### A Pluto.jl notebook ### # v0.19.27 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 # ╔═╡ ea758628-8a57-481f-9d8f-edda66f30e42 using Images # ╔═╡ 00ebaf5f-0258-4daf-840e-6f01b3bdd352 using ImageDraw # ╔═╡ e3160714-e504-48bd-898b-fdfcb07856ba using PlutoUI # ╔═╡ 81e1c4e1-89bf-4888-bf65-ce021c7a574b using ProgressLogging # ╔═╡ cf53e56a-3f21-4ba6-aae5-7b1e5fdc9623 using LinearAlgebra # ╔═╡ 49b8c58c-ba0d-4783-8a3d-888902277b75 md" ## Canvas " # ╔═╡ 5589b059-d8c8-43fa-8916-c2a5d1a36a1d function norm2(A; dims) B = sum(x -> x^2, A; dims=dims) sqrt.(B) end # ╔═╡ fede4fd1-acb3-4b2e-b2bc-2e3703e7762d HSV(240, 0.5, 1.0) # ╔═╡ 9e5c5ea0-850a-4dbf-b89b-33ae234bbce6 struct Canvas width :: Int height :: Int grid_size :: Int particle_radius :: Float64 pixels :: Matrix{HSV{Float64}} end # ╔═╡ 4312153d-d1c3-4c04-8f49-0681ebe49931 function mk_canvas(width :: Int, height :: Int, grid_size :: Int = 30) :: Canvas Canvas( width, height, grid_size, grid_size * (1/5), fill(HSV(0.0, 0.0, 1.0), grid_size * height, grid_size * width) ) end # ╔═╡ 56d8ea14-6fb7-4aed-a098-58c99a00d98f function draw_particle!(self :: Canvas, x :: Number, y :: Number) x´ = 1 + round(Int, (x - 0.5) * self.grid_size) y´ = 1 + round(Int, (y - 0.5) * self.grid_size) draw!( self.pixels, Ellipse(CirclePointRadius(x´, y´, self.particle_radius)), HSV(240, 0.5, 1.0) ) end # ╔═╡ 510a8bb6-c36f-427a-8a1f-09520ba8e372 # ╔═╡ 4435eb0e-92b9-4e2b-b010-ea30d33cca7f function draw_box!(self :: Canvas, x :: Number, y :: Number, color :: HSV{Float64}) x´ = 1 + round(Int, (x - 1) * self.grid_size) y´ = 1 + round(Int, (y - 1) * self.grid_size) self.pixels[ y´:y´ + self.grid_size - 1, x´:x´ + self.grid_size - 1 ] .= color end # ╔═╡ 02bb3de1-ac52-4c41-881f-6cbefa0f14d6 md" ## Periodic Vector Field " # ╔═╡ 95782460-370f-11ee-23f0-15d095c0cbd2 mutable struct PeriodicVectorField width :: Int height :: Int dim :: Int values :: Array{Float64, 3} end # ╔═╡ 6c328f85-2bdb-4b9a-94d6-008d5fcfcb0b function mk_field(width :: Int, height :: Int, dim :: Int; initial :: Float64 = 0.0) :: PeriodicVectorField PeriodicVectorField( width, height, dim, fill(initial, width, height, dim) ) end # ╔═╡ e047bcdc-7e68-4012-b46c-8effa9c0ec96 function wrap_index(index :: Int, n :: Int) mod1(index, n) end # ╔═╡ e8d3a92e-8e5c-4362-aefb-1937c8265b88 function get_at(self :: PeriodicVectorField, x :: Int, y :: Int) :: Vector{Float64} self.values[wrap_index(x, self.width), wrap_index(y, self.height), :] end # ╔═╡ 0e953361-2ffa-49fd-92f2-526d89761f4a function set_at!(self :: PeriodicVectorField, x :: Int, y :: Int, value :: Vector{Float64}) self.values[wrap_index(x, self.width), wrap_index(y, self.height), :] .