Technological Uncertainty

The propagation of technological (modeling) uncertainties in SAUNA is based upon the equivalence of a change in the total cross section $\sigma_{t,i}$ and concentration $C_i$ of the corresponding nuclide $i\in mat$. That is, the sensitivities of a functional $R$ to the parameters are the same: $S(R,\sigma_{t,i})=S(R,C_{i})$. In the same manner, the sensitivity to the density of material $\rho_{mat}$ is the sum of the changes:

$$S(R,\rho_{mat}) = \sum_{i\in mat}S(R,\sigma_{t,i})$$

This can be expanded onto other parameters such as atomic fraction $a_i$ and weight fraction $w_i$. However, these parameters are required to be renormalized to ensure the sums of the corresponding values are equal to unity. The renormalization is conducted in a Perfetti-like approach:

$$S'(R,a_i)=S(R,\sigma_{t,i})-\frac{a_i}{1-a_i}\sum_{j\neq i}S(R,\sigma_{t,j})$$

$$S'(R,w_i)=\frac{S(R,\sigma_{t,i})}{1-w_i}-\frac{w_i}{1-w_i}\sum_{j\neq i}\frac{S(R,\sigma_{t,j})}{1-w_j}$$

This approach does not pose any approximations beyond first-order perturbation theory since it does not assume perturbing the other technological parameters such as temperature and geometry that require special techniques to address.