Switch point and piecewise function

Questions
1

Hi, I want to fit my data, here is my data

warp
warp3600×2400 67 KB

The function is

equation2

when R < R1, psi = 0, psi starts to deviate at R1 < R < R2, and psi equals psi maximum at R = R2, with psi_maximum is set at a certain value.

I want to fit the data with these equation and need to know the best value of R1, R2, and alpha.

Can you give me advice or some references to study.

Thanks

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