# Conceptual Question in Non-dimensionalisation

• patata

#### 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

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".

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