ALTA ALTA Standard Folio Data Arrhenius-Lognormal: Difference between revisions

Revision as of 16:26, 7 March 2012

Standard Folio Data Arrhenius-Lognormal

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-The Arrhenius-lognormal model  <math>pdf</math>  can be obtained first by setting <math>\breve{T}=L(V)</math>  in Eqn. (arrhenius). Therefore:
-<math>\breve{T}=L(V)=C{{e}^{\tfrac{B}{V}}}</math>
-or:
-<math>{{e}^{{{\overline{T}}^{\prime }}}}=C{{e}^{\tfrac{B}{V}}}</math>
-Thus:
-<math>{{\overline{T}}^{\prime }}=\ln (C)+\frac{B}{V}</math>
-Substituting Eqn. (arrh-logn-mean) into Eqn. (arrh-logn-pdf) yields the Arrhenius-lognormal model  <math>pdf</math>  or:
-<math>f(T,V)=\frac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'-\ln (C)-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}</math>
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