我們實驗室和故宮博物院合作，研究古畫中的起瓦現象，起瓦是指畫軸邊緣會向上翹起的現象，這個現象已經存在千年之久，起瓦不僅會造成外觀上的不美觀，也會造成古畫的損傷，因此，如何減低起瓦就成為一個重要的課題。我們根據不同種類的畫軸，將他們分成不同型態，我們發現起瓦的高度會滿足一些簡單的冪次關係，我們用實驗、模擬(MD)來驗證我們的理論，最後，在不違背傳統修畫的原則下，我們提出三種方法來改善起瓦。
論文中第二部分則是要探討混和揉皺，之前已經有許多文章在討論薄膜的揉皺，但是他們的重點是放在單張薄膜，他們有發現許多性質，另如紙團半徑和施加的外力呈現冪次關係，但是，這些特性在混和揉皺還會成立嗎?除此以外，更有趣的問題是兩張紙團是如何分配外界系統給予的能量?我們可以用簡單的熱力學去解釋嗎(例如用熱鐵棒插入冷水中溫度最後會達到平衡的觀念來解釋)?我們利用分子動力模擬來回答這些問題，我們發現，雖然許多冪次關係依舊成立，但是他們的指數卻會有所不同，此外，很多的實驗結果可以用平均場近似的方法來解釋。

Our group collaborates with the National Palace Museum in Taipei, Taiwan on a problem that has been existed for thousands of years. Qi-Wa, a Chinese phrase, means the up curl on the edge of the scrolls. It not only decreases the value in aesthetics, but also incurs damage on the scrolls. In order to preserve the painting, it is important to alleviate the deformation. In this thesis, we construct four models to explain Qi-Wa phenomenon to different types of scrolls and try to understand their physical mechanism. We find Qi-Wa height to follow simple scaling laws and check these relations by experiment and Molecular Dynamics(MD) simulations. Furthermore, we propose ways to mitigate the Qi-Wa under conditions that will not violate the traditional and aesthetic standards.

On the second part of the thesis, we discuss a more severe type of deformation on the thin sheets; namely. the daily phenomenon of crumpling. We will focus on the crumpling of two different sheets together. There are a lot of properties that have been found in the crumpled single sheet. For example, the external force and the crumpled ball radius $R$ obey a scaling relation and the ridge length follows the log-normal distribution. However, there are no studies on whether these properties exist when we crumple two different materials together. Furthermore, how does the energy distribute on the two separate sheets when the compaction increases? Can we explain their behavior by the concept of thermodynamic temperature? What's the role of the ridge-ridge interactions? We use the MD simulation as a tool to solve these questions. We find that some scaling laws still hold in the co-crumpling system except their exponents are changed. For instance, the force and the $R$ still obey the power-law relation in co-crumpling but the exponent of the co-crumpling will be different from the exponent of single sheets. Besides, we can explain some results by the mean-field approximation.

[1] Robert Has van Gulik, Chinese pictorial art: as viewed by the connoisseur notes on the means and methods of traditional Chinese connoisseurship of pictorial art, based upon a study of the art of mounting scrolls in Chinaand Japan (Taipei: Southern Materials Center; Roma:Istituto italiano per il medio ed estremo oriente, 1993).
[2] V. D. Daniels and L. E. Fleming, The cockling and curling of paper in museum, page 155-162 in Proc. Of the Symposium in Conservation of Historic and Artistic Works on
Paper, ed. by H. D. Burgress (1988).
[3] Valerie Lee, Xiangmei Gu and Yuan-Li Hou, The treatment of Chinese ancestor portraits:An introduction to Chinese painting conservation techniques, Journal American Institute
for Conservation 42, 463-477 (2003).
[4] I. Nielsen and D. Priest, Dimensional stability of paper in relation to lining and drying procedures, Paper Conservator 21, 26-35 (1997).
[5] A. C. Jain and R. A. Cairncross, Effect of moisture sorption on microstructure and properties of paper, 12th international Coating Science and Technology Symporsium, p.190(Sep. 20-22, Rochester, 2004).
[6] T. Leppanen, Effect of fiber orientation on cockling of paper, Doctoral Dissertation (Kuo-pio, University of Kuopio, 2007).
[7] D. L. Blair and A. Kudrolli, Geometry of Crumpled Paper, Phys. Rev. Lett. 94, 166107(2005).
[8] Y. C. Lin, Y. L. Wang, Y. Liu and T. M. Hong, Crumpling under an ambient pressure.Phys. Rev. Lett. 101,125504 (2008).
[9] W. Bai, Y. C. Lin, T. K. Hou and T. M. Hong, Scaling relation for a compact crumpled thin sheet. Phys. Rev. E 82, 066112 (2010).
[10] T. Tallinen, L. A. Astrom and J. Timonen, The eect of plasticity in the crumpling of thin sheets. Nature Mater. 8, 25-29 (2009).
[11] G. A. Vliegenthaqrt and G. Gompper, Forced crumpling of self-avoiding elastic sheets. Nature Mater. 5, 216-221 (2006).
[12] A. S. Balankin, I. C.Silva, O. A. Martinez and O. S. Huerta, Scaling properties of randomly folded plastic sheets. Phys. Rev. E 75, 051117 (2007).
[13] Wood, A. J. Witten's lectures on crumpling. Physica A313, 83-109 (2002).
[14] S. F. Liou, C. C. Lo , M. H. Chou, P. Y. Hsiao and T. M. Hong, Effect of ridge-ridge interactions in crumpled thin sheets, arXiv:1303.2180v2.
[15] C. A. Andresen, A. Hansen and J. Schmittbuhl, Ridge network in crumpled paper. Phys. Rev. E 76, 026108(2007).
[16] T. Yokoyama and K. Nakai, Evaluation of in-plane orthotropic elastic constants of paper and paperboard, Proc. of Annual Conference & Exposition on Experimental and Applied Mechanics (2007).
[17] J. D. Weeks, D. Chandler and H. C. Andersen, Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 54, 5237-5247 (1971).
[18] Chiou-Ting Hsu and Marvin Huang, Ridge Network Detection in Crumpled Paper via Graph Density Maximization, IEEE Trans. Image Process, vol. 21, no. 10, pp. 44984501,
Oct. (2012)