= value end # ╔═╡ 4a7f1411-79aa-41c2-8a1f-2b55a6e3de4d @enum Direction SW=1 S SE E NE N NW W # ╔═╡ 1a26e9f9-8cf4-4d2e-9931-d7ead1f21666 [cos(Int(d) * π) for d in instances(Direction)] # ╔═╡ 03e4d872-706a-4bd8-91e6-39ca90170616 function invert_direction(d :: Direction) :: Direction Direction(mod1(Int(d) + 4, length(instances(Direction)))) end # ╔═╡ 1b5563fa-9707-4b8d-802d-1c504e201a04 @assert all(d == invert_direction(invert_direction(d)) for d ∈ instances(Direction)) # ╔═╡ d83c41b0-2efe-42e4-95cd-50270ec74659 direction_offsets = hcat( [round(Int, sin((Int(d) - 2) * π * (1/4))) for d in instances(Direction)], [round(Int, cos((Int(d) - 2) * π * (1/4))) for d in instances(Direction)] ) # ╔═╡ 52517a45-e2d8-45a4-9f33-433b2f5db9b5 function direction_to_offset(d :: Direction) :: Vector{Int} direction_offsets[Int(d), :] end # ╔═╡ 12619d0f-01b6-44de-ba05-fe4fbe3d329a md" ``` (0, 0) x ┌───────────► │ │ N │ ▲ │ │ │ │ │ W◄─── ───►E │ │ │ │ │ ▼ y▼ S ``` " # ╔═╡ 90f0da92-cf10-4309-8dcf-2713e384bd9b for d ∈ [W, N, E, S] @info d direction_to_offset(d) end # ╔═╡ cb362a50-e9ac-4fba-a7b7-864edffce0f9 function get_at_direction( self :: PeriodicVectorField, x :: Int, y :: Int, d :: Direction ) :: Float64 c = direction_to_offset(d) if d >= NE && d <= W get_at_direction(self, x + c[1], y + c[2], invert_direction(d)) else get_at(self, x + c[1], y + c[2])[Int(d)] end end # ╔═╡ 5120d3e6-0c08-4661-b845-777a3b0fd9b3 function set_at_direction!( self :: PeriodicVectorField, x :: Int, y :: Int, d :: Direction, value :: Float64 ) c = direction_to_offset(d) if d >= NE && d <= W set_at_direction!(self, x + c[1], y + c[2], invert_direction(d), value) else v = get_at(self, x + c[1], y + c[2]) v[Int(d)] = value set_at!(self, x + c[1], y + c[2], v) end return end # ╔═╡ 078d53ff-b48f-4e56-84ab-e2bab56d8ba2 rand() # ╔═╡ b323d5a8-b3ec-4dc2-98dd-a1d6a56de8d2 begin local f = mk_field(30, 30, 4) f.values = rand(30, 30, 4) for x ∈ f.width for y ∈ f.height for d ∈ instances(Direction) local off = direction_to_offset(d) local x´ = x + off[1] local y´ = y + off[2] @assert get_at_direction(f, x, y, d) == get_at_direction(f, x´, y´, invert_direction(d)) end end end local fi = 0.0 for x ∈ f.width for y ∈ f.height for d ∈ instances(Direction) set_at_direction!(f, x, y, d, fi) @assert get_at_direction(f, x, y, d) == fi fi += 1 end end end end # ╔═╡ e34a6736-6330-402c-9e94-6ad3d0cfa882 md" ## Maxwell We can numerically solve $\dot{\mathbf{F}}_i(t) = \dot{\mathbf{F}}_{i, \text{elastic}}(t) - \frac{1}{Q} \mathbf{F}_i(t)$ $\mathbf{F}_{i, \text{elastic}}(t) = - \sum_j \mathbf{F}_{ij}(t)$ $\mathbf{F}_{ij}(t) = \mathbf{n}_{ij} K_{ij} (\mathbf{u}_{ij} \cdot \mathbf{x}_{ij}) + \frac{c \mathbf{u}_{ij}}{|\mathbf{x}_{ij}|^2}$ by $\dot{\mathbf{F}}_{i, \text{elastic}}(t) = \frac{\mathbf{F}_{i, \text{elastic}}(t + \Delta t) - \mathbf{F}_{i, \text{elastic}}(t)}{\Delta t}$ $\dot{\mathbf{F}}_i(t) = \dot{\mathbf{F}}_{i, \text{elastic}}(t) - \frac{1}{Q} \mathbf{F}_i(t)$ $\mathbf{F}_i(t + \Delta t) = \mathbf{F}_i(t) + \Delta t \dot{\mathbf{F}}_i(t)$ $\mathbf{v}_i(t + \Delta t) = \mathbf{v}_i(t) + \Delta t \mathbf{F}_i(t) + \frac{1}{2} \Delta t^2 \dot{\mathbf{F}}_i(t)$ $\mathbf{u}_i(t + \Delta t) = \mathbf{u}_i(t) + \Delta t \mathbf{v}_i(t) + \frac{1}{2} \Delta t^2 \mathbf{F}_i(t) + \frac{1}{6} \Delta t^3 \dot{\mathbf{F}}_i(t)$ See [Taylor Series](https://en.wikipedia.org/wiki/Taylor_series) " # ╔═╡ 84d48419-785a-4786-9eaf-000dab9257b1 md" ### Implementation We need store the displacement, velocity, force and elastic force (for calculating $\dot{\mathbf{F}}_{i, \text{elastic}}(t)$) of each particle. " # ╔═╡ 43b1f729-ef23-44ca-8e45-c76ba158848b struct MaxwellModel width :: Int height :: Int displacement :: PeriodicVectorField velocity :: PeriodicVectorField force :: PeriodicVectorField force_change :: PeriodicVectorField elastic_force :: PeriodicVectorField fixed :: PeriodicVectorField Δt :: Float64 k :: Float64 c :: Float64 Q :: Float64 end # ╔═╡ af3f5d21-9ea3-46c2-9b85-bf42a6179f0a function mk_maxwell( width :: Int, height :: Int; Δt :: Float64 = 0.1, k :: Float64 = 1.0, c :: Float64 = 1.0, Q :: Float64 = 100.0 ) :: MaxwellModel MaxwellModel( width, height, mk_field(width, height, 2), mk_field(width, height, 2), mk_field(width, height, 2), mk_field(width, height, 2), mk_field(width, height, 2), mk_field(width, height, 1, initial = 1.0), Δt, k, c, Q ) end # ╔═╡ e8cc22d9-665e-4c0e-8af2-3b96d8f65d0b function get_elastic_force( self :: MaxwellModel, x :: Int, y :: Int, d :: Direction ) :: Vector{Float64} offset = direction_to_offset(d) x´ = x + offset[1] y´ = y + offset[2] u = get_at(self.displacement, x, y) u´ = get_at(self.displacement, x´, y´) x_ij = Float64.([x, y] - [x´, y´]) u_ij = u - u´ r_ij = x_ij + u_ij n_ij = r_ij / norm(r_ij) K_ij = self.k * norm(x_ij) n_ij * K_ij * (u_ij ⋅ x_ij) + (self.c * u_ij) / norm(x_ij)^2 end # ╔═╡ 8639a662-0dd0-4921-8617-cf1b3770fbd9 [0 0 1; 0 1 0; 1 0 0] .* [1 2 3; 1 2 3; 1 2 3] # ╔═╡ eee3a24f-78c0-47ad-8b35-56f2d76bb949 function update_maxwell!(self :: MaxwellModel) Ḟ = self.force_change.values F = self.force.values v = self.velocity.values u = self.displacement.values self.displacement.values = u + self.fixed.values .* (self.Δt * v + self.Δt^2 * (1/2) * F + self.Δt^3 * (1/6) * Ḟ) for x ∈ 1:self.width for y ∈ 1:self.height F_elastic_new = [0.0, 0.0] for d ∈ instances(Direction) F_elastic_new += get_elastic_force(self, x, y, d) end F_elastic_new *= -1 F_elastic = get_at(self.elastic_force, x, y) Ḟ_elastic = (F_elastic_new - F_elastic) / self.Δt set_at!