Hi Ed,
I double-checked once more the equations in Fushman and here what it is :
c = gN . B0 . (o_par - o_per) / 3 = wN . CSA / 3
since : c^2 = (wN . CSA)^2 / 9 = c' / 3
c = (c' / 3)**0.5
where c is the constant defined by Fushman and c' is the one we use in
relax and which is normally seen everywhere.
That said, any appearance of c in Fushman should be replaced by (c' /
3)**0.5 in relax (the squared root of : c' / 3).
This affects eta :
eta = dc [4 J(0) + 3 J(wN)] P_2 = (d' . c' / 3)**0.5 [4 J(0) + 3
J(wN)] P_2
and also F_R2
F_R2 = ( R2 - P_HF ) / {4 + 3 / [ 1 + (wN . tc)^2 ] } [d^2 + (wN .
CSA / 3)^2]
= ( R2 - P_HF ) / {4 + 3 / [ 1 + (wN . tc)^2 ] } [d^2 + c^2]
= ( R2 - P_HF ) / {4 + 3 / [ 1 + (wN . tc)^2 ] } [d^2 + c^2]
= ( R2 - P_HF ) / {4 + 3 / [ 1 + (wN . tc)^2 ] } [d' + (c' / 3)]
These definitions of eta and F_R2 are those implemented in relax. They
seem to work fine with my experimental data. Removing the 1/3 factor
from the equations doesn't affect F_eta consistency since this only
scales the obtained value by a fixed amount independent of the magnetic
field. However, removing the 1/3 factor from F_R2 changes drastically
the obtained values and then data from different fields seem scaled
linearly with the magnetic field... Thus, I'm pretty sure that these
equations are right as consistency evaluation using them seems to work
fine with some consistency between the different functions (J(0), F_eta
and F_R2).
Cheers,
Séb
Edward d'Auvergne wrote:
Hi,
Are you really sure Fushman defines it in that way is this manuscript?
It's normally defined as you say
1) c = (CSA * wN)/sqrt(3)
and in the function called by your consistency testing code, the
square of this is returned (as an aside, I should document that
function better). Assuming the CSA constant
2) c' = (CSA * wN)/3,
and the equation
3) f_r2 = (r2 - p_hf) / ((4.0 + 3.0 / (1 + (wN * tc) ** 2)) * (d +
c/3.0))
then the last multiplication factor becomes
4) x = d + c'/3,
5) x = d + (CSA * wN) / 9.
The last part of 5) is the CSA constant of 1) divided by the 3 times
the square root of 3 (3*sqrt(3)). I have a feeling that there is an
error in the constant definitions somewhere. Do you know if the
normal CSA constant divided by 3*sqrt(3) is correct for the f_r2
value? If the division by 3 is removed, then this is the CSA constant
divided by sqrt(3), which again seems not quite right. Unfortunately
I don't have Fushman's publication at hand to check the constants in
his derivations. I think this derivation needs to be very carefully
scrutinised for accidental typos.
Regards,
Edward
On Wed, Jun 25, 2008 at 8:59 PM, Sébastien Morin
<sebastien.morin.1@xxxxxxxxx> wrote:
Hi,
Well... I'm not that sure this was an error as the CSA constant, in the
Fushman paper is not defined as in relax :
Fushman
c = (CSA wN)/3
relax
c = (CSA wN)^2/3
In fact, I thought that Fushman had defined c as :
c = (CSA wN)/sqrt(3)
Hence, I removed the division by 3 in revision 6499 for the definition
of F_R2. This was an error and should have stayed in the code...
I will revert this right now.
Please forget these revisions and these two mails...
Ciao !
Séb :)
P.S. Ah... The joys of constants definitions !!!
Sébastien Morin wrote:
Hi,
I realized, when looking at the equations for consistency testing that
there was an error concerning F_R2.
This was related to the CSA constant.
This is now corrected (revision 6499).
Should we make a new release to correct this error ?
Regards,
Séb
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Re: Error in consistency testing function F_R2