在平面邊界的侷限下，微觀三維液體沿著形成層狀有序結構。瞬間焠冷
液體至凝固點附近可使表面層化影響傳至三維液體內部，形成多層堆疊之有
序結構，但熱擾動仍能破壞層狀結構。然而，儘管過去對微觀結構、微觀運
動和與體積液體不同的黏彈性響應進行了深入研究，但在淬冷後的弛豫過程
動力行為，及在此過程中螺旋差排缺陷(screw dislocations)如何產生與湮滅之動力行為，仍然是一個挑戰性問題。
螺旋差排缺陷是一種繞著螺旋前沿纏繞的絲狀拓撲缺陷，它們在分層系統中隨處可見，如分層固體和弱擾動的非穩平面波。然而，由於前者為固體，無法通過其研究螺旋差排缺陷動力行為，而後者的高波速則使其難以觀察，因此螺旋差排缺陷的通用動力學行為仍然難以捉摸。
本研究透過分子動力學電腦模擬，利用二邊界平面侷限下焠冷後的冷
Yukawa 液體對上述議題進行研究。研究以粗粒化程式建構三維微粒密度之
時空演變，確定螺旋差排缺陷的位置。數值上證明了在淬冷後限制誘導層狀
結構的弛豫過程中觀察到了具有非凍結動力學並自發生成的螺旋差排缺陷；
更揭示了它們的動力學行為和拓撲起源。我們首度觀察到空間中可形成具對
偶缺陷絲的缺陷環(defect loop)，或W 形狀多條交替對偶缺陷絲所構成的大型缺陷環。在淬冷後，缺陷絲的數目隨弛豫時間的增長而緩減。熱擾動所產生的粒子層扭動不穩定性(undulation instability) 的時空增長和衰減，可誘發層面在小尺度扭折(kink)，進而造成一連串相鄰層面的破裂與重連，形成在撕裂-重連線二端點被相反旋轉層面方向所環繞的對偶螺旋缺陷絲產生之主因。而相反的機制可使二對偶缺陷絲湮滅。粒子層扭動不穩定性也對缺陷環或缺陷絲之小尺度波動(fluctuation)具有關鍵作用。此外，二相靠近具有相反或相同螺旋性的缺陷絲可斷裂與重連，進而導致新的分離二缺陷環的形成與其相反程序，從而使缺陷環分裂或合併。此實驗之重要發現，可供建構具層狀結構之非穩系統中，如固體、非穩平面波中螺旋缺陷絲動力行為與其交互作用之普世機制。

For liquids in a tight gap, the two flat boundaries can suppress transverse particle motion and induce layered structure. Nevertheless, regardless of the past intensive studies on the micro-structure, micro-motion, and viscoelastic response deviating from those of the bulk liquid, the layering dynamics in its transient relaxation after quenching remains an elusive challenging issue, especially from the perspective of screw dislocations.
Screw dislocations (SDs) are filament-like topological defects winded around by helical fronts. They are omnipresent in layered systems such as layered solids and weakly disordered traveling waves. Nevertheless, the generic
dynamical behaviors of SDs remain elusive because the former usually exhibit frozen dynamics and high wave speed, while the latter makes them difficult to observe.
Here, using the confined liquid after quenching as a platform, we numerically demonstrate the observation of spontaneously generated SDs with unfrozen dynamics in the transient relaxation of confinement-induced layering;
and unravel their generic dynamical behaviors and topological origins. It is found that the total number of SDs decreases and levels off with increasing time after
quenching. The spatiotemporal growth and decay of layer undulation instability, which causes the layer kinking/rupturing/reconnection, play a crucial role in
forming fluctuating SD loops or strings of connected SD filaments (SDFs) with alternative helicities. In addition, the breaking/reconnection of approaching SDFs with opposite or same helicities leads to the formation of new separated
SDFs, resulting in the shedding or pinching of SD loops.

Bibliography

[1] C. L. Rhykerd, M. Schoen, D. J. Diestler, and J. H. Cushman, Epitaxy in simple classical fluids in micropores and near-solid surfaces. Nature 330, 461 (1987).

[2] P. A. Thompson, G. S. Grest, and M. O. Robbins, Phase transitions and universal dynamics in confined films. Phys. Rev. Lett. 68, 3448 (1992).

[3] D. G. Grier and C. A. Murray, The microscopic dynamics of freezing in supercooled colloidal fluids. J. Chem. Phys. 100, 9008 (1994).

[4] J. Klein and E. Kumacheva, Confinement-Induced Phase Transitions in Simple Liquids. Science 269, 816 (1995).

[5] B. Bhushan, J. N. Israelachvili, and U. Landman, Nanotribology: friction, wear and lubrication at the atomic scale. Nature 374, 607 (1995).

[6] J. Gao, W. D. Luedtke, and U. Landman, Layering Transitions and Dynamics of Confined Liquid Films. Phys. Rev. Lett. 79, 705 (1997).

[7] S. Granick, Soft Matter in a Tight Spot. Physics Today 52(7), 26 (1999).

