Failure of dimensional analysis for a rule
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Day
am 21 Sep. 2023
Kommentiert: Day
am 27 Sep. 2023
Hi,
I have a rule y=x^0.35. x has the dimension of mass. An error message showed up saying that the exponent must be an integer constant. How can I handle this situation as this rule is very important in my model?
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Arthur Goldsipe
am 21 Sep. 2023
When you enable dimensional analysis (or unit conversion) in SimBiology, fractional exponents can only be applied to dimensionless quantities. So you could write your rule as y=y0*(x/x0)^0.35, where x and x0 have the same units, and y0 is the value of y when x=x0.
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Walter Roberson
am 21 Sep. 2023
I am baffled about what unit (grams ^ 0.35) would be. Should that be interpreted as (grams ^ (35/100) so that the unit would be "the 100'th root of grams to the 35'th power" ? Or should it be interpreted as (grams ^ (7/20)) ? so that the unit would be "the 20'th root of grams to the 7'th power" ?
Mind you, I also struggle with the physical meaning of something like y = sqrt(x) when x is mass.
If this is a situation of "never mind the dimensional continuity for now, the math works out" then you are going to have to strip the units from the item, make the math transformation, and add units back to the result.
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Walter Roberson
am 22 Sep. 2023
Hmmm, it appears that people do find uses for odd units; https://www.reddit.com/r/askscience/comments/2v4gv5/the_square_root_of_a_kilogram/
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