How to fit a model to the V-shaped data?
After plotting out the density of the dependent varaible, flux, I would recommend exploring a Generalized Linear Model.

flux appears to be the output of a gamma distribution or perhaps a log-normal distribution. I would recommend exploring a GLM, especially with the lme4 package in R. GLMs are convenient transformations of the prototypical linear regression, and thus are easily interpreted. They are flexible and well-founded in theory as well.

Is there any work which might suggest a data generating process for your problem? You might ask yourself things you know about the process: is it true that x values are always greater than 0? Is there an upper bound?