I'm not entirely sure I'm posting this in the right place as I'm an engineer not a mathmatician, but it's certainly harder than anything I had to do to get my maths A-level before I went to University!
I'm using the equation below to model cracks forming in a polymer under stress. My problem is this: k (the Boltzmann constant, 1.38 x 10^23... pretty small) is part of the exponential terms. The other variables are more manageable; U is around 1.14 x 10^5, and gamma is around 3.56 x 10^-4. Sigma is the effective stress, and would be around 10^7 Pa or thereabouts. T is the absolute temperature and is about 293K. n(t) is the time at which the polymer becomes macroscopically damaged.
I'm working with MATLAB, which is limited by the IEEE 'double' precision. This means it can deal with numbers up to about 1.7*10^308. Unfortunately, if you try and perform exp(-U/kT), -U/kT is about -2 x 10^25, so MATLAB returns 0. Similarly, for exp(gamma.sigma/kT) it returns infinity. I'm sure it is possible to rescale the problem somehow or work in logs to get around this but I can't figure out how you'd do this. Can anyone offer any help on this? It will be much appreciated!