Methods for Obtaining and Using Differential Operators in Monte Carlo

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Methods for Obtaining and Using Differential
Operators in Monte Carlo

• Fusheng Li, Xiaogang Han, and Robin P. Gardner
• Oct 3 2007

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Sample Descriptions

• Reference Sample Composition (Weight Fractions)
• Cr 0.3 Fe 0.5 Mo 0.2
• Variation
• Cr is constant at 0.3, Fe varies as shown in
  Table
• -- Mo changes to keep sample Weight Fractions
  unity

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Formula to Calculate 1st Order DO

• 1st Order Derivative, for each channel i
• Def. Yij counts/channel with respect to channel
  i for weight fraction at j i1,2,,2048,
  j1,2,,47
• Def. Xj Weight fraction at j
• Def. dij 1st derivative for channel i at weight
  fraction j
• dij?Yij/ ?Xj
• ?YijYij-Y(i-1)j, ?XjXj-Xj-1
• Xj0.02,0.04,,0.505

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Formula to Calculate 2nd Order DO

• 2nd Order Derivative, for each channel i
• dij2 2nd derivative for channel i at weight
  fraction j
• dij2(Y(i-1)j-2Y(i)jY(i1)j)/ ?Xj2
• ?XjXj-Xj-1Xj1-Xj
• Xj0.02,0.04,,0.505

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Simulation Work Summary

• Successfully compiled CEARXRF Fortran code on
  CEAR clusters and deployed it on 49 nodes.
• Total 47 cases, each simulated with 1X109
  histories.
• 18 hours per case on a single node (non parallel
  mode, 99.9 CPU usage for each node)
• Matlab codes
• PROC1.m Load all simulated results into
  workspace
• PROC2.m Process data and generate desired
  results

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True Fe DO Generated by CEARXRF
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True Fe-Fe DO Generated by CEARXRF
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Calculated DOs Fe weight fraction 0.5 (1)
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Fe weight fraction 0.5 (2)
True Fe-Fe differential Operators
Calculated Fe differential Operators
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Mo Differential Operators
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Mo Benchmark
True Mo-Mo differential Operators
Calculated Mo differential Operators
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Summary

• It is possible to get differential operators
  outside the Monte Carlo code, i.e. w/o modifying
  the code.
• With the high-performance CEAR clusters computing
  capacity, it is also very feasible.