CR72 - Revision history

Bugman: /* Code */ Switch to the {{relax url}} template for the library code URL.

2017-10-27T12:15:21Z

Code: Switch to the {{relax url}} template for the library code URL.

Bugman: /* See also */ Added more categories.

2015-11-06T16:44:24Z

Bugman: /* References */ Switched to a labelled section transclusion for the citations.

2015-11-03T19:22:58Z

References: Switched to a labelled section transclusion for the citations.

Bugman: Switched to parameter templates.

2015-10-22T10:28:34Z

Switched to parameter templates.

Bugman: Removed the =intro= sectioning for better page formatting and use in the 'Did you know...' section of the main page.

2015-10-15T14:10:52Z

Removed the =intro= sectioning for better page formatting and use in the 'Did you know...' section of the main page.

Bugman: /* Links */ Updated the HTML manual link.

2014-11-26T13:07:25Z

Links: Updated the HTML manual link.

Bugman: Category link updates for the specific analyses.

2014-09-11T07:56:24Z

Category link updates for the specific analyses.

Troels Emtekær Linnet at 09:13, 26 July 2014

2014-07-26T09:13:09Z

Bugman: /* Equation */ Added some phantom goodness :)

2014-05-05T16:03:22Z

Equation: Added some phantom goodness :)

Troels Emtekær Linnet: /* Equation */

2014-05-05T15:18:42Z

Equation

@@ Line 33: / Line 33: @@
 == Code ==
-The library code.<br>
+The library code: {{relax url|path=lib/dispersion/cr72.py}}
 == Reference ==

← Older revision		Revision as of 16:44, 6 November 2015
Line 54:		Line 54:

	== See also ==		== See also ==
		+	[[Category:Models]]
		+	[[Category:Dispersion models]]
	[[Category:Relaxation_dispersion analysis]]		[[Category:Relaxation_dispersion analysis]]

@@ Line 40: / Line 40: @@
 The reference for the CR72 model is:
-* Carver, J. and Richards, R. (1972).  General 2-site solution for chemical exchange produced dependence of T2 upon Carr-Purcell pulse separation. ''J. Magn. Reson.'', '''6'''(1), 89-105. ([http://dx.doi.org/10.1016/0022-2364(72)90090-X 10.1016/0022-2364(72)90090-X]).
+* {{#lst:Citations|CarverRichards72}}
 == Related models ==

@@ Line 1: / Line 1: @@
-The Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales whereby the simplification $R_{2A}^0$ = $R_{2B}^0$ is assumed.  This model is labelled as '''CR72''' in [[Relaxation dispersion citation for relax|relax]].
+The Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales whereby the simplification {{:R2Azero}} = {{:R2Bzero}} is assumed.  This model is labelled as '''CR72''' in [[Relaxation dispersion citation for relax|relax]].
 == Equation ==
@@ Line 25: / Line 25: @@
 </math>
-<math>k_{\textrm{EX}}</math> is the chemical exchange rate constant, <math>p_A</math> and <math>p_B</math> are the populations of states A and B, and <math>\Delta \omega</math> is the chemical shift difference between the two states in ppm.
+{{:kex}} is the chemical exchange rate constant, {{:pA}} and {{:pB}} are the populations of states A and B, and {{:Deltaomega}} is the chemical shift difference between the two states in ppm.
 == Parameters ==
-The CR72 model has the parameters {$R_2^0$, $...$, $p_A$, $\Delta\omega$, $k_{ex}$}.
+The CR72 model has the parameters {{{:R2zero}}, ..., {{:pA}}, {{:Deltaomega}}, {{:kex}}}.
 == Code ==

← Older revision		Revision as of 14:10, 15 October 2015
Line 1:		Line 1:
−	~~= Intro =~~
−
	The Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales whereby the simplification $R_{2A}^0$ = $R_{2B}^0$ is assumed. This model is labelled as '''CR72''' in [[Relaxation dispersion citation for relax\|relax]].		The Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales whereby the simplification $R_{2A}^0$ = $R_{2B}^0$ is assumed. This model is labelled as '''CR72''' in [[Relaxation dispersion citation for relax\|relax]].

@@ Line 51: / Line 51: @@
 The [[Relaxation dispersion citation for relax|implementation of the CR72 model in relax]] can be seen in the:
-* [http://www.nmr-relax.com/manual/reduced_CR72_2_site_CPMG_model.html relax manual],
+* [http://www.nmr-relax.com/manual/The_reduced_CR72_2_site_CPMG_model.html relax manual],
 * [http://www.nmr-relax.com/api/3.1/lib.dispersion.cr72-module.html API documentation],
 * [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72 relaxation dispersion page of the relax website].

← Older revision		Revision as of 07:56, 11 September 2014
Line 56:		Line 56:

	== See also ==		== See also ==
−	[[Category:Relaxation_dispersion]]	+	[[Category:Relaxation_dispersion analysis]]

@@ Line 5: / Line 5: @@
 == Equation ==
 [http://www.nmr-relax.com/manual/Dispersion_model_summary.html Please see the summary of the model parameters here.]
 <math>

@@ Line 10: / Line 10: @@
 <math>
-R_{2,\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-))
+R_{2,\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-)) \\
-= R_2 + \frac{k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-))
+\phantom{R_{2,\textrm{eff}}} = R_2 + \frac{k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-))
 </math>
@@ Line 17: / Line 17: @@
 <math>
-\zeta = 2 \Delta \omega \, (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}})
+\zeta = 2 \Delta \omega \, (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}}) \\
-= - 2 \Delta \omega \, ( p_A k_{\textrm{EX}} - p_B k_{\textrm{EX}})
+\phantom{\zeta} = - 2 \Delta \omega \, ( p_A k_{\textrm{EX}} - p_B k_{\textrm{EX}}) \\
-= - 2 \Delta \omega \, ( k_{\textrm{BA}} - k_{\textrm{AB}})
+\phantom{\zeta} = - 2 \Delta \omega \, ( k_{\textrm{BA}} - k_{\textrm{AB}}) \\
-= - 2 \Delta \omega \, k_{\textrm{EX}} ( 2p_A - 1)  \\
+\phantom{\zeta} = - 2 \Delta \omega \, k_{\textrm{EX}} ( 2p_A - 1)  \\
-\Psi = (p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}})^2 + 4 p_A p_B k_{\textrm{ex}}^2 - \Delta \omega^2
+\Psi = (p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}})^2 + 4 p_A p_B k_{\textrm{ex}}^2 - \Delta \omega^2 \\
-= ( p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}} )^2 - \Delta \omega^2
+\phantom{\Psi} = ( p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}} )^2 - \Delta \omega^2 \\
-= k_{\textrm{ex}}^2 - \Delta \omega^2 \\
+\phantom{\Psi} = k_{\textrm{ex}}^2 - \Delta \omega^2 \\
 \eta_+ = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{+\Psi + \sqrt{\Psi^2 + \zeta^2}} \\
 \eta_- = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{-\Psi + \sqrt{\Psi^2 + \zeta^2}} \\