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DOE OSTI · 1765856

(U) A Linear Response Model Predicts Reactivity From a Density Profile

Disterhaupt, Jennifer Lynn Schei·Skau, Erik West·Sanzo, Dean Lawrence·Klasky, Marc Louis
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Abstract

We tested the ability to predict the system reactivity, described by alpha, given a density profile using a simple linear system response. We generated a suite of 1-dimensional density profiles that consisted of nominal density, a discontinuity, and a decay. These profiles were prescribed a functional form and the mass was conserved in all cases. From these density profiles, we calculated the alpha value of the 3-dimensional system.We calculated a linear response function given a training set of the 1-dimensional density profiles, and the system reactivity described by alpha. We tested the robustness of the response function using the remaining test data. Our results showed very good agreement between the predicted and calculated test values, where the distribution of alpha differences was centered about zero and had a standard deviation of 0.005 gens/shake. The predicted and calculated alpha values did not significantly differ (t=-0.0009 p<0.99). We used Singular Value Decomposition (SVD) to reduce the matrix rank by retaining95% of the cumulative singular value contributions. This reduced the matrix rank by 91.7%. We generated the linear response matrix and calculated the difference between the predicted and calculated alpha values. Using the reduced order matrix, we showed good agreement between the predicted and calculated alpha values where the distribution of differences was centered near zero, the standard deviation was 0.006 gens/shake, and the statistical t-test showed good agreement (t=0.02, p<0.98). These results show a linear relationship between a series of 1-dimensional density profiles,where the mass was conserved, and the system reactivity. The next steps of this work will be to investigate the linear response using 2-dimensional density profiles.

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Disterhaupt, Jennifer Lynn Schei, Skau, Erik West, Sanzo, Dean Lawrence, Klasky, Marc Louis. 2021-02-11. (U) A Linear Response Model Predicts Reactivity From a Density Profile. https://doi.org/10.2172/1765856

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