Unitful.jl - how to represent "particles per cubic centimeter"

New to Julia
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Using this equation, I’d like to create a function to calculate the velocity of the Solar Wind.

The equation has three inputs: mp (the mass of a photon), n (number of particles per cubic cm), and V (velocity in kilometers per second).

I’d like to use Unitful.jl to type the arguments. For example, I’m using the following to type Velocity:

V::typeof(1.0u"km/s")

The mass of photon is easy to represent, in fact there’s a Unitful constant for it.

What I can’t figure out is how to represent n, the number of particles per cm^3.

Unitful defines an “amount” dimension, 𝐍 (\bfN), but you don’t appear to be able to use it in units, so I can’t say 7u"𝐍/cm^3". There don’t appear to be any amount unit types other than moles, which doesn’t seem like the right choice.

I tried defining a new unit, but using the macros to do so in Pluto doesn’t work.

I’d prefer to type the variable with Unitful because, I think, you get conversions for free. So, for example, if the inputs were particles per cubic meter they’d automatically be converted.

I’d be grateful for some help! Thanks in advance.

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Presumably this is a flaw in Pluto and not Unitful.jl. You could just eval the definition in, or put it in a separate file and include that file.

This trouble with macros in Pluto.jl will hopefully be addressed soon once Analyse macros by Pangoraw · Pull Request #1032 · fonsp/Pluto.jl · GitHub is merged.

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Okay, I just checked in a Pluto notebook, and defining the unit in a module and then registering that module seems to work for me:

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image818×549 23.2 KB

### A Pluto.jl notebook ###
# v0.14.7

using Markdown
using InteractiveUtils

# ╔═╡ 2784b1a6-c274-11eb-1408-b1cfb6b90eec
using Unitful

# ╔═╡ ad245d53-7925-48e3-bfbd-f86c0219e3bf
module MyUnits 
using Unitful
@unit N "N" Number 1 false
end

# ╔═╡ e6cf3bc1-f1bb-4cf4-8335-a28938ebb1ac
Unitful.register(MyUnits)

# ╔═╡ 6d64e53c-fd95-4202-b313-8ee0da6a7fef
1u"N/cm^3"

# ╔═╡ Cell order:
# ╠═2784b1a6-c274-11eb-1408-b1cfb6b90eec
# ╠═ad245d53-7925-48e3-bfbd-f86c0219e3bf
# ╠═e6cf3bc1-f1bb-4cf4-8335-a28938ebb1ac
# ╠═6d64e53c-fd95-4202-b313-8ee0da6a7fef
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I’m not that familiar with Unitful.jl, but wouldn’t you just use the units 1/cm^3 or cm^(-3)?

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@Mason - Ah, very interesting! I had tried to create a unit that way, but not in a module. Thank you!

@DNF - Very elegant and, I bet, what the authors had in mind. It seems to work. I’ll fiddle with it a bit more to confirm that there aren’t side effects. Love that your intuition took you right to the answer!

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A postscript for people who find this in the future:

If you have created a variable with units like this:

n = 7u"cm^-3"

And, later, you want to get the 7 out, you can strip the units by using the multiplicative inverse of the units:

n*u"cm^3" == 7 # true

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Or use the ustrip function.

3 Likes