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課程名稱 |
流體非線性動力學概論
INTRODUCT TO NONLINEAR DYNAMICS IN FLUIDS |
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開課學期 |
94-2 |
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授課對象 |
工學院 水利工程組 |
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授課教師 |
劉格非 |
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課號 |
CIE7061 |
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課程識別碼 |
521 M5970 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二2(9:10~10:00)星期四6,7(13:20~15:10) |
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上課地點 |
土220綜203 |
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備註 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
1. Introduction 1 week
1.1 Examples of nonlinear and linear systems.
1.2 Harmonic oscillator — Introduction to phase plane
2. Nonlinear Vibrator 4 weeks
2.1 Phase plane techniques for systems of O.D.E.; Limit cycle.
2.2 Pertubation method for weakly nonlinear systems.
2.3 Multiple scale, Poincare-Lindstedt and Averaging methods.
2.4 Forced nonlinear vibration : Jump phenomena; Instability.
2.5 Relaxation oscillation; (Super harmonic and Subharmonic resonance).
2.6 Extension to more d.o.f. (stability of a periodic motion : Mathieu’s eq. )
3. Nonlinear Stability and Bifurcation 1 2 / 3 week
3.1 Typical examples of bifurcation.
3.2 Numerical techques for tracing bifurcation.
3.3 Introduction to chaotic behavior of nonlinear systems; logistic map.
4. Data Analysis for Nonlinear Systems 2 weeks
4.1 Fourier transform.
4.2 Poincare section.
4.3 Lyaponov exponent.
4.4 Fractal dimensions.
5. Strange Attractors 1 week
5.1 Lorenz attractor.
5.2 Henon attractor.
6. **Routes to Temporal Chaos (subject to schedule) （3 weeks）
6.1 Example of dynamical system : Rayleigh-Benard convection.
6.1 Subharmonic cascade (Period doubling).
6.2 Intermittency.
6.3 Quasiperiodicity.
7. Linearization of Nonlinear Stochastic System 1 week by Prof. Lee if poss.
7.1 Taylor’s Series Expansion, the Extended Kalman Filter.
7.2 Statistical Linearization.
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課程目標 |
This course provides an introduction to methodology in dealing with nonlinear systems. Roughly half of the course will be devoted to weakly nonlinear systems where analytical means are available. Then we deal with data analysis for fully nonlinear systems. Finally, we discuss the three routes to chaos.
Since this course is designed for engineering students, all theory derivation will be simplified or replaced by physical arguments. Students who are interested mainly in rigorous derivations for related theories should consider some other courses.
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課程要求 |
1. Home work is the extension of classes. Plenty of new material will be inserted in home work. Therefore, discussion of homework is encouraged. Midterm and final are take home exams.
2. Term paper should be a reading study of the lastest paper (within 2 yrs) from the journal “Nonlinear dynamics”(in Englineering Library). Paper subject should be decided right after midterm. Term paper due on May 27th. Everyone in the class will get a copy. Then everyone should present their paper on May 30th or June 3rd.
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
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參考書目 |
1. Berge, P.,Pomean, Y & Vidal. C. “Order Within Chaos” John Wiley & Sons, 1984. (QA614.8 B417)
2. Nayfeh, A.H. & Mood, D.T. “Nonlinear Oscillations” John Wiley & Sons, 1979. (QA402 N231)
3. Witham, G..B. “Linear and Nonlinear Waves” John Wiley & Sons, 1974. (QA927 W589)
4. Beltrami, E. “Mathematics for Dynamic modeling” , 10987
5. Shuster, H.G. “Deterministic Chaos, an introduction” (QC174.84 S38)
6. Cvitanovic, P. ed. “Universality in Chaos”, Adam Hilger Ltd. 1984.
7. Holden, A.V. ed. “Chaos”, Princeton, 1986.
8. Thompson, J.M.T. and Stewart, H.B. “Nonlinear dynamics and chaos”, Wiley, 1986.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
HW problems |
40% |
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2. |
Midterm |
30% |
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3. |
Term Paper |
30% |
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