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Diffstat (limited to 'site/content/gsoc/nondimensionalization.typ')
| -rw-r--r-- | site/content/gsoc/nondimensionalization.typ | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/site/content/gsoc/nondimensionalization.typ b/site/content/gsoc/nondimensionalization.typ index aba870a..7c6dff6 100644 --- a/site/content/gsoc/nondimensionalization.typ +++ b/site/content/gsoc/nondimensionalization.typ @@ -9,7 +9,7 @@ Here's a simple but interesting bit of math that came up while working on an imp $ R(lambda) = sigma(c_0 lambda^2 + c_1 lambda + c_2) $ -where $c_0, c_1, c_2$ are model parameters, $lambda in [360 "nm", 830 "nm"]$ and $sigma: RR -> [0, 1]$ is a sigmoid function. Reflectivities tend to be rather smooth and the values of the polynomial not too large. If wavelengths are expressed numerically in nanometers, $c_1$ and especially $c_0$ will tend to be very small. This makes it harder to find minima of the function, as solvers tend get confused, unless special care is taken to change the default tolerances properly. +where $c_0, c_1, c_2$ are model parameters, $lambda in [360 "nm", 830 "nm"]$ and $sigma: RR -> [0, 1]$ is a sigmoid function. Reflectivities tend to be rather smooth and the values of the polynomial not too large. If wavelengths are expressed numerically in nanometers, $c_1$ and especially $c_0$ will tend to be very small. This makes it harder to find minima of the function, as solvers tend to get confused, unless special care is taken to change the default tolerances properly. A more straightforward solution is to rescale $lambda$ to a more convenient range, a process a physicist would call *nondimensionalization*. Following the authors of the article, let $ |