複雜系統之簡介(梁鈞泰) - 中研院物理研究所- Academia Sinica

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Brownian motion & random walk 朗行 Let us start with a simple system: Robert Brown (1773–1858) 朗不行不 10 -6 2 µm polysteryne spheres in water doing random walks
Page 1 and 2: Introduction to Complex Systems
Page 3: What is a complex system ()? 來
Page 8 and 9: Random walk of a drunkard ( ) He mo
Page 10 and 11: 律 = 了 t 度 X 2 ≈ C t Still
Page 12 and 13: Exercises: Can we talk about the sp
Page 14 and 15: Fractal dimension 度 fractal B. M
Page 16 and 17: Sierpinski gasket l is the stick le
Page 18 and 19: Exercise: What is the average densi
Page 20 and 21: Fractal dimension of a random walk
Page 22 and 23: 切 It looks random, but it also l
Page 24 and 25: The motion of a random walker is de
Page 26 and 27: Similar result for a disk absorber:
Page 28 and 29: Diffusion Limited Aggregation (DLA)
Page 30 and 31: Power laws in thermodynamic quantit
Page 32 and 33: Scale invariance or self-similarity
Page 34 and 35: P( f ) ≈ 1 f α White noise α=0
Page 36 and 37: Self-Organized Criticality (SOC)
Page 38 and 39: Open-boundary conditions are impor
Page 40: One major success of SOC is in eart
Page 49 and 50: self-organized critical earthquake
Page 51 and 52: Note that we have only talked about
Page 53 and 54: Current research reported in first-
Page 55 and 56:
Excerpt from Microcosmos -- Claude
Page 57 and 58:
Two recent papers address those pro
Page 59 and 60:
Looking closely •SEM scans reveal
Page 61 and 62:
2. Mechanism of locomotion To move,
Page 63 and 64:
The balance of momenta For dipolar
Page 65 and 66:
How about other creatures? All rely
Page 67 and 68:
What do we learn from the water str
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複雜系統之簡介(梁鈞泰) - 中研院物理研究所- Academia Sinica

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