### A Pluto.jl notebook ### # v0.15.1 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 el = $(esc(element)) global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing el end end # ╔═╡ c028100e-f47b-11eb-2547-df779889e265 using WaterLily, StaticArrays, PlutoUI, Interpolations, Plots, Images # ╔═╡ b0c8df66-1e63-456e-be32-d469e6972e00 md""" ## Simulation of a swimming dogfish shark **Gabriel D Weymouth** [![Twitter URL](https://img.shields.io/twitter/url/https/twitter.com/gabrielweymouth.svg?style=social&label=)](https://twitter.com/gabrielweymouth) | 11 Aug 2021 --- This post will demonstrate how to set up and simulate a model of a swimming dogfish shark using [Julia](https://julialang.org/) and [WaterLily.jl](https://www.youtube.com/watch?v=YsPkfZqbNSQ). The post is actually a [Pluto notebook](https://www.youtube.com/watch?v=IAF8DjrQSSk) and can be run interactively by clicking on the top right icon. We'll use a simple model of the shark based on Lighthill's pioneering [paper on the swimming of slender fish](https://doi.org/10.1017/S0022112060001110). It focuses on the "backbone" of the fish; idealizing the shape as a thickness distribution on either side of the center, and the motion as a lateral ("side-to-side") traveling wave. Amazingly, this simple approach provides insight across a huge range of a swimming animals as illustrated in the image below. [Image credit: Gazzola et al, _Nature_ 2014](https://www.nature.com/articles/nphys3078) """ # ╔═╡ e9384124-9708-44eb-b5e7-75abc5177a69 begin url = "https://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fnphys3078/MediaObjects/41567_2014_Article_BFnphys3078_Fig1_HTML.jpg" filename = download(url) lighthill = load(filename) end # ╔═╡ c8293b7b-0585-45b3-8763-8cfa4671b155 md""" ### Modeling the shark's thickness and motion We'll define the thickness and motion distributions using `interpolate` to fit splines through a few points. """ # ╔═╡ a48ac92c-5cb0-4e51-a08f-b34bc8b06d04 fit = y-> scale(interpolate(y, BSpline(Quadratic(Line(OnGrid())))), range(0,1,length=length(y))) # ╔═╡ ad96bcbe-4482-4486-b817-e788604d1d96 md""" Here is an image of the dogfish shark we will model. [Image credit: Shark Trust](file:///C:/Users/admin/Downloads/Spiny%20Dogfish%20ST%20Factsheet.PDF) """ # ╔═╡ 47eb9e3f-5617-417a-8924-5a38d90390e8 # Fish shape begin url2 = "https://pterosaurheresies.files.wordpress.com/2020/01/squalus-acanthias-invivo588.jpg" filename2 = download(url2) dogfish = load(filename2) end # ╔═╡ 8752bf4d-50e6-42ea-8d43-c41699769f77 md""" The bottom view shows the outline we're interested in, and adding a few points along the length defines the thickness distribution function `thk`. """ # ╔═╡ 71c9bc8f-921d-4df4-acc2-7321ce6648e0 begin plot(dogfish) nose,len = (30,224),500 width = [0.02,0.07,0.06,0.048,0.03,0.019,0.01] scatter!(nose[1].+len.*range(0,1,length=length(width)), nose[2].-len.*width,color=:blue,legend=false) thk = fit(width) x = 0:0.01:1 plot!(nose[1].+len.*x, [nose[2].-len.*thk.(x),nose[2].+len.*thk.(x)],color=:blue) end # ╔═╡ d830e69e-f085-495e-be2c-8ea44582fa20 md""" Looking at [videos of swimming dogfish](https://youtu.be/nMa6lD2CQVI?t=200), we can see a couple general features - The motion of the front half of the body has a small amplitude (around 20% of the tail). This sets the amplitude envelope for the traveling wave. """ # ╔═╡ c2b7a082-c05d-41bb-af4c-eb23f6a331bf begin envelope = [0.2,0.21,0.23,0.4,0.88,1.0] amp = fit(envelope) end # ╔═╡ ea51f472-7ffc-4062-a45c-1410d26b1c3e md""" - The wavelength of the traveling wave is a bit longer than the body length. The slider below controls the wavelength of the traveling wave λ, which you can adjust to see the impact it has on the backbone over the motion cycle. """ # ╔═╡ 454f7849-2d9b-4250-94bb-9aed4c2f0d54 md"λ: $@bind λ Slider(0.5:0.1:2, show_value=true, default = 1.1)" # ╔═╡ 67f29fd6-11ed-415f-abc0-2ed3c84fe60f begin scatter(0:0.2:1, envelope) colors = palette(:cyclic_wrwbw_40_90_c42_n256) for t in 1/12:1/12:1 plot!(x,amp.(x).*sin.(2π/λ*x.-2π*t),color=colors[floor(Int,t*256)]) end plot!