Spiral-coil Formation in Semi-flexible Self-propelled Chain System

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姓名

王耀寬(Yao-Kuan Wang) 查詢紙本館藏

畢業系所

物理學系

論文名稱

(Spiral-coil Formation in Semi-flexible Self-propelled Chain System)

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摘要(中)

主動的自我推進粒子系統與被動系統相比，有著更為豐富的行為。在不同尺度的自我推進粒子系統中，皆可觀察到與粒子單元相比規模較大的群聚效應：從細胞的聚集，到魚群的群游。許多不同的理論模型已經根據這種跨尺度的群聚效應提出解釋。他們歸納出局部速度方向的統一是群體運動的起源。

在之前的溶藻弧菌實驗上，我們發現長細菌會二維洋菜膠表面上會因為和短細菌的相互作用而纏繞自己，形成以等速度旋轉的螺旋結構。因為細菌本身硬度的限制，這種現象在只有一條長細菌單獨存在時並不會發生。受啟發於實驗，我們模擬了一個二維的可調硬度自我推進鍊系統，並探討了兩種不同型態的條件。在純短鍊系統中，每一條短鍊有著一樣的長度和硬度。我們發現調整硬度也可以造成群聚效應的差異。隨著硬度的增加，短鍊會形成更大的群體。

有趣的是加入一條極長鍊到上述的短鍊系統中後，本來很硬的長鏈會因為背景短鍊的碰撞而形成實驗上所看到的自我螺旋結構。我們歸納出此結構的發生是背景短鍊密度和長鍊硬度的平衡結果。來自短鍊的碰撞讓長鍊的等效硬度減少。為了更進一步了解這個現象，我們透過模擬探索了由長鍊硬度和背景短鍊密度所構成的相空間。結果顯示在長鍊極硬的情況下，若要形成完美的螺旋結構，需要有密度適當的背景短鍊。

摘要(英)

Large scale patterns such as clustering can be observed in different self-propelled systems:from cell aggregations to fish schools.Several models have been proposed to describe these diverse systems which all show the collective behaviours.They conclude that, the alignment of velocities between two self-propelled elements explains the mechanism.

Inspired by the experimental observation of swarming bacteria self-assembled into rotating spiral-coil structures, we conduct a 2-dimensional semi-flexible self-propelled chain simulation. In the monodisperse system,
the system comprises several short self-propelled chains with the same length. Under this condition, self-propelled chains with spatial interactions, shows cluster formation.
We provide a novel way to describe the attraction between self-propelled chains by changing the stiffness of chains.
With the increase of stiffness, the cluster size
distribution exhibits larger clusters.

Interestingly, in the bidisperse system, an rigid ultra-long chain interacted with short chain backgrounds can form self-rotated and rotational structure. The onset of spiral-coil conformation is related to the balance of background density and stiffness of long chain. We investigate the spiral coil formation by varying long-chain stiffness and short-chain density. The collisions from the background decrease the effective stiffness of long chain. As a result, our finding can be demonstrated by phase diagram of those two parameters. Our results explain the self-assembled spiral coils in the stiff long bacterial swarm systems.

關鍵字(中)

★ 主動系統
★ 持久長度
★ 細菌

關鍵字(英)

★ active matter
★ persistence length
★ bacteria

論文目次

Abstract i
Glossary x
Acronym x
Symbol x
1 Introduction 1
Motivation 1
Spiral coil experiment 3
Collective motion of self-propelled rods 6
Vicsek model 6
Self propelled rods 8
Myxobacteria 14
Semi-ﬂexible chain 15
Persistence length 15
Self-propelled semi-ﬂexible chain 19
2 Method 20
Simulation Model 20
Brownian motion and Langevin equation 20
Interaction between beads 22
Propulsion force 25
Randon noise 25
Detail of the system 26
Computation Method 27
The linked cell method 27
Implementation of the linked cell method 30
Analysis 30
DBSCAN 30
3 Result 32
Pure short chain system 32
Mean-squared angular deviation 32
Mean-squared displacement 37
Cluster size distribution 39
Local number ﬂuctuation 42
Mixture system with long chain 44
Criteria of spiral coil 44
Diﬀerent patterns of spiral coil 45
Bending threshold 45
Phase diagram of spiral-coil formation 47
4 Conclusion 51
Reference 53

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指導教授

羅健榮(Chien-Jung Lo)

審核日期

2018-6-29

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