamical feedback

  3. http://astro-canada.ca/_photos/a4201_univers1_g.jpg http://www.astronomycast.com/wp-content/uploads/2007/05/abell2218.jpg http://img.dailymail.co.uk/i/pix/2007/07_01/galaxy11_468x468.jpg http://www.spacetoday.org/images/DeepSpace/Stars/StarWR124Hubble.jpg http://www.wnps.org/ecosystems/images/middle_lakes_wl.jpg http://farm2.static.flickr.com/1287/588319871_a2304d87bf.jpg?v=0 http://www.moneypit.com/members2/AardvarkPublisher/9990261456922/image1.jpg http://www.ices.dk/marineworld/photogallery/images/jellyfish.jpg http://addiandcassi.com/wordpress/wp-content/uploads/dna-image.jpg http://radio.weblogs.com/0105910/images/hiphop_atom.jpg http://www.pasteur.fr/actu/presse/images/plasmodium.jpg SOS SELF-ORGANIZED SYSTEMS ??? V Manasson, EDU-2008

  4. Standard Model (QT) Self-Organized Systems (SOS) ? ? ? ? ? WHICH THEORY? Empirical Constants V Manasson, EDU-2008 http://www-d0.fnal.gov/Run2Physics/WWW/results/final/NP/N04C/N04C_files/standardmodel.jpg

  5. STABILITY and DYNAMICAL PHASE PORTRAITS j J Attractor J+DJ Center ħ ħ +DJ Jn=n ħ Bohr-Sommerfeld Classical Conservative Dynamics Idealistic (Closed Systems) Realistic (Open Systems) SOS ABSOLUTE (ASYMPTOTIC) STABILITY CONDITIONAL STABILITY Limit cycle Center Quantum Systems Center with selected orbits constrained by fundamental constants like ħ ABSOLUTE STABILITY Realistic (Open Systems) V Manasson, EDU-2008

  6. Permitted Orbit = Attractor? Heisenberg's uncertainty principle QT SOS Dt ~ /DE ħ Quantum systems resemble SOS Dissipation time? Y-function collapses Non-reversibility Perturbation technique Renormalization Non-Abelian Yang-Mills fields Nonlinearity V Manasson, EDU-2008

  7. PHENOMENON of QUANTIZATION in Nonlinear Dissipative Dynamics V Manasson, EDU-2008

  8. LOGISTIC MAP AS A SOS PARADIGM yn+1 Jj J yn+1 y y 8 8 yn yn Poincaré Section J Jj Ji A yn+1=FJ(yn) xn+1=Axn(1-xn) A parameterizeslimit points in the same way generalized angular momentum J parameterizes attractors Ji V Manasson, EDU-2008

  9. y1 y2 y BIFURCATIONS CHANGE DIMENSIONALITY AND TOPOLOGY OF THE PHASE SPACE SU(2) Spinor U(1) Vector 4p 2p F(y) F(F(y)) Feigenbaum point http://www.lactamme.polytechnique.fr/Mosaic/images/MOB2.11.D/image.jpg V Manasson, EDU-2008

  10. UNIVERSAL BEHAVIOR AND FEIGENBAUM DELTA 1 a) F(y) 0 2 3 4 DJ1 1 b) 1. UNIMODAL 2. QUADRATIC EXTREMUM DJ2 y y 8 8 0 0.4 0.6 0.8 1 2 c) 0 -2 0 1 2 d=DJn/DJn+1=4.669.. yn+1=FJ(yn) J V Manasson, EDU-2008

  11. QUANTIZATION SPRINGS from SUPERATTRACTORS J1 J2 J3 Lyapunov exponent y 8 http://web.mst.edu/~vojtat/class_355/chapter1/lyapunov_logistic.jpg Superattractors J F(y) Dissipation Rate, D J1 J3 J2 V Manasson, EDU-2008 J

  12. E Coulomb-wave potential Bifurcation diagram 8 Continuous spectrum E3 J 8 J3 E2 J2 E1 Discrete spectrum J1 One More Similarity between SOS and QT Hydrogen atom V Manasson, EDU-2008


  14. QUANTIZATION OF COUPLING CONSTANTS? a 8 y 8 a a3 ELECTROMAGNETIC a2 WEAK a1 GUT STRONG V Manasson, EDU-2008 http://webplaza.pt.lu/public/fklaess/pix/merging_forces.gif

  15. MAJOR RESULT Accuracy ~ 0.04% Fine structure constant Presence of d implies routes to chaos, which are dynamics that cannot be properly described by QT Presence of d underscores the relevance of period-doubling bifurcation dynamics and SU(2) symmetry Value d = 4.669.. suggests that we are dealing with dissipative dynamics Quantization of charge (e) and quantization of action (ħ) have the same origin V Manasson, EDU-2008

  16. SU(2) SYMMETRY, SPINORS, and 4p ROTATION ANGLE Family I Leptons Family I Family I Quarks y1 y1 y2 y2 p y3 y4 n V Manasson, EDU-2008

  17. Family I Family III Leptons Family II Leptons Family I Leptons Family II Family III Quarks Family II Quarks Family I Quarks Family III BIFURCATION DIAGRAM and PARTICLE "PHYLOGENETIC" TREE

  18. EXCITATION DIAGRAM EXCITATION RELAXATION (SPONTANEOUS SYMMETRY BREAK) Electromagnetic Excitation Level Spin 2 Graviton? Bosons (2 photons) Spin 1 Fermions (4, including charge and spin) Spin 1/2 Electron Branch Dirac spinor V Manasson, EDU-2008

  19. EXCITATION DIAGRAM Weak Excitation Level Lepton Branch Bosons (4 electroweak) Fermions (8) Electron Branch Neutrino Branch V Manasson, EDU-2008

  20. EXCITATION DIAGRAM Strong Excitation Level GUT Lepton Branch Bosons (8 gluons) Fermions (16) Quark Branch Electron Branch Neutrino Branch V Manasson, EDU-2008

  21. Nonlinear Dynamics Classical Conservative Dynamics Duffing Oscillator F(F(F(y))) time Numerical Perturbation Theory Renormalization A. L. Fetter, J. D. Walecka, Nonlinear Mechanics, Dover Publications, 2006 Nonlinear Dynamics Quantum Theory Is QT a quasi-linear surrogate of Nonlinear Dynamics? Statistical Physics Quantum Theory V Manasson, EDU-2008

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