Hi, I'll do the patch right away.
Sorry for the attachment, I'll put a link next time... Cheers Séb Edward d'Auvergne wrote: > Hi, > > In this IUPAC report, on page 11, the radian unit is described as "The > units radian (rad) and steradian (sr), for plane angle and solid angle > respectively, are described as 'SI supplementary units' [3]. Since > they are of dimension 1 (i.e. dimensionless), they may be included if > appropriate, or they may be omitted if clarity is not lost thereby, in > expressions for derived SI units." This is the part meaning that > radians are implied if you are doing anything angular. I don't know > what they mean by clarity because by omitting them it complicates > things. Maybe you have to be a physicist before you can see this > clarity. > > Séb, would you be able to create a single patch that contains your bug > fixes, the changes to the system tests for the reduced spectral > density mapping, and with the multiplication by 2pi added back (the > first patch removed it), that would be very much appreciated. I can > then apply a single patch with a single commit message saying that bug > #9259 (http://gna.org/bugs/?9259) has been fixed (by you of course). > > Thanks, > > Edward > > > P. S. As a side note, could you provide a link rather than attach a > file to a post to a mailing list. Thanks. Because this mailing list > is archived in many different internet repositories and because the > message is sent out to all those subscribed to this list, the system > is not designed to handle large attachments. > > > > On 6/19/07, Sebastien Morin <[EMAIL PROTECTED]> wrote: >> Hi, >> >> I agree quite well with what you say. >> >> However, I would have thought that, even if radians are often implied >> and not discussed, they should be present in the IUPAC reports (see >> attached file). See, for example, that the Planck constant divided by 2 >> pi has units of J s, and that the magnetogyric ratio has also units >> devoid of radians (s^-1 T^-1), and even the Larmor angular frequency has >> units of s^-1 (without radians). Maybe even the IUPAC treats the radians >> as implied and doesn't bother with them... >> >> I just checked with data from the Lefevre paper (1996) and I can >> approximately reproduce their data (approximately, since I don't know >> the exact values and precisions they used for the different constants) >> when I multiply the frequencies by 2 pi... However, the discrepancy >> between spectral densities calculated with frequencies multiplied or not >> by 2 pi is small... so this verification is not really that precise... >> Here are the values : >> >> Res R1 R2 NOE J(0) J(wN) J(wH) My values... J(0) >> J(wN) J(wH) >> >> 4 1.8 4.92 0.162 1.23 0.32 0.027 ----- 1.50 0.40 >> 0.024 >> x 2 pi 1.24 >> 0.33 0.024 <- Best >> >> 14 2.08 11.16 0.757 3.15 0.42 0.009 ----- 3.86 >> 0.51 0.008 >> x 2 pi 3.18 >> 0.42 0.008 <- Best >> >> >> It seems that Ed is right and that radians are part of the units and >> that the frequencies in Hz should be multiplied by 2 pi (as in the >> Lefevre paper). >> >> Cheers >> >> >> Séb >> >> >> >> >> Edward d'Auvergne wrote: >> > Hi, >> > >> > I have thoroughly checked all the units of the physical constants, >> > spectral densities, rotational correlation times, and relaxation rates >> > and have a few important corrections about the units which are used in >> > relax and elsewhere. Please read below for the details and a long >> > story about SI vs. CGS units, frequency vs. angular frequency, and how >> > it all relates to angular momentum. >> > >> > >> > On 6/15/07, Sebastien Morin <[EMAIL PROTECTED]> wrote: >> >> Hi, >> >> >> >> Here are the different values I obtain for a residue with R1 = >> 1.1336 +- >> >> 0.0851 ; R2 = 12.9336 +- 0.9649 ; and NOE = 0.463921 +- 0.045 >> >> >> >> >> >> J(0) J(wN) J(wH) >> >> ===================== ===================== >> >> ===================== >> >> >> >> Here are the results with Leo Spyracopoulos's Mathematica notebook. >> >> >> >> 4.704231413115747e-9 2.664085520910741e-10 >> >> 9.485555428699657e-12 >> >> >> >> >> >> Here are the results with relax without multiplying frequencies in >> Hz by >> >> 2 pi. >> >> >> >> 4.6978912534878238e-09 2.6603551824374712e-10 >> >> 9.478993207668287e-12 >> >> >> >> ratio >> >> 0.9986522432526923179 0.9985997677461966745 >> >> 0.9993081880043085706 >> >> >> >> >> >> Here are the results with relax when multiplying frequencies in Hz by >> >> 2 pi. >> >> >> >> 3.4634030539343071e-09 1.9612804482358541e-10 >> >> 9.478993207668287e-12 >> >> >> >> ratio >> >> 0.7362314371436068543 0.7361927508863804185 >> >> 0.9993081880043085706 >> >> >> >> >> >> The very small discrepancy we get (ratio 0.999...) is due to several >> >> small differences in the definitions of constants (e.g. gn = >> -2.7126 in >> >> relax and -2.7108 in Leo's notebook). This is not important. However, >> >> there is a non negligible difference with the use of either >> frequencies >> >> in Hz or frequencies transformed to rad/s. >> >> >> >> Now, what do we do with that ? >> >> >> >> The spectral densities are in units of rad / s = rad s^-1. (these are >> >> not SI units, however) >> > >> > The units of radians per second, or radian Hertz, is the angular >> > frequency (omega) rather than the frequency (nu), yet both are >> > nevertheless SI units. For example see >> > http://en.wikipedia.org/wiki/Angular_frequency or related sites. >> > These SI units are the same in the CGS unit system. The reason that >> > we use the angular frequency rather than frequency is because we are >> > talking about angular momentum. >> > >> > >> >> The rates (R1, R2 and sigmaNOE) are in units of s^-1. >> >> >> >> The constant 'd' is in units of s^-2. >> > >> > This is not correct. The correct units are rad^2.s^-2. This can be >> > found by doing a unit analysis on the SI dipolar constant with the >> > mu0/4pi component (or alternatively doing the analysis in the CGS >> > system). The reason for the radians being part of the equation is >> > because we are using Dirac's constant (h_bar) rather than Planck's >> > constant (h). While Planck's constant has the units of Joules per >> > Hertz (or Joule seconds) because Dirac's constant is divided by 2pi >> > its units are Joules per Hertz per radian. However in most cases the >> > radian units of Dirac's constant are not stated as we are usually >> > talking about angular momentum (the angular part means we use radians >> > hence it is indirectly implied). The other reason is because the >> > gyromagnetic ratio also has units of radian, and again this is usually >> > not reported (for example see Table 1.1 of Cavanagh in which the >> > gyromagnetic ratios are in fact in rad.s^-1.T^-1, although they are >> > not reported as such). All of this is still in SI units - the radian >> > components are independent of the SI or CGS systems. >> > >> > The relevant units in the SI system for the dipolar constant, >> defined as >> > >> > d = (mu0/4pi)^2 . (gH.gX.h_bar/<r>^3)^2, >> > >> > are >> > >> > mu0 -> kg.m.s^-2.A^-2, >> > h_bar -> J.s.rad^-1, >> > gx -> rad.s^-1.T^-1, >> > r -> m, >> > >> > where tesla (T) is equal to the units kg.A^-1.s^-2. >> > >> > The SI units for the CSA constant, defined as >> > >> > c = (omegaX . csa / 3)^2, >> > >> > are >> > >> > omegaX -> rad.s^-1, >> > csa -> unitless. >> > >> > Hence both constants have the units of rad^2.s^-2. >> > >> > >> >> The constant 'c' is in units of s^-2 also (or rad^2 s^-2 if we use >> >> frequencies in rad s^-1, which are not SI units). >> > >> > The constant c is defined by the angular frequency (omega) rather than >> > the frequency (nu). Hence the units of this constant in the >> > relaxation equations, in both SI and CGS units, is always rad^2.s^-2 >> > as well. >> > >> > >> >> I now hesitate between 3 views. >> >> >> >> 1. Should the spectral densities be in SI units (i.e. in s, as the >> >> frequencies are in s^-1 and the rates in s^-1) ? >> > >> > relax currently reports the spectral densities in the SI units for >> > angular frequency of radian Hertz. Although often reported as Hertz, >> > the correct unit is radian Hertz. This is again because radians are >> > implied, but this time because we are talking about rotations. The >> > reason is as follows: >> > >> > The spectral