扭轉氣球是大家兒時共同的回憶，可以做成狗、劍跟花。在製作這些玩具的時候，最基礎的技巧是扭轉跟彎曲。在這篇論文中，我們專注於扭轉不同長度與半徑所產生不同的相，例如：直線（straight）, 塌縮（snapping）, 彎曲型（spiral） and 超螺旋（supercoiling），實驗上得到了一個相圖。我們建立了一個理論模型跟運算分子動力學模擬，重複驗證了實驗的正確性。最後我們比較了氣球塌縮跟水滴截斷的現象。

Twisting balloons, a common childhood memory, can turn them into different shapes, such as dogs, swords, flowers, crowns etc. To make a balloon toy, the most basic and useful tricks are twisting and bending. In this thesis, we focus on twisting and possible configurations for balloons with different radius and length. It turns out that they exhibit four distinct phases, i.e., straight, snapping, spiral and supercoiling. Phase diagram is determined by experiment and double-checked by Molecular Dynamics (MD) simulations. There exists hysteresis when twist is reversed. We provide theoretical models that can explain and predict the correct form of phase boundaries. Finally, comparisons are made between the snapping of balloons and the pinch-off phenomenon for liquid drops.

Acknowledgements
Abstract i
Introduction 1
Method. 9
Results 15
Conclusion and Discussions 31
References 33

[1] Mattia Gazzola, Nicholas Charles and L. Mahadevan. Topology, geometry, and mechanicsof strongly stretched and twisted filaments: Solenoids, plectonemes, and artificial musclefibers. Phys. Rev. Lett., 123, 208003 (2019).
[2] Julien Chopin and Arshad Kudrolli. Helicoids,wrinkles,andloopsintwistedribbons. Phys.Rev. Lett., 111, 174302 (2013).
[3] Itai Cohen, Michael Brenner, Eggers Jens, and Nagel Sidney, R. Two fluid drop snap-offproblem: Experiments and theory. Phys. Rev. Lett., 83, 1147 (1999)
[4] Amir A Pahlavan, Howard A Stone, Gareth H McKinley, and Ruben Juanes. Restoringuniversality to the pinch-off of a bubble. Proc. Natl. Acad. Sci. U.S.A., 116, 13780 (2019)
[5] Benny Davidovitch, Robert D. Schroll, Mokhtar Adda-Bedia Dominic Vella, and En-rique A. Cerda. Prototypical model for tensional wrinkling in thin sheets. Proc. Natl.Acad. Sci. U.S.A., 108, 18227 (2011)