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

• 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

Email:

[email protected]