density function for isotropic diffusion is >> > >> > J(w) = tm / (1 + (w.tm)^2). >> > >> > The units for w (or omega) is rad.s^-1. Because the product w.tm is >> > unitless the units for tm are in reality s.rad^-1. Hence the units of >> > the spectral density function J(w) is also s.rad^-1. >> > >> > Although not reported in text books such as Cavanagh, you can still >> > see remnants of the radians. For example in that book tc (or tm) is >> > described as being "approximately the average time for the molecule to >> > rotate by one radian". All the external and internal correlation >> > times are in units of s.rad^-1 as they are all rotational correlation >> > times! But because the are rotational times, the radians are implied >> > and do not need to be reported. >> > >> > >> >> 2. If the spectral densities are in s rad^-1, the frequencies used to >> >> calculate them should also be in rad s^-1, thus the constant 'c' >> should >> >> be in rad^2 s^-2 and the constant 'd' also (so we should calculate it >> >> without multiplying by the factor of (mu/4pi)^2). This would be about >> >> using old units instead of the SI units, but then the spectral >> densities >> >> would be in s rad^-1. >> > >> > In SI units the spectral density function is in units of s.rad^-1 >> > whereas the physical constants (dipolar, csa, etc.) are in rad^2.s^-2. >> > Hence the units for the relaxation rates - hold on to your seat - is >> > in radian Hertz! The R1 relaxation rate is in rad.s^-1. Or the T1 >> > relaxation time is in s.rad^-1. >> > >> > The reason that all of this is hardly ever discussed is because the >> > units of radians is implied by the fact that this all relates to >> > angular momentum. In the rotational world, radians are ubiquitous. >> > Yet they are silent because they are implied. Unfortunately this >> > 'hiding' of radians, combined with the CGS vs. SI unit systems, >> > creates large amounts of confusion. >> > >> > >> >> 3. We could calculate everything in SI units (as we do right now) and >> >> normalize to rs ad^-1 in the end. >> >> >> >> Either way, I think that Leo's notebook yields spectral densities >> s and >> >> not the usual s rad^-1 (as in the 2006 paper : JBNMR,36:215-224, for >> >> which I calculated back spectral density values and yielded the >> same as >> >> published where they say it's in s rad^-1, but the units deriving >> says >> >> it's s). >> > >> > relax reports spectral densities in the SI (and CGS) units of s.rad^-1 >> > as dictated by angular momentum. Hence the input frequency of Hz must >> > be multiplied by 2pi. Otherwise the product w.tc is not unitless and >> > hence its square cannot be added to 1 as J(w) = tm/(1+(w.tm)^2). >> > >> > >> >> Can you please tell me if I'm right with those ideas before I >> write to >> >> Leo to report this apparent bug or typo or whatever... >> > >> > I hope that what I've written clarifies a few of the problems. >> > >> > Sincerely, >> > >> > Edward >> > >> >> -- >> ______________________________________ >> _______________________________________________ >> | | >> || Sebastien Morin || >> ||| Etudiant au PhD en biochimie ||| >> |||| Laboratoire de resonance magnetique nucleaire |||| >> ||||| Dr Stephane Gagne ||||| >> |||| CREFSIP (Universite Laval, Quebec, CANADA) |||| >> ||| 1-418-656-2131 #4530 ||| >> || || >> |_______________________________________________| >> ______________________________________ >> >> >> > -- ______________________________________ _______________________________________________ | | || Sebastien Morin || ||| Etudiant au PhD en biochimie ||| |||| Laboratoire de resonance magnetique nucleaire |||| ||||| Dr Stephane Gagne ||||| |||| CREFSIP (Universite Laval, Quebec, CANADA) |||| ||| 1-418-656-2131 #4530 ||| || || |_______________________________________________| ______________________________________ _______________________________________________ relax (http://nmr-relax.com) This is the relax-devel mailing list relax-devel@gna.org To unsubscribe from this list, get a password reminder, or change your subscription options, visit the list information page at https://mail.gna.org/listinfo/relax-devel
