二維非彈性顆粒子之簇集現象

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和正平(C-P He) 查詢紙本館藏

畢業系所

物理學系

論文名稱

二維非彈性顆粒子之簇集現象
(Clustering Phenomena of Inelastic Granular Particles in Two Dimensions)

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摘要(英)

domain, with three kinds of dierent boundary conditions, (i) double periodic bound-
aries, (ii) a pair of smooth, elastic walls in the x-direction and periodic boundaries in
the y-direction, (iii) four smooth and elastic walls. Starting with the almost elastic
case, in which the coeÆcient of restitution is just a little less than 1, the homoge-
neous regime resembles a classical non-dissipative gas and there is no large structure.
When decreases, the system becomes inhomogeneous and spatial non-uniformity
occurs. Clusters appear when is even smaller, large clusters of disks form, break,
and reform. As time goes by, the cluster stays in a status of hydrodynamic shear
state, or collapse. Inelastic collapse, which is a dynamic singularity of the binary
collision model, is caused by the many-body dynamics. Numerical simulations show
that the energy decay in the homogeneous regime is proportion to t

關鍵字(中)

★ 顆粒子
★ 簇集現象

關鍵字(英)

★ Granular
★ Clustering

論文目次

Contents
1 Introduction 7
2 Theory 10
2.1 Ha's Cooling Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 The Continuity Equation . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 The Momentum Conservation Equation . . . . . . . . . . . . . 11
2.1.3 The Energy Conservation Equation . . . . . . . . . . . . . . . 11
2.1.4 Main Assumptions and The Result of Ha's Cooling Law . . . 12
2.2 Clustering and Collapse in Simulations . . . . . . . . . . . . . . . . . 14
2.2.1 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Inelastic Collapse . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Molecular dynamics Method and Simulation details 17
3.1 Molecular dynamics of Hard Systems . . . . . . . . . . . . . . . . . . 17
3.1.1 Collision Times between Two Particles . . . . . . . . . . . . . 18
3.1.2 Collision Times between a Particle and the Wall . . . . . . . . 19
3.2 The Collision Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Particle-Particle Collision . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Particle-Wall Collision . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Initial and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 23
4 Results and Discussions 25
4.1 Inelastic Particles with Smooth surface . . . . . . . . . . . . . . . . . 25
4.1.1 Probability of Non-Collapse . . . . . . . . . . . . . . . . . . . 25
4.1.2 Order Parameter . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.3 Energy Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.4 Number of Collisions and Time . . . . . . . . . . . . . . . . . 48
4.2 Inelastic Rough Particles with Periodic Boundary Conditions . . . . . 59
5 Conclusion and Outlook 66
6 Appendix 68

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指導教授

黎璧賢(Pik-Yin Lai)

審核日期

2000-7-10

推文