2. 揉皺的鋁罐和液晶 有什麼共通的性質?
清華大學物理系
洪在明

3. 小組成員和合作者： 林彥誌、侯宗昆、張菀馨、楊修維、蕭人豪 王永利、劉瑩、孫濟明、高文斾、裴東斐（北大）、白武斌（科大）、謝寧波（交大）
李晉元、王柏庭、譚弘、沈佳樑 3

4. 參考文獻：
Y. C. Lin, Y. L. Wang, Y. Liu, and TMH, “Crumpling under an ambient pressure”, PRL 101, (2008)
Y. C. Lin, Y. W. Lin, and TMH, “Crumpling wires in two dimensions”, PRE 78, (2008)
Y. C. Lin, J. M. Sun, H. W. Yang, Y. K. Hwu, C. L. Wang, and TMH, “X-ray tomography of a crumpled plastoelastic thin sheet”,
PRE 80, (2009)
Y. C. Lin, J. M. Sun, J. H. Hsiao, Y. K. Hwu, C. L. Wang, and TMH, “The spontaneous emergence of ordered phases in crumpled sheets”, PRL 103, (2009)
林彥誌、王永利、劉瑩和洪在明，The physics of crumpling淺談皺摺力學，物理雙月刊30卷4期，457頁(2008)

6. 演講大綱： Introduction (10 min) Intermediate pressure crumpling (5 min)
Wire crumpling (1D simulation) (2 min)
X-ray tomography (5 min)
High-pressure crumpling (2 min)
Theoretical approach (10 min)
Discussions (5 min) 6

7. 演講大綱： Introduction (10 min) Intermediate pressure crumpling (5 min)
Wire crumpling (1D simulation) (2 min)
X-ray tomography (5 min)
High-pressure crumpling (2 min)
Theoretical approach (10 min)
Discussions (5 min) 7

13. K. Matan, R. B. Williams, T. A. Witten, and S. R. Nagel,
The meta stable states
K. Matan, R. B. Williams, T. A. Witten, and S. R. Nagel,
PRL 88, (2002)

14. Noises due to crumpling
P. A. Houle and J. P. Sethna, PRE 54, 278 (1996)

15. Self-organized Voronoi diagram
C. A. Andresen and A Hansen, and J. Schmittbuhl,
Phys. Rev. E 76, (2007) 15

16. Simulations conclude:
Y. Kantor, M. Kardar, and D. R. Nelson, PRL 57, 791 (1986)
G. A. Vliegenthart and G. Gompper, Nature Mater. 5, 216 (1006)
T. Tallinen, J. A. Astrom, and J. Timonen, Nature Mater. 8, 25 (2009)

17. 演講大綱： Introduction (10 min) Intermediate pressure crumpling (5 min)
Wire crumpling (1D simulation) (2 min)
X-ray tomography (5 min)
High-pressure crumpling (2 min)
Theoretical approach (10 min)
Discussions (5 min) 17

18. 實驗裝置和樣品： Aluminum, copper, and lead foils BOPP, HDPE, PVC
Tissue, cloth
Different surface friction 18

21. 演講大綱： Introduction (10 min) Intermediate pressure crumpling (5 min)
Wire crumpling (1D simulation) (2 min)
X-ray tomography (5 min)
High-pressure crumpling (2 min)
Theoretical approach (10 min)
Discussions (5 min) 21

22. Y. C. Lin, Y. W. Lin, and TMH, PRE 78, 067101 (2008)

24. 演講大綱： Introduction (10 min) Intermediate pressure crumpling (5 min)
Wire crumpling (1D simulation) (2 min)
X-ray tomography (5 min)
High-pressure crumpling (2 min)
Theoretical approach (10 min)
Discussions (5 min) 24

25. Y. C. Lin, J. M. Sun, H. W. Yang, Y. K. Hwu, C. L. Wang, and TMH,
PRE 80, (2009)

27. Y. C. Lin, J. M. Sun, J. H. Hsiao, Y. K. Hwu, C. L. Wang, and TMH,
壓扁的鋁罐和液晶有什麼共通？
Y. C. Lin, J. M. Sun, J. H. Hsiao, Y. K. Hwu, C. L. Wang, and TMH,
PRL 103, (2009)

32. 演講大綱： Introduction (10 min) Intermediate pressure crumpling (5 min)
Wire crumpling (1D simulation) (2 min)
X-ray tomography (5 min)
High-pressure crumpling (2 min)
Theoretical approach (10 min)
Discussions (5 min) 32

35. 演講大綱： Introduction (10 min) Intermediate pressure crumpling (5 min)
Wire crumpling (1D simulation) (2 min)
X-ray tomography (5 min)
High-pressure crumpling (2 min)
Theoretical approach (10 min)
Discussions (5 min) 35

36. Why F-R power law?

37. 當 Smart撞上 Benz

38. 演講大綱： Introduction (5 min) Intermediate pressure crumpling (5 min)
Wire crumpling (1D simulation) (2 min)
X-ray tomography (5 min)
High-pressure crumpling (2 min)
Theoretical approach (10 min)
Discussions (10 min) 38

39. 後續工作： 複合材料的揉皺力學反應 把兩張相同的紙用不同數量的釘書針固定 模擬橡膠的硫化反應
設法將進入第二個power law行為的揉皺紙團直徑縮小到釐米尺寸，以便用x-ray觀察
檢驗摺痕所需的功和長度的1/3次冪成正比
（觸礁的其他嘗試包括大腦摺疊的機制和邊界條件對於指（掌）紋形狀的影響等）

40. 參考文獻：
Y. C. Lin, Y. L. Wang, Y. Liu, and TMH, “Crumpling under an ambient pressure”, PRL 101, (2008)
Y. C. Lin, Y. W. Lin, and TMH, “Crumpling wires in two dimensions”, PRE 78, (2008)
Y. C. Lin, J. M. Sun, H. W. Yang, Y. K. Hwu, C. L. Wang, and TMH, “X-ray tomography of a crumpled plastoelastic thin sheet”,
PRE 80, (2009)
Y. C. Lin, J. M. Sun, J. H. Hsiao, Y. K. Hwu, C. L. Wang, and TMH, “The spontaneous emergence of ordered phases in crumpled sheets”, PRL 103, (2009)
林彥誌、王永利、劉瑩和洪在明，The physics of crumpling淺談皺摺力學，物理雙月刊30卷4期，457頁(2008)

41. 感謝：
國科會、清華大學、清大理學院的支助
物理系地下室液態氮工廠的廖紹達和機械工廠的田振滿先生
物理系同仁施宙聰、林秀豪、陳培亮教授

42. Evolution model for cyclic competitions - 林彥誌、TMH和林秀豪石頭
Frey et al., PRL 102,
(2009) 剪刀 布

44. Fluctuations lead to
dissipation
where
and

45. The crumpling lab around the world
uniaxial
uniaxial 2D
M A F Gomes
Brazil
A Boudaoud
ENS Paris
Alexander S. Balankin
Mexico
The crumpling lab around the world 3D 3D
uniaxial
Clark University
Kudrolli
Cornell University
James P. Sethna
U. Chicago
S. R. Nagel 45