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姓名	羅偉碩(Wei-Shuo Lo)  查詢紙本館藏	畢業系所	物理學系
論文名稱	(Multiscale vorticity waves and vorticity wave vortices in two-dimensional dusty plasma crystals)
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摘要(中)	波渦（Wave vortices）作為一種相干實體（coherent entity），已被廣泛觀察存在於各種波動系統中，例如光學波、聲學波、彈性波、水面波、量子流體波及原子波等。其特徵為螺旋形波前（helical wavefronts）圍繞具有相位無法定義與零振幅的螺旋位錯絲（screw dislocation filaments）纏繞。先前的研究已證實，在線性波動介質中，通過不同傳播方向的單尺度平面波的疊加，或相同傳播方向但具有不同相位的平面波疊加，以產生波渦。在非線性波動介質中，調制不穩定性(modulational instability)會引發波形起伏破裂，進而在弱無序波中產生對偶波渦，並在波湍流中產生多尺度波渦。然而，在線性無序多尺度波動系統中，多尺度波渦是否存在以及如何產生仍然未知。 微觀層面上，粒子間的相互作用與無序熱擾動之間的競爭，會在冷晶體中激發出具有不同傳播方向的多尺度無序聲子（disordered phonons）。在遠低於熔點的低溫晶體中，聲子彼此正交，不會相互作用。因此，諧和晶體（harmonic crystal）成為探索多尺度時空波動動力學及檢驗波渦是否在線性無序多尺度波動系統中作為相干實體的絕佳範例。 在本研究中，我們通過經驗模態分解（empirical mode decomposition），以實驗與數值模擬的方式，首次在低粘滯阻尼下的二維微粒電漿晶格與Yukawa晶體的熱驅動多尺度無序振動中，證實多尺度聲渦波(acoustic vorticity waves)與聲渦波渦（vorticity wave vortices）作為多尺度相干實體的存在。在每一低頻模態中，聲渦波以不規則的渦狀結構出現，渦漩的形狀與渦度在時空中演化，主要由橫向聲子貢獻。在xyt空間中，這些無序波可視為一組局域化的相干實體，其中聲渦波的波峰環繞蟲狀的螺旋錯位絲(screw-dislocation filaments)，聲渦波渦以不規則存活時間運動，並與對偶渦度波渦湮滅，呈現拉伸指數分佈(stretched exponential)的生命週期與短程空間相關性。
摘要(英)	Wave vortices (WV), as coherent entities, have been widely observed in various wave systems, such as optical, acoustic, elastic, water surface, quantum-fluid and atom waves. They are characterized by helical wave fronts winding around screw dislocation filaments with undefined phases and null amplitudes. Previous studies have demonstrated the generation of WVs in linear wave media through the superposition of single-scale plane waves with different propagation directions or the same propagation direction with different phases. In nonlinear wave media, modulation instability induces waveform undulations, leading to pair generation of WVs and multiscale WVs in weakly disordered waves and wave turbulence, respectively. However, whether multiscale WVs exist and how multiscale WVs can be generated in the linear disordered multiscale wave system remains open question. Down to the microscopic level, the competition between mutual interactions among particles and thermal agitations excites multiscale disordered phonons with various propagation directions in cold crystals. In cold solids far from the melting transition, thermally excited small-amplitude phonons do not interact with each other, making harmonic crystals excellent examples for exploring multiscale spatiotemporal waveform dynamics and testing whether WVs act as coherent entities in linear disordered multiscale wave system. In this work, employing empirical mode decomposition, we experimentally and numerically demonstrate the observations of multiscale acoustic vorticity waves and vorticity wave vortices as multiscale coherent entities in thermally driven disordered vibrations of two-dimensional dusty plasma and Yukawa crystals under low viscous damping. In each low-frequency mode, the vorticity waves appear in the form of irregular vortex arrays with spatiotemporally varying vortex shapes and vorticities, predominately contributed by transverse phonons. These disordered waves can be viewed as a collection of localized coherent entities of multiscale vorticity wave vortices with vorticity wave crests winding around worm-like screw-dislocation filaments in the xyt space, exhibiting stretched-exponential lifetime distribution and short-range spatial correlations. These findings provide insights into the complex dynamics of disordered linear wave systems and offers a novel framework to study disordered waves in various media for advances in condensed matter physics and material science.
關鍵字(中)	★ 微粒電漿 ★ 波渦	關鍵字(英)	★ Dusty plasmas ★ Wave vortex
論文目次	Chapter 1 Introduction………………………………………………..……… 1 Chapter 2 Background………………………………………………...……... 4 2.1 Coherent excitations in wave systems…..………….…....…. 4 2.1.1 wave vortices……...………………………….……….. 4 2.1.2 Generation of wave vortices……..……………....…… 4 2.2 Vibrational modes in solids………….………………...…… 6 2.2.1 Phonons…...…………………………………...….…... 6 2.2.2 Dynamical matrix and Hessian matrix methods for studying vibrations in condensed states…………....……….. 6 2.3 Dusty plasmas for acoustic wave investigations…….…..…. 8 Chapter 3 Methods……………………………………………………..…….. 11 3.1 Experiment………...…………………………………….….. 11 3.2 Simulation………...………………………………………… 12 3.3 Data analysis………………………………………...……… 14 3.2.1 Wave dispersion relation…….…….…….…….….. 14 3.3.2 Empirical mode decomposition…….……….…… 15 3.3.3 Vorticity field…….……….………………….…… 18 Chapter 4 Result and Discussion……………………………….….…………. 19 4.1 Multiscale phonons in two-dimensional dusty plasma crystals………………………………………………………. 19 4.2 Decomposition of particle displacement into multiscale modes..…………….………………….……….……….…… 21 4.3 Multiscale vorticity waves and vorticity wave vortices as coherent excitations……………………….………………… 23 4.4 Self-similar dynamical behaviors of multiscale vorticity wave vortices…………………………….………….……… 26 4.5 Simple physical model of vorticity waves and VWV generation…………………………………………………… 28 4.6 Simulation results………………………………………….... 31 Chapter 5 Conclusion……………………………………………………….. 34 Reference 37
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指導教授	伊林(Lin I)	審核日期	2025-1-20
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