預測類二維電漿微粒液體中的崩潰型激發行為

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姓名

劉以旋(Yu-Hsuan Liu) 查詢紙本館藏

畢業系所

物理學系

論文名稱

預測類二維電漿微粒液體中的崩潰型激發行為
(Predicting the Avalanche Type Excitations in Quasi-2D Dusty Plasma Liquids)

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摘要(中)

在動力學及微觀尺度下，液體展現「停滯—脫滑」式的運動行為，但其結構並非是完全無序的狀況。熱擾動與強耦合作用力的競爭導致晶格狀的有序結構與不規則的無序缺陷之共存。這兩者區域的邊界分布及晶格的排列方向，皆因結構重整而變動消長。粒子的「停滯—脫滑」運動由兩種行為組成：停留於由周圍鄰近粒子所形成的位能井內的騷動(停滯) ，與具不定性強度的崩潰式集體跳躍(脫滑) 。
從更普遍性的觀點而言，這些具冪次法則分布的崩潰行為，如地震、超導漩渦、生物演化、股市漲跌，皆屬於非線性強耦合的複雜系統。其自我導向的臨界性質(SOC) ，使得這些崩潰行為具高度的不可預測性，因在高維度中的極微小或隨機的擾動皆可能引發其行為，並藉強耦合作用傳遞到整個系統，造成崩潰。雖然這些系統無法被長期或是極準確的預測，對時空結構的「粗粒式」的分析可能提供短期內系統演化的資訊。亦即在適當的時空尺度，結構與運動的行為確實存在。
在這篇研究中，我們以實驗調查在電漿微粒液體中，粒子崩潰式的集體跳躍行為的預測性。在此系統，帶負電的微米顆粒懸浮於弱解離的電漿，藉強耦合庫倫力及熱擾動逕行組織成類二維液體，由光學顯微鏡可直接追蹤其微觀下的動態結構與運動。
我們確立了粒子崩潰式的集體跳躍行為與時空中微觀結構改變的關聯。藉由「粗粒化」的鍵方向次序(BOO) 及高頻率位能井內騷動的強度可作短期的崩潰預測。大空間尺度的結構變化與短時間尺度的結構騷動之間的關聯支持以下的推論。相長性的隨機擾動的累積扭曲了晶格狀的有序區域，導致結構與排列的劣化及結構不均性。而伴隨著結構弱化的是由鄰近粒子強耦合作用所形成的位能井的平坦化，高頻的井內騷動也因而更激烈。

摘要(英)

Microscopically, the motion of liquid is stick-slip type at the discrete kinetic level, and the structure of cold liquid is not completely disordered. The competition between thermal perturbation and the strong mutual coupling interaction leads to the coexistence between ordered crystalline domain and disordered defect clusters. The boundary and orientation of these domains fluctuate due to the structural rearrangement induced by the intermittent stick-slip type motions of particles, which are composed of rattling in the cage formed by organized neighbors and the avalanche-like cooperative hopping with the indefinite magnitude.
From a more general view, the power-law distributed avalanches, including nature phenomena such as earthquakes, superconducting vortices, biological evolution, stock markets, are also strongly coupled nonlinear extended system. By the concept of “self-organized criticality (SOC)”, they are very unpredictable because the most minor persistent or stochastic perturbation can trigger the activation which cascades through the strong coupling to the whole system and gives rise to the cooperative motion. Though these systems cannot be long-term, exactly predicted, the spatiotemporal structure of coarse-graining can provide short-term information about how the system will evolve, which means that in an appropriate spatial-temporal scale, the correlation between structure and motion do exist.
We investigate experimentally the predictability of the avalanche type cooperative hopping in dusty plasma liquid. In this system, the negatively charged micrometer sized dusts are suspended in weakly ionized plasma, self-organized into quasi-2D liquids through strongly coupled Coulomb forces and thermal kicks. The dynamic microstructure and micromotion can be traced by direct optical microscopy.
It is found that there are correlation between the avalanche type cooperative hopping and the spatiotemporal structural changes. The short-term prediction can be achieved by coarse-grained bond orientational order, and by the intensity of high frequency caged rattling motion. The coupling between the structural change at larger length scale and the motional fluctuation at small time scale supports the scenario that the accumulation of constructive stochastic perturbation distorts the crystalline ordered domain, and therefore deteriorates the structural order, raises the structural heterogeneity. This is accompanied by the structural weakening and the lowering of cage potential formed by the strong coupling with neighbors, and the high frequency rattling motion becomes more violent.

關鍵字(中)

★ 預測
★ 自組織臨界現象
★ 結構重整
★ 電漿微粒液體

關鍵字(英)

★ dusty plasma liquid
★ structural rearrangement
★ self-organized criticality
★ coarse grain
★ prediction

論文目次

List of Figures v
1 Introduction 1
2 Background and Theory 5
2.1 Micromotion and microstructure in liquids . . . . . . . . . . . 5
2.1.1 The characteristic of liquid and solid . . . . . . . . . . 5
2.1.2 The slow dynamics in supercooled liquid . . . . . . . . 6
2.1.3 The dynamical heterogeneity in supercooled liquid . . . 7
2.2 Self-organized criticality . . . . . . . . . . . . . . . . . . . . . 10
2.3 Strongly Coupled Coulomb Systems (SCCSs) . . . . . . . . . . 11
2.3.1 Strongly coupled Coulomb system . . . . . . . . . . . . 11
2.3.2 Dusty plasma liquid . . . . . . . . . . . . . . . . . . . 12
3 Experiment and Data Analysis 14
3.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 Bond-orientational order . . . . . . . . . . . . . . . . . 17
3.2.2 Spatial coarse-graining . . . . . . . . . . . . . . . . . . 18
3.2.3 Separation of time scale . . . . . . . . . . . . . . . . . 18
3.2.4 Correlation function . . . . . . . . . . . . . . . . . . . 19
iii
Contents
4 Result and Discussion 20
4.1 Spatial coarse-graining analysis . . . . . . . . . . . . . . . . . 21
4.1.1 The Map of structural order and micromotion . . . . . 21
4.1.2 Evolution of coarse-grained BOO for small spatial scale
and micromotion . . . . . . . . . . . . . . . . . . . . . 24
4.1.3 Evolution of coarse-grained BOO for larger spatial scale 26
4.1.4 Correlation probability between coarse-grained variables
and micromotion . . . . . . . . . . . . . . . . . . . . . 30
4.2 Separation of time scale analysis . . . . . . . . . . . . . . . . . 31
4.2.1 Evolution of BOO and micromotion in various time scales 33
4.2.2 Evolution of structural variables in short time scale . . 34
4.2.3 Evolution of motional variables in short time scale . . . 36
4.2.4 Correlation Probability between time-scale separated
variables . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5 Conclusion 43
6 Bibliography 46

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指導教授

伊林(Lin I)

審核日期

2011-7-26

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