[8] M. Zuzic, A. V. Ivlev, J. Goree, G. E. Morfill, H. M. Thomas, H. Rothermel, U. Konopka, R. Sütterlin, and D. D. Goldbeck, Three-Dimensional Strongly Coupled Plasma Crystal under Gravity Conditions. Phys. Rev. Lett. 85, 4064 (2000).

[9] M. Heuberger, M. Zäch, and N. D. Spencer, Density Fluctuations Under Confinement: When Is a Fluid Not a Fluid? Science 292, 905 (2001).

[10] L. W. Teng, P. S. Tu, and L. I, Microscopic Observation of Confinement-Induced Layering and Slow Dynamics of Dusty-Plasma Liquids in Narrow Channels. Phys. Rev. Lett. 90, 245004 (2003).

[11] R. Haghgooie and P. S. Doyle, Structure and dynamics of repulsive magnetorheological colloids in two-dimensional channels. Phys. Rev. E 72, 011405 (2005).

[12] K. Sandomirski, E. Allahyarov, H. L öwen, and S. U. Egelhaaf, Heterogeneous crystallization of hard-sphere colloids near a wall. Soft Matter 7, 8050 (2011).

[13] S. A. Khrapak, B. A. Klumov, P. Huber, V. I. Molotkov, A. M. Lipaev, V. N. Naumkin, A. V. Ivlev, H. M. Thomas, M. Schwabe, G. E. Morfill, O. F. Petrov, V. E. Fortov, Yu. Malentschenko, and S. Volkov, Fluid-solid phase transitions in three-dimensional complex plasmas under microgravity conditions. Phys. Rev. E 85, 066407 (2012).

[14] L. Chen, C. R. Cao, J. A. Shi, Z. Lu, Y. T. Sun, P. Luo, L. Gu, H. Y. Bai, M. X. Pan, and W. H. Wang, Fast Surface Dynamics of Metallic Glass Enable Superlatticelike Nanostructure Growth. Phys. Rev. Lett. 118, 016101 (2017).

[15] S. Arai and H. Tanaka, Surface-assisted single-crystal formation of charged colloids. Nature Phys. 13, 503 (2017).

[16] B. Steinmüller, C. Dietz, M. Kretschmer, and M. H. Thoma, Crystallization process of a three-dimensional complex plasma. Phys. Rev. E 97, 053202 (2018).

[17] Q. L. Bi, Y. J. Lü,and W. H. Wang, Multiscale Relaxation Dynamics in Ultrathin Metallic Glass-Forming Films. Phys. Rev. Lett. 120, 155501 (2018).

[18] W. Wang, H. W. Hu, and L. I, Surface-Induced Layering of Quenched 3D Dusty Plasma Liquids: Micromotion and Structural Rearrangement. Phys. Rev. Lett. 124, 165001 (2020).

[19] Q. Gao, J. Ai, S. Tang, M. Li, Y. Chen, J. Huang, H. Tong, L. Xu, H. Tanaka, and P. Tan, Fast crystal growth at ultra-low temperatures. Nat. Mater. 20, 1431 (2021).

[20] Y. C. Zhao, H. W. Hu, and L. I, Percolation transitions of confinement-induced layering and intralayer structural orders in three-dimensional Yukawa liquids Phys. Rev. E 107, 044119 (2023).

[21] H. Moffatt, The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117 (1969).

[22] J. Koplik and H. Levine, Vortex reconnection in superfluid helium. Phys. Rev. Lett. 71, 1375 (1993).

[23] A. T. A. M. de Waele and R. G. K. M. Aarts, Route to vortex reconnection. Phys. Rev. Lett. 72, 482 (1994).

[24] M. Farge, G. Pellegrino, and K. Schneide, Coherent vortex extraction in 3D turbulent flows using orthogonal wavelets. Phys. Rev. Lett. 87, 054501 (2001).

[25] T. Galantucci, and H. Saito, Orthogonal and antiparallel vortex tubes and energy cascades in quantum turbulence. Phys. Rev. Fluids 3, 104606 (2018).

[26] G. P. Bewley, M. S. Paoletti, K. R. Sreenivasan, and D. P. Lathro, Characterization of reconnecting vortices in superfluid helium. Proc. Natl. Acad. Sci. U.S.A. 105(37), 13707 (2008).

[27] L. Galantucci, A. W. Baggaley, N. G. Parker, and C. F. Barenghi, Crossover from interaction to driven regimes in quantum vortex reconnections. Proc. Natl. Acad. Sci. U.S.A. 116(25), 12204 (2019).

[28] M. Vinson, S. Mironov, S. Mulvey, and A. Pertsov, Control of spatial orientation and lifetime of scroll rings in excitable media. Nature 386, 477 (1997).

[29] S. Alonso, F. Sagués, and A. S. Mikhailov, Taming Winfree Turbulence of Scroll Waves in Excitable Media. Science 299, 1722 (2003).

