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Refactor kernel parameters - #68

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molmod:mainfrom
RobbeBohy:refactor/kernel-params
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Refactor kernel parameters#68
RobbeBohy wants to merge 2 commits into
molmod:mainfrom
RobbeBohy:refactor/kernel-params

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@RobbeBohy

@RobbeBohy RobbeBohy commented Aug 6, 2026

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In this PR, we introduce two new parameters $n_{90}$ and $f_{90}$. The parameter $n_{90}$ quantifies the settling timelag of the ACF and is defined as the lag at which its cumulative sum remains within a 10% tolerance band around the analytical ACF integral. The parameter $f_{90}$ is defined as the frequency at which the cumulative integral of the PSD reaches 90% of the analytical variance.

The kernel parameters have been reformulated taking into consideration the fixed ACF integral of 1, the integrated correlation time, and the two new parameters $n_{90}$ and $f_{90}$.

Note that the $f_{90}$ of the pow1p and pow1w are close to the Nyquist frequency, implyinig that the sampled spectra will inevitably contain aliasing. As a result, adding a white-noise component to the pow1w kernel provides little additional value. We therefore replace this kernel with a new kernel, pow1sho, which combines a power-law term with an underdamped SHO term.

Note that the text in overview.typ has not yet been updated to reflect these changes. This will be addressed as a part of a large upcoming documentation PR, which will contain many new insights we have gained over the last couple of weeks.

@RobbeBohy
RobbeBohy requested a review from tovrstra August 6, 2026 11:28
@RobbeBohy RobbeBohy changed the title Refactor/kernel params Refactor kernel parameters Aug 6, 2026
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