Difference between revisions of "The coordination number of granular cylinders"

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==Soft Matter Keywords==
 
==Soft Matter Keywords==
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====[[Coordination Number]], ====
  
 
==Summary==
 
==Summary==
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 +
In a granular material, the average coordination number <math>\langle z\rangle</math> is defined as the average number of touching neighbors per particle.  For hard spheres, <math>\langle z\rangle</math> has been well-studied and is widely-agreed upon.  This is paper discusses <math>\langle z\rangle</math> for cylindrical grains.  Using constraint equations, the authors prove the following equations:
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{| class="wikitable" style="text-align:center"
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|-
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| Grain Type || <math>\langle z\rangle</math>
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|-
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| Frictionless Cylinder| 10
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|}
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{| class="wikitable" style="text-align:center"
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|+Multiplication table
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|-
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! &times; !! 1 !! 2 !! 3
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|-
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! 1
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| 1 || 2 || 3
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|-
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! 2
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| 2 || 4 || 6
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|-
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! 3
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| 3 || 6 || 9
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|-
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! 4
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| 4 || 8 || 12
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|-
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! 5
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| 5 || 10 || 15
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|}
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First, the authors prove that frictionless cylinder grains have <math>\langle z\rangle = 10</math>, which comes right out of constraint equations. 
  
 
==Relevance to Soft Matter==
 
==Relevance to Soft Matter==
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 +
==References==
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J. Blouwolff and S. Fraden. "The coordination number of granular cylinders." ''Europhys. Letters'', '''76''' (6), pp. 1095-1101 (2006).

Revision as of 15:53, 4 November 2009

(in progress)

Soft Matter Keywords

Coordination Number,

Summary

In a granular material, the average coordination number <math>\langle z\rangle</math> is defined as the average number of touching neighbors per particle. For hard spheres, <math>\langle z\rangle</math> has been well-studied and is widely-agreed upon. This is paper discusses <math>\langle z\rangle</math> for cylindrical grains. Using constraint equations, the authors prove the following equations:

Grain Type <math>\langle z\rangle</math>
10
Multiplication table
× 1 2 3
1 1 2 3
2 2 4 6
3 3 6 9
4 4 8 12
5 5 10 15

First, the authors prove that frictionless cylinder grains have <math>\langle z\rangle = 10</math>, which comes right out of constraint equations.

Relevance to Soft Matter

References

J. Blouwolff and S. Fraden. "The coordination number of granular cylinders." Europhys. Letters, 76 (6), pp. 1095-1101 (2006).