Why NonLinear Physics? Everything is Nonlinear –Macro Systems –Gauge Theory, General Relativity Qualitative Differences from Linear Case –Chaos / Fractals.

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Presentation transcript:

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 Von Neumann: Cellular Automata Lorenz: Weather Model Mandelbrot: Fractals Prigogine: Brusselator

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

NonLinear Physics with Mathematica (Maple) for Scientists and Engineers R.H.Enns and G.C.McGuire Simon Fraser University Birkhauser 2001 (1997)

Content 1.Introduction 2.Nonlinear Systems. Part I 3.Nonlinear Systems. Part II 4.Topological Analysis 5.Analytic Methods 6.The Numerical Approach

7.Limit Cycles 8.Forced Oscillators 9.Nonlinear Maps 10.Nonlinear PDE Phenomena 11.Numerical Simulation 12.Inverse Scattering Method

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)

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