mailRe: Error in consistency testing function F_R2


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Posted by Sébastien Morin on July 04, 2008 - 17:07:
Hi Ed,

This is a good point.

Is the CSA value for 13C positive or negative ?

For F_eta, it may only affect the sign of the obtained value, thus not
changing the analysis (comparison between different fields).

For J(0), the analysis shouldn't be affected also as the square values
are used.

For F_R2 also, the square values are used, thus the analysis wouldn't be
affected.

Nevertheless, there will be a need for a redesign of the equations so
they are eaiser to use and more flexible in regards to the gyromagnetic
ratio or CSA and dipolar constants used...

I put this on my 'todo' list !

Cheers,


Séb



Edward d'Auvergne wrote:
Would this be a problem if carbon is being looked at rather than
nitrogen?  In this case, gC is positive and the dipolar constant is
negative.  For the CSA value, this could be negative or positive,
changing the CSA constant.  Would this affect the analysis?

Regards,

Edward


On Fri, Jul 4, 2008 at 4:09 PM, Sébastien Morin
<sebastien.morin.1@xxxxxxxxx> wrote:
  
Hi again,

I realized that even though the gN value was negative in eta, the CSA
value (o_par - o_per) being also negative would make eta positive...

Indeed, figures in the Fushman paper show positive values of F_eta, thus
positive values of eta...

Thus, eta is positive and no further change is needed in the consistency
tests code... except for what you proposed about putting eta in ri.py
and ri_comps.py...

Cheers,


Séb




Sébastien Morin wrote:
    
Hi Ed,

You're absolutely right. I'll change the code right away so eta becomes
negative as it should be.

Cheers,


Séb


Edward d'Auvergne wrote:

      
For future extensibility and compatibility, trying be as technically
accurate as possible would be best.  For example in the future the eta
code could be shifted into the ri.py and ri_comps.py files to allow
full model-free analysis (and spectral density mapping) using the
additional cross correlated relaxation rates eta_z and eta_xy.  So if
eta should physically be negative then I think we should observe that,
even if it makes no difference in the consistency testing code.

Cheers,

Edward


On Thu, Jul 3, 2008 at 11:53 PM, Sébastien Morin
<sebastien.morin.1@xxxxxxxxx> wrote:


        
Hi Ed,

Good !

For the negative sign, Fushman described the dipolar constant as d = -
(u0/4pi) gH gN h / (4pi r^3).

Hence, the negative sign introduced by gN is neutralized there by a '-'
sign...

For the CSA constant, however, there is no '-' sign in the equation and
the negative sign introduced by gN should be still present... Hence, for
eta, I should add a '-' sign in the equation for our definition (in
relax) being the same as in Fushman. Again, however, this would change
consistency evaluation since it would only inverse the obtained values
(+ to -).

Am I right ?

If so, I should commit a change where eta = [...] would become eta = - 
[...]

Cheers,


Séb






Edward d'Auvergne wrote:


          
Ah, now I get it.  I should really get around to changing these
functions so that there is one function for the dipolar constant, and
one for constant squared (and the same thing for the CSA constant).
Be careful with the square root of the dipolar contant squared though,
unsquared it should have a negative sign at the front.

Regards,

Edward



On Thu, Jul 3, 2008 at 8:01 PM, Sébastien Morin
<sebastien.morin.1@xxxxxxxxx> wrote:



            
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.
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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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