[30] J. C. Reid, H. Chaté,and J. Davidsen, Filament turbulence in oscillatory media. Europhys. Lett. 94, 68003 (2011).

[31] R. H. Clayton, E. A. Zhuchkova, and A. V. Panfilovc, Phase singularities and filaments: Simplifying complexity in computational models of ventricular fibrillation. Prog. Biophys. Mol. Biol 90, 378 (2006).

[32] T. H. Tan, J. Liu, P. W. Miller, J. Dunkel, and N. Fakhri, Topological turbulence in the membrane of a living cell. Science 16, 657 (2020).

[33] J. Liu, J. F. Totz, P. W.Miller, A. D. Hastewell, Y. C. Chao, J. Dunkel, and N. Fakhri, Topological braiding and virtual particles on the cell membrane. Proc. Natl Acad. Sci. U.S.A. 118(34), e2104191118 (2021).

[34] P. M. Chaikin, T. C. Lubensky, and T. A. Witten, Principle of Condensed Matter Physics Vol. 1 (Cambridge Univ. Press, 1995), Chapter 9.

[35] M. Beliaev, D. Z öllner, A. Pacureanu, P. Zaslansky, and I. Zlotnikov, Dynamics of topological defects and structural synchronization in a forming periodic tissue. Nature Phys. 17, 410 (2021).

[36] J. Gim, A. Koch, L. M. Otter, B. H. Savitzky, S. Erland, L. A. Estroff, D. E. Jacob, and R. Hovden, The mesoscale order of nacreous pearls. Proc. Natl. Acad. Sci. U.S.A. 118(42), e2107477118 (2021).

[37] H. S. Kang, C. Park, H. Eoh, C. E. Lee, D. Y. Ryu, Y. Kang, X. Feng, J. Huh, E. L. Thomas, and C. Park, Visualization of nonsingular defect enabling rapid control of structural color. Science Advances 8, eabm5120 (2022).
[38] J. F. Nye and M. V. Berry, Dislocations in wave trains. Proc. B. Soc. Lond. A 336, 165 (1974).

[39] B. T. Hefner and P. L. Marston, An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems. J.
Acoust. Soc. Am. 10, 3313 (1999).

[40] J. L. Thomas and R. Marchiano, Pseudo Angular Momentum and Topological Charge Conservation for Nonlinear Acoustical Vortices. Phys. Rev. Lett. 91, 244302 (2003).

[41] S. Gspan, A. Meyer, S. Bernet, and M. Ritsch-Marte, Optoacoustic generation of a helicoidal ultrasonic beam. J. Acoust. Soc. Am. 115, 1142 (2004).

[42] K. Volke-Sepulveda, A. O. Santillan, and R. R. Boullosa, Transfer of Angular Momentum to Matter from Acoustical Vortices in Free Space. Phys. Rev. Lett. 100, 024302 (2008).

[43] R. Marchiano and J. L. Thomas, Doing Arithmetic With Nonlinear Acoustic Vortices. Phys. Rev. Lett. 101, 064301 (2008).

[44] A. M. Yao and M. J. Padgett, Orbital angular momentum: origins, behavior and applications. Adv. Opt. Photon. 3, 161 (2011).

[45] P. K. Shukla, Twisted dust acoustic waves in dusty plasmas. Physics of Plasmas 19, 083704 (2012).

[46] E. Hemsing, A. Knyazik, M. Dunning, D. Xiang, A. Marinelli, C. Hast, and J. B. Rosenzweig, Coherent optical vortices from relativistic electron beams. Nature Phys. 9, 549 (2013).

[47] M. C. Chang, Y. Y. Tsai, and L. I, Observation of 3D defect mediated dust acoustic wave turbulence with fluctuating defects and amplitude hole filaments. Phys. Plasmas 20 083703 (2013).

[48] Y. Y. Tsai and L. I, Observation of self-excited acoustic vortices in defect-mediated dust acoustic wave turbulence. Phys. Rev. E 90, 013106 (2014).

[49] Y. Y. Tsai, J. Y. Tsai, and L. I, Generation of acoustic rogue waves in dusty plasmas through three-dimensional particle focusing by distorted waveforms. Nature Phys. 12, 573 (2016).

[50] J. I. Tsai, P. C. Lin, and L. I, Single to multiple acoustic vortex excitations in the transition to defect-mediated dust acoustic wave turbulence. Phys. Rev. E 101, 023210 (2020).

[51] M. Cromb, G. M. Gibson, E. Toninelli,  M. J. Padgett, E. M. Wright, and D. Faccio, Amplification of waves from a rotating body. Nat. Phys. 16, 1069 (2020).

[52] S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 117, 1 (1995).

[53] See D. Gabor, Theory of Communication. J. Inst. Elect. Eng. Part III, Radio Commun. 93, 429 (1946) for the Hilbert transform.

[54] Y. X. Zhang, H. W. Hu, Y. C. Zhao, and L. I, Screw dislocation dynamics in confinement-induced layering of Yukawa liquids after quenching. Physics Review Letter (2023). Currently under revision.