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  • doc/guide/pd/polydispersity.rst

    r75e4319 r1f058ea  
    4040calculations are generally more robust with more data points or more angles. 
    4141 
    42 The following six distribution functions are provided: 
     42The following five distribution functions are provided: 
    4343 
    4444*  *Rectangular Distribution* 
    45 *  *Uniform Distribution* 
    4645*  *Gaussian Distribution* 
    4746*  *Lognormal Distribution* 
    4847*  *Schulz Distribution* 
    4948*  *Array Distribution* 
    50 *  *Boltzmann Distribution* 
    5149 
    5250These are all implemented as *number-average* distributions. 
     
    8583    Rectangular distribution. 
    8684 
    87 Uniform Distribution 
    88 ^^^^^^^^^^^^^^^^^^^^^^^^ 
    89  
    90 The Uniform Distribution is defined as 
    91  
    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| > \sigma 
    98         \end{cases} 
    99  
    100     where $\bar x$ is the mean of the distribution, $\sigma$ is the half-width, and 
    101     *Norm* is a normalization factor which is determined during the numerical 
    102     calculation. 
    103  
    104     Note that the polydispersity is given by 
    105  
    106     .. math:: \text{PD} = \sigma / \bar x 
    107  
    108     .. figure:: pd_uniform.jpg 
    109  
    110         Uniform distribution. 
    111  
    11285.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    11386 
     
    208181^^^^^^^^^^^^^^^^^^ 
    209182 
    210 This user-definable distribution should be given as a simple ASCII text 
     183This user-definable distribution should be given as as a simple ASCII text 
    211184file where the array is defined by two columns of numbers: $x$ and $f(x)$. 
    212185The $f(x)$ will be normalized to 1 during the computation. 
     
    227200given for the model will have no affect, and will be ignored when computing 
    228201the 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. 
     202not be fittable. 
    256203 
    257204.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
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