(self.elastic_force, x, y, F_elastic_new) F_i = get_at(self.force, x, y) Ḟ = Ḟ_elastic - (1 / self.Q) * F_i set_at!(self.force_change, x, y, Ḟ) end end Ḟ = self.force_change.values self.force.values = F + self.fixed.values .* (self.Δt * Ḟ) self.velocity.values = v + self.fixed.values .* (self.Δt * F + self.Δt^2 * (1/2) * Ḟ) end # ╔═╡ 5dc38b5c-156f-4450-8a8e-83379f88ea1d function draw_maxwell(self :: MaxwellModel) :: Canvas min_u = minimum(norm2(self.displacement.values, dims = 3)) max_u = maximum(norm2(self.displacement.values, dims = 3)) c = mk_canvas(self.width, self.height * 2) for x ∈ 1:self.width for y ∈ 1:self.height u = get_at(self.displacement, x, y) draw_particle!(c, x + u[1], y + u[2]) draw_box!(c, x, y + self.height, HSV(240, 1.0, (norm(u) - min_u) / (max_u - min_u))) end end c end # ╔═╡ 2a0ca777-0323-4b23-8874-2d816daf6d1d @bind i Clock(interval = 0.05) # ╔═╡ d3e98246-2144-421d-9546-d57086a60e79 import Plots # ╔═╡ 0ef8b6b8-e4ad-4610-a2d6-5985830b23f3 Plots.plotly() # ╔═╡ 9fe9acfc-e696-4f7d-8841-6325e9fd4733 md" ## Interlude: Cool Colors for the Heatmap " # ╔═╡ a183601a-33e8-413d-ae02-93407375edfc function c1(x :: Float64) :: HSV{Float64} HSV(60 * x, 0.5 + (1 - x) * 0.5, x) end # ╔═╡ 67740373-7db8-4e72-9098-77b288c14cc3 [c1(i / 10) for i in 0:10] # ╔═╡ 7f458f26-0abe-4e16-911b-265da7f21a5b md" ## Zener Given $\textbf{F}_{ij}(t) = K_0 \textbf{u}_{ij} + K_1 \textbf{u}^s_{ij} + \frac{c \dot{\textbf{u}}^d_{ij}}{\Delta x^2}$ $\textbf{u} = \textbf{u}^s + \textbf{u}^d$ $K_1 \textbf{u}^s = \eta \dot{\textbf{u}}^d$ we need to derive a set of equations to calculate the new forces, velocities and displacements for a timestep. $\textbf{u}^d(t) \in \mathbb{R}$ $\textbf{u}^s(t) \in \mathbb{R} = |\textbf{u}(t)| - \textbf{u}^d(t)$ $\dot{\textbf{u}}^d(t) = \frac{K_1 \textbf{u}^s(t)}{\eta}$ Updates: $\textbf{u}^d(t + \Delta t) = \textbf{u}^d(t) + \Delta t \dot{\textbf{u}}^d(t)$ " # ╔═╡ 650aae02-8622-481e-8827-cb4c81e6fce5 struct ZenerModel width :: Int height :: Int Δt :: Float64 Δx :: Float64 K0 :: Float64 K1 :: Float64 c :: Float64 η :: Float64 displacement :: PeriodicVectorField velocity :: PeriodicVectorField force :: PeriodicVectorField dampers :: PeriodicVectorField end # ╔═╡ 4be0d852-b22f-41dc-8de4-1025a38ce87c function mk_zener( width :: Int, height :: Int; Δt :: Float64 = 0.1, Δx :: Float64 = 1.0, K0 :: Float64 = 1.0, K1 :: Float64 = 1.0, c :: Float64 = 1.0, η :: Float64 = 1.0 ) :: ZenerModel ZenerModel( width, height, Δt, Δx, K0, K1, c, η, mk_field(width, height, 2), mk_field(width, height, 2), mk_field(width, height, 2), mk_field(width, height, 4), ) end # ╔═╡ 82952bba-d451-4bc0-8cf6-0823a9e2ceac function get_zener_force( self :: ZenerModel, x :: Int, y :: Int, d :: Direction ) :: Vector{Float64} offset = direction_to_offset(d) x´ = x + offset[1] y´ = y + offset[2] u = get_at(self.displacement, x, y) u´ = get_at(self.displacement, x´, y´) u_ij = u - u´ un_ij = if norm(u_ij) == 0.0 [0.0, 0.0] else u_ij / norm(u_ij) end x_ij = [x, y] - [x´, y´] ud_ij = get_at_direction(self.dampers, x, y, d) us_ij = norm(u_ij) - ud_ij u̇d_ij = (self.K1 / self.