Conceptual Question in Non-dimensionalisation

[patata]

Hi there everybody, while not a specific homework problem, in my PDE class i have come along a question which i don't quite understand.

Now, when non-dimensionalising an equation, i believe the purpose is to remove the units from it? Now, we are talking about a biological population and are told 't' is time, 'a' is the age of the animal and amax is the maximum age an animal can reach. Now when non-dimensionalising the given equation we're told that

tau = t / amax

I'm not to sure what exactly time over the maximum age of the animal actually represnts, could anybody help enlighten me? Thanks

 

[HallsofIvy]

Dividing the variable t, measured in years, by any specific number of years will give you a "non-dimensional" variable. The specific divisor is not terribly important until it comes time to "interpret" the variables. Here, it looks like "t/amax" is just the fraction of the maximum age the animal has lived. If tau= 0, this is a new born. If tau= .5, it has lived half of the "maximum age".

 

[patata]

Thanks for your help Halls, your reasoning makes sense, however, the next non-dimensionalised variable we have to introduce is

y = a / amax,

so wouldn't this also represent the fraction of the maximum age the animal has lived? keeping in mind that 'a' is the age of the organism..

Thanks once again for your help