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

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Power laws 數律 When two physical variables are related, the simplest relationship is a power law. E.g. x = 1 2 gt 2 ∝ t 2 g Free fall x = vt ∝t Constant speed 2 x ≈ C t Random walk
Dimension D ( 度 ) Two ways to define D: 1. Mass ( 量 ) M~L D M~L D=1 M~L 2 D=2 M~L3 D=3 2. Stick length ( 度 ) l Coverage ( 數 ) N ~ 1/l D 數律 l=1, N=64 l=2, N=16=64/2 2 l=4, N=4=16/2 2
Page 1 and 2: Introduction to Complex Systems
Page 3 and 4: What is a complex system ()? 來
Page 8 and 9: The random walker’s trajectory ()
Page 10 and 11: 律 = 了 t 度 x 2 ≈ C t Still
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: Koch curve () Exercise: Can you sho
Page 20 and 21: Self-similarity cut Blow up Sierpi
Page 22 and 23: A practical example of self-similar
Page 24 and 25: Steady diffusion absorber ρ=0 R Cu
Page 26 and 27: If some sea animal is fed by taking
Page 28 and 29: Phase transitions Critical tempera
Page 30 and 31: Lattice-gas model of phase transiti
Page 32 and 33: A self-similar trajectory lacks cha
Page 34 and 35: Outline of talk • What is complex
Page 36 and 37: Sandpile as a paradigm of SOC Bak &
Page 38 and 39: Outline of talk • What is complex
Page 47 and 48: Gutenberg-Richter law for earthquak
Page 49 and 50: Slip-size distribution in earthquak
Page 51 and 52: The scales of cracks monolayer of m
Page 53 and 54: In presence of dissipation (e.g. fr
Page 55 and 56: σ xx Stress field Crack path A cr
Page 57 and 58: Length scale fragment area without
Page 59 and 60: Simulating cracks: a spring-block m
Page 61 and 62: Simulation using spring-block model
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Simulation using spring-block model
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Current research reported in first-
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Excerpt from Microcosmos -- Claude
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Two recent papers address those pro
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Looking closely •SEM scans reveal
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2. Mechanism of locomotion To move,
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The balance of momenta For dipolar
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How about other creatures? All rely
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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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