Changeset 5ed76f8 in sasview for src/sas/sasgui/perspectives/fitting/media/pd_help.rst
- Timestamp:
- Apr 7, 2017 1:11:41 AM (7 years ago)
- Branches:
- master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, magnetic_scatt, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
- Children:
- fca1f50
- Parents:
- 727c05f
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src/sas/sasgui/perspectives/fitting/media/pd_help.rst
r6aad2e8 r5ed76f8 24 24 form factor is normalized by the average particle volume such that 25 25 26 *P(q) = scale* * \ <F*\F> / *V + bkg* 26 .. math:: 27 27 28 where F is the scattering amplitude and the \<\> denote an average over the size 29 distribution. 28 P(q) = \text{scale} \langle F^*F rangle V + \text{background} 29 30 where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an average 31 over the size distribution. 30 32 31 33 Users should note that this computation is very intensive. Applying polydispersion … … 57 59 .. image:: pd_image001.png 58 60 59 where *xmean* is the mean of the distribution, *w* is the half-width, and *Norm* is a60 normalization factor which is determined during the numerical calculation.61 where $x_{mean}$ is the mean of the distribution, $w$ is the half-width, and $Norm$ 62 is a normalization factor which is determined during the numerical calculation. 61 63 62 Note that the standard deviation and the half width *w*are different!64 Note that the standard deviation and the half width $w$ are different! 63 65 64 66 The standard deviation is … … 81 83 .. image:: pd_image005.png 82 84 83 where *xmean* is the mean of the distribution and *Norm*is a normalization factor85 where $x_{mean}$ is the mean of the distribution and $Norm$ is a normalization factor 84 86 which is determined during the numerical calculation. 85 87 … … 100 102 .. image:: pd_image007.png 101 103 102 where |mu|\ =ln(*xmed*), *xmed*is the median value of the distribution, and103 *Norm*is a normalization factor which will be determined during the numerical104 where $\mu=\ln(x_{med})$, $x_{med}$ is the median value of the distribution, and 105 $Norm$ is a normalization factor which will be determined during the numerical 104 106 calculation. 105 107 … … 107 109 size parameter in the *FitPage*, for example, radius = 60. 108 110 109 The polydispersity is given by |sigma|111 The polydispersity is given by $\sigma$ 110 112 111 113 .. image:: pd_image008.png … … 115 117 .. image:: pd_image009.png 116 118 117 The mean value is given by *xmean*\ =exp(|mu|\ +p\ :sup:`2`\ /2). The peak value118 is given by *xpeak*\ =exp(|mu|-p\ :sup:`2`\ ).119 The mean value is given by $x_{mean} =\exp(\mu + p^2 /2)$. The peak value 120 is given by $x_{peak} =\exp(\mu-p^2)$. 119 121 120 122 .. image:: pd_image010.jpg 121 123 122 This distribution function spreads more, and the peak shifts to the left, as *p*124 This distribution function spreads more, and the peak shifts to the left, as $p$ 123 125 increases, requiring higher values of Nsigmas and Npts. 124 126 … … 132 134 .. image:: pd_image011.png 133 135 134 where *xmean* is the mean of the distribution and *Norm*is a normalization factor135 which is determined during the numerical calculation, and *z*is a measure of the136 where $x_{mean}$ is the mean of the distribution and $Norm$ is a normalization factor 137 which is determined during the numerical calculation, and $z$ is a measure of the 136 138 width of the distribution such that 137 139 138 z = (1-p\ :sup:`2`\ ) / p\ :sup:`2` 140 .. math:: 141 142 z = (1-p^2 ) / p^2 139 143 140 144 The polydispersity is … … 156 160 157 161 This user-definable distribution should be given as as a simple ASCII text file 158 where the array is defined by two columns of numbers: *x* and *f(x)*. The *f(x)*162 where the array is defined by two columns of numbers: $x$ and $f(x)$. The $f(x)$ 159 163 will be normalized by SasView during the computation. 160 164 … … 172 176 173 177 SasView only uses these array values during the computation, therefore any mean 174 value of the parameter represented by *x*present in the *FitPage*178 value of the parameter represented by $x$ present in the *FitPage* 175 179 will be ignored. 176 180 … … 181 185 182 186 Many commercial Dynamic Light Scattering (DLS) instruments produce a size 183 polydispersity parameter, sometimes even given the symbol *p*! This parameter is187 polydispersity parameter, sometimes even given the symbol $p$! This parameter is 184 188 defined as the relative standard deviation coefficient of variation of the size 185 189 distribution and is NOT the same as the polydispersity parameters in the Lognormal
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