Why NonLinear Physics? Everything is Nonlinear –Macro Systems –Gauge Theory, General Relativity...
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Transcript of Why NonLinear Physics? Everything is Nonlinear –Macro Systems –Gauge Theory, General Relativity...
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 Physicswith Mathematica (Maple)
for Scientists and Engineers
R.H.Enns and G.C.McGuireSimon 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)
Web Site: http://ckw.phys.ncku.edu.tw
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