How do I fit multiple curves with same fitting parameters?

I have three different curves for three different temperatures. The expression I'm trying to fit the data to looks like this: $$E_b=E_0(1-\tau/\tau_0)^{\alpha} (1-T/T_m)$$. So I'm trying to fit the energy barrier ($$E_b$$) data to stress and want same $$E_0, \tau_0, \alpha, T_m$$ fitting parameters for each curves so that with different temperatures the fitting will produce the individual curves. I tried the following with MATLAB: lattice_const_calc.m ( but the fitting is way off). Would appreciate it if someone could help out.

Thanks!

• Can you provide the data in a spreadsheet format like the first column $E_\text{b}$, second column $\tau$ and third column $T$? – MachineLearner Mar 5 at 21:55
• Sure! [drive.google.com/open?id=1iz_O12JL6nmNDKF9NJt5yVp0HnUOGSrT] here it is! Thanks for helping out – anikfaisal Mar 5 at 22:18
• Your dataset is very small. Can you get more data points? Normally you should try to aim for 50 data points for every parameter that you want to estimate. So 200 data points would be something like a minimum requirement. Are there any constraints on $E_0$ and $alpha$? – MachineLearner Mar 5 at 22:37
• Unfortunately no. These are the data points I get out of NEB simulations. generating the dataset I provided took a long time, NEB runs are very computationally expensive. $E_{0}$ is can be anything, $\alpha$ should be between 0.5 to 4 – anikfaisal Mar 5 at 23:56