Re: [fluka-discuss]: Max and Min Limit of FLUKA result

From: Santana, Mario <msantana_at_slac.stanford.edu>
Date: Thu, 26 Sep 2013 23:03:31 -0700

Hi Prasanta,

1) When you look at rare events (e.g. areas of the geometries where there is a very small fluence), it is normal to find those 'quantum jumps' in the numbers between adjacent voxels, i.e. Fluctuations from some small number in given voxel to 0.0 in neighboring voxels. Please remember that the Monte Carlo code is not a continuous way to solve a problem. You may have a track that reaches a given volume of your geometry, but once your particle is absorbed/killed/etc, the neighboring zones may not see any dose (fluence, etc.) at all if all secondaries have already been tracked. Of course this effect is smoothened when you increase the sample of your simulation (e.g. You simulate more particles, and/or you apply some good variance reduction).

2) But going back to your question, 1E-18 is not the minimum value that FLUKA can score. FLUKA uses double precision (=64 bit) so you could theoretically get much smaller values. I have seen results as small as 1E-40, and I'd think that you could even get less (probably close to 1E-99) if you managed to have such small quantities.

3) Yes, you are right, that's the principle of the Monte Carlo code. Obviously, if you increase the sample by a factor n^2, then the error is EXPECTED to go down by a factor n. This means that if you repeated that experiment many times and you made an average of the new error, this average would tend to be reduced by 'n' when the sample would be infinite.
By the same token, please note that if the error in a given initial simulation is large, then if you increase your sample by a factor n^2, it does not mean that the error will be reduced exactly (or even nearly) by a factor n.

Mario

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Dear FLUKA users,

    I want to know the maximum and minimum limit of FLUKA results.
Sometimes straight after 1E-18 its shows the result 0.0, is it the
minimum value that FLUKA can score.
    Even I want to know does this max and min value depends on type of
scoring, geometry used or any other parameters?



My next query is about FLUKA Monte Carlo, The statistical error shown by
FLUKA is the standard deviation calculated from the data point observed in
each run. Suppose I have 10 runs, then I will generate 10 data, Result is
the average of these 10 data and error is the std. dev. of these 10 data.
As per Central limit theorem, these 10 data generated by 10 runs
(i.e,10samples of size say 10^6 particles/histories) from the actual
sample space or main population is also having the same average value. So
the average value observed in FLUKA result does represent the expected
result of mean population (i.e the problem modelled). So If I want to
reduce the error, I have to increase sample size say from 10^6 to 10^8 to
reduce the error by a factor of 10. This is my understanding about FLUKA
Monte Carlo result error. Is it correct? please guide me.

Thank you.


Regards
Prasanta
Received on Fri Sep 27 2013 - 08:49:49 CEST