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Why NonLinear Physics?

Why NonLinear Physics?. Everything is Nonlinear Macro Systems Gauge Theory, General Relativity Qualitative Differences from Linear Case Chaos / Fractals Solitons Self-Organization / Complexity. History. Rayleigh-Benard: Patterns Russell: Soliton Waves Poincare: 3-Body Problem

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Why NonLinear Physics?

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  1. Why NonLinear Physics? • Everything is Nonlinear • Macro Systems • Gauge Theory, General Relativity • Qualitative Differences from Linear Case • Chaos / Fractals • Solitons • Self-Organization / Complexity

  2. History • Rayleigh-Benard: Patterns • Russell: Soliton Waves • Poincare: 3-Body Problem • Von Neumann: Cellular Automata • Lorenz: Weather Model • Mandelbrot: Fractals • Prigogine: Brusselator

  3. Recent Interests • Statistical Mechanics • Ergodic Problem • Complexity • Turbulence / Noises • Life • Natural Laws As Codes • S. Wolfram, “A New Kind od Science”

  4. NonLinear Physicswith Mathematica (Maple) for Scientists and Engineers R.H.Enns and G.C.McGuireSimon Fraser University Birkhauser 2001 (1997)

  5. Content Introduction Nonlinear Systems. Part I Nonlinear Systems. Part II Topological Analysis Analytic Methods The Numerical Approach

  6. Limit Cycles Forced Oscillators Nonlinear Maps Nonlinear PDE Phenomena Numerical Simulation Inverse Scattering Method

  7. References • R.L.Zimmerman, F.I.Olness “Mathematica for Physics”, Addison Wesley (1995) • D.Gulick, “Encounter with Chaos”, McGraw Hill (1992) • R.C. Hilborn, “Chaos & Nonlinear Dynamics”, 2nd ed., Oxford Univ Press (2000)

  8. Web Site: http://ckw.phys.ncku.edu.tw Email: class@ckw.phys.ncku.edu.tw

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