(ylim=(-1.4,1.4),legend=false) end # ╔═╡ db1ed38c-a1aa-4173-bb43-d81afedbfab9 md""" ### Setting up the simulation Now the thickness and motion are defined, but how will we apply these to a fluid simulation? `WaterLily`uses an [immersed boundary method](https://eprints.soton.ac.uk/369635/) and [automatic differentiation](https://en.wikipedia.org/wiki/Automatic_differentiation) to embed a body into the flow. The upshot is that we don't need to do any meshing; all we need is a signed distance function (SDF) to the surface. Let's start by defining the SDF to the "backbone", which is a line segment from $x=0\ldots 1$. [See this great video from Inigo Quilez for a derivation of this sdf.](https://www.youtube.com/watch?v=PMltMdi1Wzg) The plot below shows the sdf and the zero contour, which is ... just a line segment. Simple adjustments to the SDF give us more control of the shape and position. By shifting the y offset as `y = y-shift`, we can move the body laterally. And by subtracting a thickness from the distance as `sdf = sdf-thickness`, we can give the line some width. This is all we need to model the shark. """ # ╔═╡ bfc73784-8c27-4cdb-a8e4-fbcbf9ddb3c2 md"shift: $@bind shift Slider(-1:0.5:2, show_value=true, default=0.5)" # ╔═╡ 76dc572f-3cd2-4f1a-9296-2065c877a6ef md"thickness: $@bind T Slider(0.001:0.25:2, show_value=true)" # ╔═╡ 839db88c-a477-4718-88bb-796ab0cd6591 begin function segment_sdf(x,y) s = clamp(x,0,1) # distance along the segment y = y-shift # shift laterally sdf = √sum(abs2,(x-s,y)) # line segment SDF return sdf-T*thk(s) # subtract thickness end grid = -1:0.05:2 contourf(grid,grid,segment_sdf,clim=(-1,2),linewidth=0) contour!(grid,grid,segment_sdf,levels=[0],color=:black) # zero contour end # ╔═╡ f33b9315-b2d1-4fab-91c9-ed3b63fb4d41 md""" With the basic SDF tested out, we are ready to set up the WaterLily simulation using the function `fish` defined below: - The functions `thk` is passed in to create the `sdf` and the function `amp` is passed in to create the traveling wave `map`. - The only numerical parameter passed into `fish` is the length of the fish `L` measured in computational cells. This sets the resolution of the simulation and the size of the fluid arrays. - The other parameters are the tail amplitude `A` as a fraction of the length, the [Stouhal number](https://en.wikipedia.org/wiki/Strouhal_number) which sets the motion frequency `ω`, and the [Reynolds number](https://en.wikipedia.org/wiki/Reynolds_number) which sets the fluid viscosity `ν`. """ # ╔═╡ 11702be3-d125-4ea4-b7e9-74d34943a164 begin function fish(thk,amp,k=5.3;L=2^6,A=0.1,St=0.3,Re=1e4) # fraction along fish length s(x) = clamp(x[1]/L,0,1) # fish geometry: thickened line SDF sdf(x,t) = √sum(abs2,x-L*SVector(s(x),0.))-L*thk(s(x)) # fish motion: travelling wave U=1 ω = 2π*St*U/(2A*L) function map(x,t) xc = x.-L # shift origin return xc-SVector(0.,A*L*amp(s(xc))*sin(k*s(xc)-ω*t)) end # make the fish simulation return Simulation((4L+2,2L+2),[U,0.],L; ν=U*L/Re,body=AutoBody(sdf,map)) end # Create the swimming shark L,A,St = 3*2^5,0.1,0.3 swimmer = fish(thk,amp;L,A,St); # Save a time span for one swimming cycle period = 2A/St cycle = range(0,23/24*period,length=24) end # ╔═╡ d844c02d-41c8-43a8-95dd-742ea6c24f86 md""" We can test our geometry by plotting the immersed boundary function `μ₀`; which equals 1 in the fluid and 0 in the body. """ # ╔═╡ e618b2d9-abe8-4e97-aab2-e87c6278378f @gif for t ∈ cycle measure!(swimmer,t*swimmer.L/swimmer.U); contour(swimmer.flow.μ₀[:,:,1]', aspect_ratio=:equal,legend=false,border=:none) end # ╔═╡ 7329a0ba-c57c-4d77-99da-2f8f66d5a94e md""" ### Running visualizing and measuring the simulation That animation of the motion looks great, so we are ready to run the flow simulator! The `sim_step!(sim,t,remeasure=true)` function runs the simulator up to time `t`, remeasuring the body position every time step. (`remeasure=false` by default since it takes a little extra computational time and isn't needed for statics geometries.) """ # ╔═╡ 845cbd96-c01b-49f7-94df-15836a68ebba # run the simulation a few cycles (this takes few seconds) begin sim_step!(swimmer,3,remeasure=true) sim_time(swimmer) end # ╔═╡ d5c82801-8387-4ef0-9f34-3279a54603c5 md""" The simulation has now run forward in time, but there are no visualizations or measurements by default. To see what is going on, lets make a gif of the vorticity `ω=curl(u)` to visualize the vortices in the wake of the shark. This requires simulating a cycle of motion, and computing the `curl` at all the points `@inside` the simulation. """ # ╔═╡ a5c9b186-332f-4812-bb07-0bbe288f5091 begin # plot the vorcity ω=curl(u) scaled by the body length L and flow speed U function plot_vorticity(sim) @inside sim.flow.σ[I] = WaterLily.curl(3,I,sim.flow.u)*sim.L/sim.U contourf(sim.flow.