I've generated these curves from a set of data and would like to fit them to come up with a model for a program I'm writing. Can anyone suggest functions that might approximate my curves? I'm a physicist so I immediately saw similarities with Planck's law for black body radiation for the blue curve (which fits well for positive values) and the Lennard-Jones potential for the red curve (although this doesn't come above zero after the initial trench)
Any help or suggestions will be greatly appreciated.
OK, the blue curve is $$ B(x)=\frac{x^2-0.015^2}{30x^2[1+(x/0.07)^4]} $$ The parameters may be not exactly optimal, but, frankly speaking, with as much noise in the data as you gave me, I didn't see any point in trying to fit them any better. Once you produce something that has less crazy jumps from one point to another (especially near the end where the values get smaller), I can try to get a better fit. I am pretty sure about the general kind of the expression up to minor tweaks, which are meaningless to discuss without getting minimally decent experimental precision first.
See if this helps. I'll try the red curve next :-)
Edit:
The red curve may possibly be $$ R(y)=\int_y^\infty\frac{0.34(x-0.015)(x-0.16)}{x^2[1+(x/0.18)^4]}\,dx $$ except this gives the value at $0.005$ ten times less than in your table (whether your number, as recorded, is a misprint with one head zero missing or not I cannot tell; the information near $0$ is severely insufficient).
The formula $$ R(y)=\int_y^\infty\frac{0.27(x^2-0.0155^2)(x-0.16)}{x^3[1+(x/0.185)^4]}\,dx $$ would fit all data almost perfectly, but cubic polynomial in the numerator seems to be an overkill (after all, everything can be approximated by rational functions if the degree is high enough).
My current guess is that, in general, you have some (radial?) force field given by $$ F(r)=A\frac{(r-u)(r-v)}{r^2[1+(r/w)^4]} $$ or something like that and the blue curve is the force while the red curve is the potential.
If my assumption is correct, the only thing that remains to discuss is how to do the best fit of parameters for noisy data and what measurements to make (all your points for the red curve beyond $0.65$ are total gibberish: your equipment cannot even make its mind about whether the value is positive or negative, so it makes no sense to look there at all, while I would really love smaller steps and more values near $0$). If not, let me know what is really going on :-).