Changes between Version 9 and Version 10 of GuarDyan_PhysModel

Timestamp:

Feb 13, 2018, 3:43:32 PM (7 years ago)

Author:

dieda

Comment:

--

GuarDyan_PhysModel

@@ -39 +39 @@
 
 
-With each $\chi$^2^2 calculated, we obtain N= 412 x 5 energies . These results are summarized in Fig.3.
+With each $\chi$^2^ calculated, we obtain N= 412 x 5 energies . These results are summarized in Fig.3. in a histogram.
+
+[[Image(chi_square_histogram.jpg​​, 400px, title=Reduced Chi-squared histogram)]] \\ ''Figure 3.: Reduced $\chi$^2^ histogram '' 
+
+As Fig. 3 shows GUARDYAN and MCNP results agree very well within statistics having the majority of the cases with match within 1.5$\sigma$. 
+
+For lower energies, in vast majority of the isotopes the dominant interaction is elastic scattering. For fissionable materials ACE laws 3, 4, 7, 9, 11, 44, 61 and 66 occur even at low energies, for higher energies many isotopes undergo such interactions, still elastic scattering being the dominant interaction in case of the basic model. To ensure that promising $\chi$^2^  values are not only caused by a properly implemented elastic scattering algorithm, we have registered the number of samplings of certain ACE laws. To assess the impact of a certain ACE law on the $\chi$^2^ value we have calculated the (Pearson) correlation coefficient between x,,i,, and y,,i,, data points with $\overline{x}$ and  $\overline{y}$ averages respectively:
+
+  $corr=\frac{\sum_{N}^{i=1}\left ( x_{i}-\overline{x} \right )\left ( y_{i}-\overline{y} \right )}{\sqrt{\sum_{N}^{i=1}\left ( x_{i}-\overline{x} \right )^{2}}\sqrt{\sum_{N}^{i=1}\left ( y_{i}-\overline{y} \right )^{2}}}$
 
 
 
 
-  
-
-
 ----
 [[Image(NRDI.jpg, 80%)]]