This document summarizes a study that used a two-dimensional granular fission toy model to simulate the evolution of granular compaction. The model considers repulsive, attractive, electrostatic, and center forces between granules. Molecular dynamics simulations were run for different system sizes using Euler algorithms. The results show that the granular configurations compact over time and tend to form hexagonal close packings under the influence of the modeled forces. Future work is planned to further quantify compaction, introduce charged particles, and add probabilistic factors to the model.

1. APS 2015 19-20 Agustus 2015, Bandung, Indonesia 1
Two-Dimension Granular Fission Toy
Model and Evolution of Granular
Compaction
Sparisoma Viridi*, Rizal Kurniadi, and Abdul Waris
Nuclear Physics and Biophysics Research Division
Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
*dudung@gmail.com

2. APS 2015 19-20 Agustus 2015, Bandung, Indonesia 2
Outline
• Previous studies
• Interactions
• Molecular dynamics method
• Simulation parameters
• Results and discussion
• Summaries

3. Previous study
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 3
Viridi et al., AIP-CP 2012

4. Previous study (cont.)
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 4
Viridi et al., JPFSM 2015

5. Interactions
• Repulsive force
• Attractive force
• Electrostatic force
• Center force
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 5

6. Interactions: Repulsive force
• Linear spring dash-pot model
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 6
ijNijijNij vrkF ˆˆ γξ −=

( )ijij rD −= ,0maxξ
ijijijij
ij
ij
ij rrrr
r
r
r


⋅=== ,ˆ
ijijijij
ij
ij
ij vvvv
v
v
v


⋅=== ,ˆ

7. Interactions: Attractive force
• Gravitational-like force
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 7
ij
ij
Gij r
r
m
kG ˆ2
2
−=


8. Interactions: Electrostatic force
• Coulomb-like force
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 8
ij
ij
ji
Qij r
r
qq
kQ ˆ2
=


9. Interactions: Center force
• Near earth gravitation-like force
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 9
( )
ci
ci
gi
rr
rr
mkF 

−
−
−=

10. Molecular dynamics method
• Newton second law of motion
• Euler algorithm
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 10








+++= ∑≠ij
ijijijii GQFF
m
a

1
1
( ) ( ) tatvttv ∆+=∆+

( ) ( ) tvtrttr ∆+=∆+


11. Simulation parameters
• kN = 5×103
, γN = 0
• kG = 0.5
• kQ = 1
• kg = 100, rc± =
• D = 0.5, m = 1, qi = 0
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 11
)1,1(22 ±±

12. Simulation parameters (cont.)
• L = 2, 3, 4, 5
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 12

13. Results and discussion
• Initial and final configurations
• Evolution of compaction
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 13

14. Initial and final config.. (L = 2)
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 14

15. Initial and final config.. (L = 3)
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 15

16. Initial and final config.. (L = 4)
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 16

17. Initial and final config.. (L = 5)
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 17

18. Evolution of compaction
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 18

19. Summaries
• Considered forces and chosen parameters 
fission-like process for 2-d spherical granular
configuration
• Compaction tends to form 2-d hexagonal close
packed (HCP) system under influence of the
forces
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 19

20. Future plan
• Formulation to quantify compaction for multi-
center compaction
• Introduce charged particles
• Add probabilistic factor
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 20

21. Acknowledgement
• This work is supported by Riset Inovasi Batch II
with contract number 1763/I1.B04.1/KU/2015
APS 2015 19-20 Agustus 2015, Bandung, Indonesia 21

22. APS 2015 19-20 Agustus 2015, Bandung, Indonesia 22
Thank you