η) * us_ij self.K0 * u_ij + self.K1 * ud_ij * un_ij + self.c * u̇d_ij * un_ij end # ╔═╡ 9459bdf3-5ff4-48df-8007-b0ba0bed894d function update_zener!(self :: ZenerModel) u = self.displacement.values v = self.velocity.values F = self.force.values self.displacement.values = u + self.Δt * v + self.Δt^2 * (1/2) * F for x ∈ 1:self.width for y ∈ 1:self.height # Update force at particle [x, y] F_i = [0.0, 0.0] for d ∈ instances(Direction) F_i += get_zener_force(self, x, y, d) end F_i *= -1 set_at!(self.force, x, y, F_i) end end # Update spring at [x, y, d] # Move up? # Also: Very inefficient for x ∈ 1:self.width for y ∈ 1:self.height for d ∈ [SW, S, SE, E] offset = direction_to_offset(d) x´ = x + offset[1] y´ = y + offset[2] u = get_at(self.displacement, x, y) u´ = get_at(self.displacement, x´, y´) u_ij = u - u´ ud_ij = get_at_direction(self.dampers, x, y, d) us_ij = norm(u_ij) - ud_ij u̇d_ij = (self.K1 / self.η) * us_ij set_at_direction!(self.dampers, x, y, d, ud_ij + self.Δt * u̇d_ij) end end end v = self.velocity.values F = self.force.values self.velocity.values = v + self.Δt * F end # ╔═╡ 68a560b8-85bc-4077-9338-507c813f3a73 function draw_zener(self :: ZenerModel) :: Canvas min_u = 0 max_u = maximum(norm2(self.displacement.values, dims = 3)) c = mk_canvas(self.width * 2, self.height, 10) for x ∈ 1:self.width for y ∈ 1:self.height u = get_at(self.displacement, x, y) draw_particle!(c, x + u[1], y + u[2]) draw_box!(c, self.width + x, y, c1((norm(u) - min_u) / (max_u - min_u))) end end c end # ╔═╡ 078754ac-326d-4d55-a050-473b8f866960 begin dist_xs = 30:34 dist_ys = 21:22 dist_dir = 0.5 * direction_to_offset(S) η = 0.25 K0 = 0.25 K1 = 0.25 zc = 4.0 z = mk_zener(61, 61, η = η, K0 = K0, K1 = K1, c = zc) # set_at!(z.displacement, 5, 5, 0.5 * direction_to_offset(NW)) for x ∈ dist_xs for y ∈ dist_ys set_at!(z.displacement, x, y, dist_dir) end end z_frames = [] z_max_f = [] z_max_u = [] z_sum_u = [] dist_sum_u = [] function z_log_stuff!() push!(z_max_f, maximum(norm2(z.force.values, dims=3))) push!(z_max_u, maximum(norm2(z.displacement.values, dims=3))) push!(z_sum_u, sum(norm2(z.displacement.values, dims=3))) push!(dist_sum_u, sum(norm2(z.displacement.values[dist_xs, dist_ys, :], dims=3))) push!(z_frames, draw_zener(z).pixels) end z_log_stuff!() @progress for i ∈ 1:100 update_zener!(z) z_log_stuff!