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[cellml-discussion] Dimensional consistency and units conversions (was [Fwd: Re: ten Tusscher model])


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  • From: matt.halstead at auckland.ac.nz (Matt )
  • Subject: [cellml-discussion] Dimensional consistency and units conversions (was [Fwd: Re: ten Tusscher model])
  • Date: Sat, 21 Apr 2007 01:58:28 +1200
>
> The CellML specification distinguishes expansion and simplification. The
> expansion algorithm given maintains a scale factor in the expanded unit,
> and hence the *expansion* of m/km is *not* the same as dimensionless. It
> is only when you then simplify that the scale factor is lost. For
> checking dimensional consistency, this is fine. For performing units
> conversions, it is not, and so the units conversion algorithm in the spec
> does *not* drop the scale factor, even though it claims in the text that
> the units involved are "fully expanded and simplified", this is according
> to C.3.4 (expansion) not C.3.1 (simplification).
>
> So there are two separate questions here:
> 1) checking the dimensional consistency of mathematics

Which we can already do given our variables and constants need to all
have dimensions and it is easy to discover if they do not.

> 2) ensuring a sensible semantics for simulating a model
>

What are sensible semantics in the case of 'units'?

How do you ensure something like units consistency has been applied
correctly by an author? You are never going to be able to ensure any
unit multiplication factors are correct, even if they are given units
of their own.

going back to the following equation Andrew supplied:

amount_Na [nmol] = 10^-6 [dimensionless] * conc_Na [nmol / L] * vol[microL]

How do you make this more 'valid'? (it is already valid dimensionally
and numerically).


Also, I'm not sure what 'converting units at connections' has to do
with this discussion - that only ensures value consistency in the
assigning of values to inputs and outputs of components and has
nothing to do with ensuring units consistency inside the math.

cheers
Matt


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