Breaking of Granular Cluster in Two-Dimension due to Splitting of the Central Forces

2015-11-19 ICANSE 2015, Bandung, Indonesia 1

Breaking of Granular Cluster in Two-Dimension due to Splitting of the

Central Forces

Sparisoma Viridi*, Rizal Kurniadi, Abdul Waris

Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia*[email protected]


Outline

• Model formulation• Cluster separation stages• Clusters separation types• Simulation parameters• Discussion• End

FORCES AND NUMERICAL METHODModel formulation


Short range repulsive force

• Act on grain i due to presence of grain j

with


ijijjiNij rrRRkN ˆ,0max

jiij rrr

ijij

ijij

rr

rr

ˆ

Short range gravitation force

• Act on mass i due to existence of mass j

with u(x) is step function and RG is interaction range


Gijij

jiGij Rurrmm

kG 1ˆ2

Central force

• Act on grain i due to existence of point of central force k

which could move with certain velocity


ikgik rkg ˆ

tvv kk

Molecular dynamics

• Newton's second law of motion

• Euler method (n = 0, 1)


kik

jijij

ii gGNm

a 1

1

1

n

n

n

n

n

n

dttrdt

dttrd

dtttrd

STRETCHING AND DISLOCATINGClusters separation stages



Stage 1: Stretching

• #100

Stage 2: Dislocating

• #100


Stage 2: Dislocating (other site)

• #100


CLUSTER SEPARATION: TRANSClusters separation types


Cluster Separation: Trans

• #089


CLUSTER SEPARATION: ROTClusters separation types


Cluster Separation: Rot

• #062



• #062


CLUSTER SEPARATION: ROT+TRANSClusters separation types


Cluster Separation: Rot+trans

• #066



• #066


ONE PARTICLE CHANGING SITEClusters separation types


One particle changing site

• #064



• #064


TWO PARTICLES CHANGING SITEClusters separation types


Two particles changing site

• #061



• #061


ONE PARTICLE MIGRATINGClusters separation types


One particle migrating

• #056



• #056


PARAMETERS VALUESSimulation


Simulation parameters valuesParameter Value

D 0.5

m 1

Nlayer, configuration, N 5, 2-D HCP, 61

G, RG 1, 2

g1, g2, v1, v2 10 – 20, 10 – 20, ±0.05

Δt, Tdata, tbeg, tend 10–3, 1, 0, 40

kN 104


CLUSTERS: MEMBERSHIPS, TIMEDiscussion


Influence of g2 to N2


20

24

28

32

36

40

10 12 14 16 18 20

N2

g2

Influence of g2 to N2 (cont.)


20

24

28

32

36

40

10 12 14 16 18 20

<N

2>

g2

Influence of g1, g2 to N2 (cont.)


1011121314151617181920

1 2 3 4 5 6 7 8 9 10 11

g2

N2

g1 - 9

30-40

20-30

10-20

0-10

Cluster separation time (for each g1)


10

15

20

25

30

10 12 14 16 18 20

T s

g2

Cluster separation time (average)


10

15

20

25

30

10 12 14 16 18 20

<T s>

g2

Cluster separation time (contour)


10

11

12

13

14

15

16

17

18

19

20

1 2 3 4 5 6 7 8 9 10 11

g2

Ts

g1 - 9

20-25

15-20

10-15

5-10

0-5

Fission yield-like feature


0

4

8

12

16

20

0 10 20 30 40 50 60

E

N

SUMMARIES, ACKNOWLEDGEMENTEnd


Summaries

• Simulation system for observing breaking of granular cluster in two-dimension has been conducted

• Most of the time within value of simulation parameters all grains construct a 2-d HCP

• Time for cluster separation depends on grain-grain individual interactions

• Fission yield-like feature has been obtained


Acknowledgements

• Calculation part of this work is supported by Riset Inovasi Batch II in year 2015 with contract number 1763/I1.B04.1/KU/2015

• Presentation of this work is supported by Nuclear Physics and Biophysics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung



Thank you

Breaking of Granular Cluster in Two-Dimension due to Splitting of the Central Forces

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