thinprofiles.jl

### A Pluto.jl notebook ###
# v0.19.9

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ c1ea4e34-b9d1-490f-87a2-f91b372d9a1e
begin
	using PlutoUI
	using Plots
	using NLsolve
end

# ╔═╡ b70e2ecf-b0af-4f7c-9583-d723020e4aea
md"""
!!! danger "Thin profile with camber effect"

	_by [Jean-François Barthélémy](https://jfbarthelemy.github.io/)_

	This tutorial provides tool to visualize 2D streamlines of incompressible fluid around a thin profile with camber effect.
"""

# ╔═╡ 3c39dd00-ba5e-4a5d-b0d4-ff65b106469b
begin
md"""
- Remote velocity $\underline{U}=U\left(\cos{\alpha}\underline{e}_x+\sin{\alpha}\underline{e}_y\right)$ 
- Eccentricity $iB=c-R\,e^{-i\beta}$ with $c=R\,cos{\beta}$ et $R^2=c^2+B^2$
- Complex potential $Z$ $\to$ $F(Z)=U\left((Z-iB)\,e^{-i\alpha}+\frac{R^2}{Z-iB}\,e^{i\alpha}\right)-\frac{i\,m}{2π}\log{\frac{(Z-iB)}{R}}$
- Joukovski conformal map $z=h(Z)=Z+\frac{c^2}{Z}$
- Kutta condition $F'(c)=0 \Rightarrow m=-4πRU\sin{(\alpha+\beta)}$ (by default)
"""
end

# ╔═╡ bababbb4-3b41-4d17-a29e-afe3edc85e92
md"""`𝑈` = $(@bind U Slider(0:0.1:2, default=1,show_value=true))"""

# ╔═╡ d9e751b7-9028-44c2-96f2-f770c0d76225
md"""`c` = $(@bind c Slider(0:0.1:2, default=1,show_value=true))"""

# ╔═╡ b8f12d57-6762-4a29-8e02-9c152821e5e9
md"""`α` = `π*`$(@bind α₀ Slider(0:1/60:1/6, default=0.1,show_value=true))"""

# ╔═╡ c13b8ff5-f84d-44ba-8f30-9865391f8c61
md"""`β` = `π*`$(@bind β₀ Slider(0:1/60:1/4, default=0.1,show_value=true))"""

# ╔═╡ 8b390f6c-fad5-465c-878a-a9509cfff8cf
md"""Kutta condition $(@bind Kutta CheckBox(default=true)) """

# ╔═╡ 691f8f1c-ae36-42c0-9cda-802af9d847d6
begin
	myasin(x) = abs(x)<=1 ? asin(x) : NaN
	θ₁(r,ψ=0,R=1,m=0,U=1) = myasin((ψ+m/2π*log(r/R))/(U*r*(1-R^2/r^2))) ;
	θ₂(r,ψ=0,R=1,m=0,U=1) = π - θ₁(r,ψ,R,m,U) ;
	h(Z,c) = Z+c^2/Z
	Z₀(Z,α) = Z*exp(im*α)
	ζ(Z,c,α,β) = c-c*exp(-im*β)/cos(β)+Z*exp(im*α)
	reim(tab) = real.(tab), imag.(tab)
	cercle(R=1,n=100) = [R*exp(im*θ) for θ ∈ range(0,2π,length=n)]
	# streamline(θᵢ,lr,ψ,R,m,U) = [r*exp(im*θᵢ(r,ψ,R,m,U)) for r ∈ lr]
	streamline01(lr,R,m,U) = [r*exp(im*θ₁(r,0,R,m,U)) for r ∈ reverse(lr)]
	streamline02(lr,R,m,U) = [r*exp(im*θ₂(r,0,R,m,U)) for r ∈ lr]
	streamline(lr,ψ,R,m,U) = [[r*exp(im*θ₁(r,ψ,R,m,U)) for r ∈ reverse(lr)]...,[r*exp(im*θ₂(r,ψ,R,m,U)) for r ∈ lr]...]
	function solve_rmin(ψ,UR,m)
		ϵ = ψ>=0 ? 1 : -1
		f(x) = ψ-ϵ*UR*(x[1]-1/x[1])+m/2π*log(x[1])
		return nlsolve(f, [1.,], autodiff=:forward).zero[1]
	end
	
	if !Kutta
		_α = α₀ * π ;
		_β = β₀ * π ;
		_R = c / cos(_β) ;
		_m = max(4π * U * _R * sin(_α + _β), 4π * U * _R * 1.e-3)
		md"""`m` = $(@bind mvar Slider(-_m*2:_m/10:_m*2, default = 0, show_value=true))"""
	end