σ', color=palette(:BuGn), clims=(-10,10),linewidth=0, aspect_ratio=:equal,legend=false,border=:none) end # make a gif over a swimming cycle @gif for t ∈ sim_time(swimmer).+cycle sim_step!(swimmer,t,remeasure=true) plot_vorticity(swimmer) end end # ╔═╡ 85c555bb-f584-4064-9da7-f7f1e4fd5320 md""" This is pretty (CFD does stand for _Colorful Fluid Dynamics_ after all), but also tells us something important about the flow. Notice that there are no eddies coming off the body anywhere other than the tail! This is a sign of efficiency since energy is only used to create those trailing vortices. We can dig in and get some quantitative measurements from the simulation as well. The function `∮nds` takes a integral over the body surface. By passing in the pressure `p`, we can measure the thrust force and side force generated by the shark! """ # ╔═╡ c4c3fa5c-79bc-4d55-827f-c952b129ab5f begin function get_force(sim,t) sim_step!(sim,t,remeasure=true) return WaterLily.∮nds(sim.flow.p,sim.body,t*sim.L/sim.U)./(0.5*sim.L*sim.U^2) end forces = [get_force(swimmer,t) for t ∈ sim_time(swimmer).+cycle] "got forces" end # ╔═╡ 9fc14582-108f-4434-83da-f7b32b676bd3 scatter(cycle./period,[first.(forces),last.(forces)], labels=permutedims(["thrust","side"]), xlabel="scaled time", ylabel="scaled force") # ╔═╡ 9c67282b-e26a-42bf-836e-fc464b8ca63d md""" We can learn a lot from this simple plot. For example, the side-to-side force has the same frequency as the swimming motion itself while the thrust force has double the frequency, with a peak every time the tail passes through the centerline. ### Next steps This simple model is a great start and it opens up a ton of avenues for improving the shark simulation and suggesting research questions: - The instantaneous net forces should be zero in a free swimming body! We could add reaction motions to our model to achieve this. Would the model shark swim in a straight line if we did this, or is a control-loop needed? - Real sharks are 3D (gasp!). While we could easily extend this approach using 2D splines, it will take much longer to simulate. Is there a way use GPUs to accelerate the simulations without completely changing the solver? - If we were going to make a bio-inspired robot of this shark, we will have constraints on the shape and motion and powering available. Can we use this framework to help optimize our robotic within it's constraints? Below you can find links to all the packages used in this notebook. Happy Simulating! 1. [Interpolations.jl](https://juliamath.github.io/Interpolations.jl/stable/) 1. [JuliaDiff](https://juliadiff.org/) 1. [JuliaImages](https://juliaimages.org/stable/) 1. [Plots.jl](http://docs.juliaplots.org/latest/) 1. [Pluto.jl](https://github.com/fonsp/Pluto.jl) and [PlutoUI.jl](https://github.com/fonsp/PlutoUI.jl) 1. [StaticArrays.jl](https://github.com/JuliaArrays/StaticArrays.jl) 1. [WaterLily.jl](https://github.com/weymouth/WaterLily.jl) """ # ╔═╡ 00000000-0000-0000-0000-000000000001 PLUTO_PROJECT_TOML_CONTENTS = """ [deps] Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0" Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" WaterLily = "ed894a53-35f9-47f1-b17f-85db9237eebd" [compat] Images = "~0.24.1" Interpolations = "~0.13.3" Plots = "~1.20.0" PlutoUI = "~0.7.9" StaticArrays = "~1.2.11" WaterLily = "~0.2.3" """ # ╔═╡ 00000000-0000-0000-0000-000000000002 PLUTO_MANIFEST_TOML_CONTENTS = """ # This file is machine-generated - editing it directly is not advised [[ANSIColoredPrinters]] git-tree-sha1 = "574baf8110975760d391c710b6341da1afa48d8c" uuid = "a4c015fc-c6ff-483c-b24f-f7ea428134e9" version = "0.0.1" [[AbstractFFTs]] deps = ["LinearAlgebra"] git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0" uuid = 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= ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"] uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0" [[LibGit2]] deps = ["Base64", "NetworkOptions", "Printf", "SHA"] uuid = "76f85450-5226-5b5a-8eaa-529ad045b433" [[LibSSH2_jll]] deps = ["Artifacts", "Libdl", "MbedTLS_jll"] uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8" [[LibVPX_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "12ee7e23fa4d18361e7c2cde8f8337d4c3101bc7" uuid = "dd192d2f-8180-539f-9fb4-cc70b1dcf69a" version = "1.10.0+0" [[Libdl]] uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" [[Libffi_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "761a393aeccd6aa92ec3515e428c26bf99575b3b" uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490" version = "3.2.2+0" [[Libgcrypt_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"] git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae" uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4" version = "1.8.7+0" [[Libglvnd_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"] git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf" uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29" version = "1.3.0+3" [[Libgpg_error_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9" uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8" version = "1.42.0+0" [[Libiconv_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778" uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531" version = "1.16.1+1" [[Libmount_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73" uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9" version = "2.35.0+0" [[Libtiff_jll]] deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"] git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9" uuid = "89763e89-9b03-5906-acba-b20f662cd828" version = "4.3.0+0" [[Libuuid_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066" uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700" version = "2.36.0+0" [[LinearAlgebra]] deps = ["Libdl"] uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" [[LogExpFunctions]] deps = ["DocStringExtensions", "LinearAlgebra"] git-tree-sha1 = "7bd5f6565d80b6bf753738d2bc40a5dfea072070" uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688" version = "0.2.5" [[Logging]] uuid = "56ddb016-857b-54e1-b83d-db4d58db5568" [[MKL_jll]] deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"] git-tree-sha1 = "c253236b0ed414624b083e6b72bfe891fbd2c7af" uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7" version = "2021.1.1+1" [[MacroTools]] deps = ["Markdown", "Random"] git-tree-sha1 = "0fb723cd8c45858c22169b2e42269e53271a6df7" uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" version = "0.5.7" [[MappedArrays]] git-tree-sha1 = "18d3584eebc861e311a552cbb67723af8edff5de" uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900" version = "0.4.0" [[Markdown]] deps = ["Base64"] uuid = "d6f4376e-aef5-505a-96c1-9c027394607a" [[MbedTLS]] deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"] git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe" uuid = "739be429-bea8-5141-9913-cc70e7f3736d" version = "1.0.3" [[MbedTLS_jll]] deps = ["Artifacts", "Libdl"] uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1" [[Measures]] git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f" uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e" version = "0.3.1" [[Missings]] deps = ["DataAPI"] git-tree-sha1 = "4ea90bd5d3985ae1f9a908bd4500ae88921c5ce7" uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28" version = "1.0.0" [[Mmap]] uuid = "a63ad114-7e13-5084-954f-fe012c677804" [[MosaicViews]] deps = ["MappedArrays", "OffsetArrays", "PaddedViews", "StackViews"] git-tree-sha1 = "b34e3bc3ca7c94914418637cb10cc4d1d80d877d" uuid = "e94cdb99-869f-56ef-bcf0-1ae2bcbe0389" version = "0.3.3" [[MozillaCACerts_jll]] uuid = "14a3606d-f60d-562e-9121-12d972cd8159" [[NaNMath]] git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb" uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3" version = "0.3.5" [[Netpbm]] deps = ["ColorVectorSpace", "FileIO", "ImageCore"] git-tree-sha1 = "09589171688f0039f13ebe0fdcc7288f50228b52" uuid = "f09324ee-3d7c-5217-9330-fc30815ba969" version = "1.0.1" [[NetworkOptions]] uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" [[OffsetArrays]] deps = ["Adapt"] git-tree-sha1 = "5cc97a6f806ba1b36bac7078b866d4297ae8c463" uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881" version = "1.10.4" [[Ogg_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f" uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051" version = "1.3.5+0" [[OpenSSL_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a" uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" version = "1.1.10+0" [[OpenSpecFun_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1" uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e" version = "0.5.5+0" [[Opus_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720" uuid = "91d4177d-7536-5919-b921-800302f37372" version = "1.3.2+0" [[OrderedCollections]] git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c" uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d" version = "1.4.1" [[PCRE_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488" uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc" version = "8.44.0+0" [[PNGFiles]] deps = ["Base64", "CEnum", "ImageCore", "IndirectArrays", "OffsetArrays", "libpng_jll"] git-tree-sha1 = "520e28d4026d16dcf7b8c8140a3041f0e20a9ca8" uuid = "f57f5aa1-a3ce-4bc8-8ab9-96f992907883" version = "0.3.7" [[PaddedViews]] deps = ["OffsetArrays"] git-tree-sha1 = "59925f4ae6861cddc2313a47514b93b6740f9b6f" uuid = "5432bcbf-9aad-5242-b902-cca2824c8663" version = "0.5.9" [[Parameters]] deps = ["OrderedCollections", "UnPack"] git-tree-sha1 = "2276ac65f1e236e0a6ea70baff3f62ad4c625345" uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a" version = "0.12.2" [[Parsers]] deps = ["Dates"] git-tree-sha1 = "477bf42b4d1496b454c10cce46645bb5b8a0cf2c" uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0" version = "2.0.2" [[Pixman_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29" uuid = "30392449-352a-5448-841d-b1acce4e97dc" version = "0.40.1+0" [[Pkg]] deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"] uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" [[PkgVersion]] deps = ["Pkg"] git-tree-sha1 = "a7a7e1a88853564e551e4eba8650f8c38df79b37" uuid = "eebad327-c553-4316-9ea0-9fa01ccd7688" version = "0.1.1" [[PlotThemes]] deps = ["PlotUtils", "Requires", "Statistics"] git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d" uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a" version = "2.0.1" [[PlotUtils]] deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"] git-tree-sha1 = "501c20a63a34ac1d015d5304da0e645f42d91c9f" uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043" version = "1.0.11" [[Plots]] deps = ["Base64", "Contour", "Dates", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs"] git-tree-sha1 = "e39bea10478c6aff5495ab522517fae5134b40e3" uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" version = "1.20.0" [[PlutoUI]] deps = ["Base64", "Dates", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "Suppressor"] git-tree-sha1 = "44e225d5837e2a2345e69a1d1e01ac2443ff9fcb" uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8" version = "0.7.9" [[Preferences]] deps = ["TOML"] git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a" uuid = "21216c6a-2e73-6563-6e65-726566657250" version = "1.2.2" [[Printf]] deps = ["Unicode"] uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" [[ProgressMeter]] deps = ["Distributed", "Printf"] git-tree-sha1 = "afadeba63d90ff223a6a48d2009434ecee2ec9e8" uuid = "92933f4c-e287-5a05-a399-4b506db050ca" version = "1.7.1" [[Qt5Base_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"] git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8" uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1" version = "5.15.3+0" [[REPL]] deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" [[Random]] deps = ["Serialization"] uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" [[RangeArrays]] git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5" uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d" version = "0.3.2" [[Ratios]] git-tree-sha1 = "37d210f612d70f3f7d57d488cb3b6eff56ad4e41" uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439" version = "0.4.0" [[RecipesBase]] git-tree-sha1 = "b3fb709f3c97bfc6e948be68beeecb55a0b340ae" uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01" version = "1.1.1" [[RecipesPipeline]] deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"] git-tree-sha1 = "2a7a2469ed5d94a98dea0e85c46fa653d76be0cd" uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c" version = "0.3.4" [[Reexport]] git-tree-sha1 = "5f6c21241f0f655da3952fd60aa18477cf96c220" uuid = "189a3867-3050-52da-a836-e630ba90ab69" version = "1.1.0" [[Requires]] deps = ["UUIDs"] git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621" uuid = "ae029012-a4dd-5104-9daa-d747884805df" version = "1.1.3" [[Rotations]] deps = ["LinearAlgebra", "StaticArrays", "Statistics"] git-tree-sha1 = "2ed8d8a16d703f900168822d83699b8c3c1a5cd8" uuid = "6038ab10-8711-5258-84ad-4b1120ba62dc" version = "1.0.2" [[SHA]] uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" [[Scratch]] deps = ["Dates"] git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda" uuid = "6c6a2e73-6563-6170-7368-637461726353" version = "1.1.0" [[Serialization]] uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" [[SharedArrays]] deps = ["Distributed", "Mmap", "Random", "Serialization"] uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383" [[Showoff]] deps = ["Dates", "Grisu"] git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de" uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f" version = "1.0.3" [[SimpleTraits]] deps = ["InteractiveUtils", "MacroTools"] git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231" uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d" version = "0.9.4" [[Sockets]] uuid = "6462fe0b-24de-5631-8697-dd941f90decc" [[SortingAlgorithms]] deps = ["DataStructures"] git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508" uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c" version = "1.0.1" [[SparseArrays]] deps = ["LinearAlgebra", "Random"] uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" [[SpecialFunctions]] deps = ["ChainRulesCore", "LogExpFunctions", "OpenSpecFun_jll"] git-tree-sha1 = "508822dca004bf62e210609148511ad03ce8f1d8" uuid = "276daf66-3868-5448-9aa4-cd146d93841b" version = "1.6.0" [[StackViews]] deps = ["OffsetArrays"] git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c" uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15" version = "0.1.1" [[Static]] deps = ["IfElse"] git-tree-sha1 = "62701892d172a2fa41a1f829f66d2b0db94a9a63" uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3" version = "0.3.0" [[StaticArrays]] deps = ["LinearAlgebra", "Random", "Statistics"] git-tree-sha1 = "b28f39450421d07d89ab5d126fd15e5246350e8a" uuid = "90137ffa-7385-5640-81b9-e52037218182" version = "1.2.11" [[Statistics]] deps = ["LinearAlgebra", "SparseArrays"] uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" [[StatsAPI]] git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510" uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0" version = "1.0.0" [[StatsBase]] deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"] git-tree-sha1 = "fed1ec1e65749c4d96fc20dd13bea72b55457e62" uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" version = "0.33.9" [[StructArrays]] deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"] git-tree-sha1 = "000e168f5cc9aded17b6999a560b7c11dda69095" uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a" version = "0.6.0" [[Suppressor]] git-tree-sha1 = "a819d77f31f83e5792a76081eee1ea6342ab8787" uuid = "fd094767-a336-5f1f-9728-57cf17d0bbfb" version = "0.2.0" [[TOML]] deps = ["Dates"] uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76" [[TableTraits]] deps = ["IteratorInterfaceExtensions"] git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39" uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c" version = "1.0.1" [[Tables]] deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"] git-tree-sha1 = "d0c690d37c73aeb5ca063056283fde5585a41710" uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c" version = "1.5.0" [[Tar]] deps = ["ArgTools", "SHA"] uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" [[TensorCore]] deps = ["LinearAlgebra"] git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6" uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50" version = "0.1.1" [[Test]] deps = ["InteractiveUtils", "Logging", "Random", "Serialization"] uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [[TiffImages]] deps = ["ColorTypes", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "OrderedCollections", "PkgVersion", "ProgressMeter"] git-tree-sha1 = "03fb246ac6e6b7cb7abac3b3302447d55b43270e" uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69" version = "0.4.1" [[TiledIteration]] deps = ["OffsetArrays"] git-tree-sha1 = "52c5f816857bfb3291c7d25420b1f4aca0a74d18" uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac" version = "0.3.0" [[URIs]] git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355" uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4" version = "1.3.0" [[UUIDs]] deps = ["Random", "SHA"] uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" [[UnPack]] git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b" uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed" version = "1.0.2" [[Unicode]] uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" [[WaterLily]] deps = ["Documenter", "ForwardDiff", "LinearAlgebra", "StaticArrays"] git-tree-sha1 = "9d17cfa8a5e12d568bddd18f4332d1919316fc28" uuid = "ed894a53-35f9-47f1-b17f-85db9237eebd" version = "0.2.3" [[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" [[Wayland_protocols_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"] git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670" uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91" version = "1.18.0+4" [[WoodburyMatrices]] deps = ["LinearAlgebra", "SparseArrays"] git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c" uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6" version = "0.5.3" [[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" [[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" [[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" [[Xorg_libXau_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e" uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec" version = "1.0.9+4" [[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" [[Xorg_libXdmcp_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4" uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05" version = "1.1.3+4" [[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" [[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" [[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" [[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" [[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" [[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" [[Xorg_libpthread_stubs_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb" uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74" version = "0.1.0+3" [[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" [[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" [[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" [[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" [[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" [[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" [[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" [[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" [[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" [[Xorg_xtrans_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845" uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" version = "1.4.0+3" [[Zlib_jll]] deps = ["Libdl"] uuid = "83775a58-1f1d-513f-b197-d71354ab007a" [[Zstd_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6" uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" version = "1.5.0+0" [[libass_jll]] deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c" uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" version = "0.14.0+4" [[libfdk_aac_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab" uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" version = "0.1.6+4" [[libpng_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" version = "1.6.38+0" [[libvorbis_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb" uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" version = "1.3.7+0" [[nghttp2_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" [[p7zip_jll]] deps = ["Artifacts", "Libdl"] uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" [[x264_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f" uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" version = "2020.7.14+2" [[x265_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab" uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" version = "3.0.0+3" [[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: # ╠═c028100e-f47b-11eb-2547-df779889e265 # ╟─b0c8df66-1e63-456e-be32-d469e6972e00 # ╟─e9384124-9708-44eb-b5e7-75abc5177a69 # ╟─c8293b7b-0585-45b3-8763-8cfa4671b155 # ╠═a48ac92c-5cb0-4e51-a08f-b34bc8b06d04 # ╟─ad96bcbe-4482-4486-b817-e788604d1d96 # ╟─47eb9e3f-5617-417a-8924-5a38d90390e8 # ╟─8752bf4d-50e6-42ea-8d43-c41699769f77 # ╠═71c9bc8f-921d-4df4-acc2-7321ce6648e0 # ╟─d830e69e-f085-495e-be2c-8ea44582fa20 # ╠═c2b7a082-c05d-41bb-af4c-eb23f6a331bf # ╟─ea51f472-7ffc-4062-a45c-1410d26b1c3e # ╟─454f7849-2d9b-4250-94bb-9aed4c2f0d54 # ╠═67f29fd6-11ed-415f-abc0-2ed3c84fe60f # ╟─db1ed38c-a1aa-4173-bb43-d81afedbfab9 # ╟─bfc73784-8c27-4cdb-a8e4-fbcbf9ddb3c2 # ╟─76dc572f-3cd2-4f1a-9296-2065c877a6ef # ╠═839db88c-a477-4718-88bb-796ab0cd6591 # ╟─f33b9315-b2d1-4fab-91c9-ed3b63fb4d41 # ╠═11702be3-d125-4ea4-b7e9-74d34943a164 # ╟─d844c02d-41c8-43a8-95dd-742ea6c24f86 # ╠═e618b2d9-abe8-4e97-aab2-e87c6278378f # ╟─7329a0ba-c57c-4d77-99da-2f8f66d5a94e # ╠═845cbd96-c01b-49f7-94df-15836a68ebba # ╟─d5c82801-8387-4ef0-9f34-3279a54603c5 # ╠═a5c9b186-332f-4812-bb07-0bbe288f5091 # ╟─85c555bb-f584-4064-9da7-f7f1e4fd5320 # ╠═c4c3fa5c-79bc-4d55-827f-c952b129ab5f # ╟─9fc14582-108f-4434-83da-f7b32b676bd3 # ╟─9c67282b-e26a-42bf-836e-fc464b8ca63d # ╟─00000000-0000-0000-0000-000000000001 # ╟─00000000-0000-0000-0000-000000000002