Changes in doc/guide/pd/polydispersity.rst [75e4319:1f058ea] in sasmodels
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doc/guide/pd/polydispersity.rst
r75e4319 r1f058ea 40 40 calculations are generally more robust with more data points or more angles. 41 41 42 The following sixdistribution functions are provided:42 The following five distribution functions are provided: 43 43 44 44 * *Rectangular Distribution* 45 * *Uniform Distribution*46 45 * *Gaussian Distribution* 47 46 * *Lognormal Distribution* 48 47 * *Schulz Distribution* 49 48 * *Array Distribution* 50 * *Boltzmann Distribution*51 49 52 50 These are all implemented as *number-average* distributions. … … 85 83 Rectangular distribution. 86 84 87 Uniform Distribution88 ^^^^^^^^^^^^^^^^^^^^^^^^89 90 The Uniform Distribution is defined as91 92 .. math::93 94 f(x) = \frac{1}{\text{Norm}}95 \begin{cases}96 1 & \text{for } |x - \bar x| \leq \sigma \\97 0 & \text{for } |x - \bar x| > \sigma98 \end{cases}99 100 where $\bar x$ is the mean of the distribution, $\sigma$ is the half-width, and101 *Norm* is a normalization factor which is determined during the numerical102 calculation.103 104 Note that the polydispersity is given by105 106 .. math:: \text{PD} = \sigma / \bar x107 108 .. figure:: pd_uniform.jpg109 110 Uniform distribution.111 112 85 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 113 86 … … 208 181 ^^^^^^^^^^^^^^^^^^ 209 182 210 This user-definable distribution should be given as a simple ASCII text183 This user-definable distribution should be given as as a simple ASCII text 211 184 file where the array is defined by two columns of numbers: $x$ and $f(x)$. 212 185 The $f(x)$ will be normalized to 1 during the computation. … … 227 200 given for the model will have no affect, and will be ignored when computing 228 201 the average. This means that any parameter with an array distribution will 229 not be fitable. 230 231 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 232 233 Boltzmann Distribution 234 ^^^^^^^^^^^^^^^^^^^^^^ 235 236 The Boltzmann Distribution is defined as 237 238 .. math:: 239 240 f(x) = \frac{1}{\text{Norm}} 241 \exp\left(-\frac{ | x - \bar x | }{\sigma}\right) 242 243 where $\bar x$ is the mean of the distribution and *Norm* is a normalization 244 factor which is determined during the numerical calculation. 245 The width is defined as 246 247 .. math:: \sigma=\frac{k T}{E} 248 249 which is the inverse Boltzmann factor, 250 where $k$ is the Boltzmann constant, $T$ the temperature in Kelvin and $E$ a 251 characteristic energy per particle. 252 253 .. figure:: pd_boltzmann.jpg 254 255 Boltzmann distribution. 202 not be fittable. 256 203 257 204 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
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