	α = α₀ * π ;
	β = β₀ * π ;
	R = c / cos(β) ;
	B = R * sin(β) ;
	mKutta = -4π * U * R * sin(α + β) ;
	m = Kutta ? mKutta : mvar ;

	lψ = range(-2*U*R,2*U*R,length=21)
	A = m/(4π*R*U)
	if abs(A)>1
		X₀ = abs(A)+√(A^2-1)
		ψ₀ = R*U*(X₀-1/X₀)*sign(A)-m/2π*log(X₀)
		lψ = push!(collect(lψ),ψ₀)
	end
	p1 = plot()
	for ψ ∈ lψ
		r_min = R
		try
			r_min = R*max(solve_rmin(ψ,U*R,m)*1.0001,1)
		catch e
			r_min = R
		end
		lr = exp10.(range(log10(r_min),log10(5*R),length=200))
		if iszero(ψ)
			plot!(p1,reim(ζ.(streamline01(lr,R,m,U),c,α,β))...,legend=false,aspect_ratio=:equal)
			plot!(p1,reim(ζ.(streamline02(lr,R,m,U),c,α,β))...,legend=false,aspect_ratio=:equal)
		else
			plot!(p1,reim(ζ.(streamline(lr,ψ,R,m,U),c,α,β))...,legend=false,aspect_ratio=:equal)
		end
	end
	plot!(p1,reim(ζ.(cercle(R,200),c,α,β))...,fill=(0,:black),legend=false,aspect_ratio=:equal)

		p2 = plot()
	for ψ ∈ lψ
		r_min = R
		try
			r_min = R*max(solve_rmin(ψ,U*R,m)*1.0001,1)
		catch e
			r_min = R
		end
		lr = exp10.(range(log10(r_min),log10(5*R),length=200))
		if iszero(ψ)
			plot!(p2,reim(h.(ζ.(streamline01(lr,R,m,U),c,α,β),c))...,legend=false,aspect_ratio=:equal)
			plot!(p2,reim(h.(ζ.(streamline02(lr,R,m,U),c,α,β),c))...,legend=false,aspect_ratio=:equal)
		else
			plot!(p2,reim(h.(ζ.(streamline(lr,ψ,R,m,U),c,α,β),c))...,legend=false,aspect_ratio=:equal)
		end
	end
	plot!(p2,reim(h.(ζ.(cercle(R,200),c,α,β),c))...,fill=(0,:black),lw=5,legend=false,aspect_ratio=:equal)
end ;

# ╔═╡ b7412c86-ab71-4580-879c-47e33837047e
plot(p1,p2,layout=(1,2), size=(650,300))

# ╔═╡ 00000000-0000-0000-0000-000000000001
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git-tree-sha1 = "87e9954dfa33fd145694e42337bdd3d5b07021a6"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.6.0"

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "74fb527333e72ada2dd9ef77d98e4991fb185f04"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.4.1"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "c3d8ba7f3fa0625b062b82853a7d5229cb728b6b"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.2.1"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "8977b17906b0a1cc74ab2e3a05faa16cf08a8291"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.16"

[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "57617b34fa34f91d536eb265df67c2d4519b8b98"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.5"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"

[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"]
git-tree-sha1 = "5ce79ce186cc678bbb5c5681ca3379d1ddae11a1"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.7.0"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.1.2"

[[deps.Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
# ╟─b70e2ecf-b0af-4f7c-9583-d723020e4aea
# ╟─3c39dd00-ba5e-4a5d-b0d4-ff65b106469b
# ╟─bababbb4-3b41-4d17-a29e-afe3edc85e92
# ╟─d9e751b7-9028-44c2-96f2-f770c0d76225
# ╟─b8f12d57-6762-4a29-8e02-9c152821e5e9
# ╟─c13b8ff5-f84d-44ba-8f30-9865391f8c61
# ╟─8b390f6c-fad5-465c-878a-a9509cfff8cf
# ╟─b7412c86-ab71-4580-879c-47e33837047e
# ╟─c1ea4e34-b9d1-490f-87a2-f91b372d9a1e
# ╟─691f8f1c-ae36-42c0-9cda-802af9d847d6
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002