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*dudung@gmail.com

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Outline

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

FORCES AND NUMERICAL METHODModel formulation

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Short range repulsive force

• Act on grain i due to presence of grain j

with

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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

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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

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ikgik rkg ˆ

tvv kk

Molecular dynamics

• Newton's second law of motion

• Euler method (n = 0, 1)

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kik

jijij

ii gGNm

a 1

1

1

n

n

n

n

n

n

dttrdt

dttrd

dtttrd

STRETCHING AND DISLOCATINGClusters separation stages

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Stage 1: Stretching

• #100

Stage 1: Stretching

• #100

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Stage 2: Dislocating

• #100

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Stage 2: Dislocating

• #100

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Stage 2: Dislocating (other site)

• #100

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Stage 2: Dislocating (other site)

• #100

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CLUSTER SEPARATION: TRANSClusters separation types

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Cluster Separation: Trans

• #089

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Cluster Separation: Trans

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Cluster Separation: Trans

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Cluster Separation: Trans

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CLUSTER SEPARATION: ROTClusters separation types

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Cluster Separation: Rot

• #062

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Cluster Separation: Rot

• #062

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Cluster Separation: Rot

• #062

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Cluster Separation: Rot

• #062

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CLUSTER SEPARATION: ROT+TRANSClusters separation types

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Cluster Separation: Rot+trans

• #066

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Cluster Separation: Rot+trans

• #066

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Cluster Separation: Rot+trans

• #066

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Cluster Separation: Rot+trans

• #066

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Cluster Separation: Rot+trans

• #066

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ONE PARTICLE CHANGING SITEClusters separation types

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One particle changing site

• #064

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One particle changing site

• #064

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One particle changing site

• #064

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One particle changing site

• #064

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One particle changing site

• #064

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TWO PARTICLES CHANGING SITEClusters separation types

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Two particles changing site

• #061

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Two particles changing site

• #061

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Two particles changing site

• #061

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Two particles changing site

• #061

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ONE PARTICLE MIGRATINGClusters separation types

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One particle migrating

• #056

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One particle migrating

• #056

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One particle migrating

• #056

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One particle migrating

• #056

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PARAMETERS VALUESSimulation

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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

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CLUSTERS: MEMBERSHIPS, TIMEDiscussion

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Influence of g2 to N2

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20

24

28

32

36

40

10 12 14 16 18 20

N2

g2

Influence of g2 to N2 (cont.)

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20

24

28

32

36

40

10 12 14 16 18 20

<N

2>

g2

Influence of g1, g2 to N2 (cont.)

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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)

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10

15

20

25

30

10 12 14 16 18 20

T s

g2

Cluster separation time (average)

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10

15

20

25

30

10 12 14 16 18 20

<T s>

g2

Cluster separation time (contour)

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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

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0

4

8

12

16

20

0 10 20 30 40 50 60

E

N

SUMMARIES, ACKNOWLEDGEMENTEnd

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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

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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

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Thank you