() end end # ╔═╡ 923ed671-b139-47b6-a10b-10cdc8c4b87a @bind zir Clock(interval = 0.05) # ╔═╡ 0335032b-06b9-4b9e-bc78-c21ce95c5bb3 zi = mod1(zir, length(z_frames)) # ╔═╡ df0eda58-f1c9-4040-98e8-e1db173bb2f9 z_frames[zi] # ╔═╡ 01d400ee-953b-4f75-852a-b30f672acc31 z_max_f[zi] # ╔═╡ f6b50ef9-94d9-4f80-b778-ef00f3635279 Plots.plot([ z_max_f, z_max_u, z_sum_u, dist_sum_u ], layout = (4, 1)) # ╔═╡ 16db9976-fc91-4010-98fd-8d4cda6117d8 w, h = size(z_frames[1]) # ╔═╡ 5c79d594-a3a0-472e-a4cc-0c78df3ecf9d begin anim = fill(HSV(0, 1.0, 1.0), w, h, length(z_frames)) for i ∈ 1:length(z_frames) anim[:, :, i] = z_frames[i] end end # ╔═╡ 91e05e7f-70bd-4ded-9a1e-f62602386a40 gif_path = "/home/paul/zener_$(η)_$(K0)_$(K1)_$(zc).gif" # ╔═╡ f75e6776-e2a7-4a54-9bf9-e674d778bc66 function draw_line!(self :: Canvas, x :: Number, y :: Number, x´ :: Number, y´ :: Number) p1 = Point(round(Int, (x + 0.5) * self.grid_size), round(Int, (y + 0.5) * self.grid_size)) p2 = Point(round(Int, (x´ + 0.5) * self.grid_size), round(Int, (y´ + 0.5) * self.grid_size)) draw!(self.pixels, LineSegment(p1,p2), HSV(0.0, 1.0, 1.0)) end # ╔═╡ 00000000-0000-0000-0000-000000000001 PLUTO_PROJECT_TOML_CONTENTS = """ [deps] ImageDraw = "4381153b-2b60-58ae-a1ba-fd683676385f" Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" ProgressLogging = "33c8b6b6-d38a-422a-b730-caa89a2f386c" [compat] ImageDraw = "~0.2.6" Images = "~0.26.0" Plots = "~1.38.17" PlutoUI = "~0.7.52" ProgressLogging = "~0.1.4" """ # ╔═╡ 00000000-0000-0000-0000-000000000002 PLUTO_MANIFEST_TOML_CONTENTS = """ # This file is machine-generated - editing it directly is not advised julia_version = "1.8.5" manifest_format = "2.0" project_hash = "e0b9e852a96a15580effb0ccde770b4f16d1de17" [[deps.AbstractFFTs]] deps = ["ChainRulesCore", "LinearAlgebra", "Test"] git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef" uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" version = "1.5.0" [[deps.AbstractPlutoDingetjes]] deps = ["Pkg"] git-tree-sha1 = "91bd53c39b9cbfb5ef4b015e8b582d344532bd0a" uuid = "6e696c72-6542-2067-7265-42206c756150" version = "1.2.0" [[deps.Adapt]] deps = ["LinearAlgebra", "Requires"] git-tree-sha1 = "76289dc51920fdc6e0013c872ba9551d54961c24" uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" version = "3.6.2" [[deps.ArgTools]] uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" version = "1.1.1" [[deps.ArnoldiMethod]] deps = ["LinearAlgebra", "Random", "StaticArrays"] git-tree-sha1 = 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"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 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a" uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" version = "1.4.1+0" """ # ╔═╡ Cell order: # ╟─49b8c58c-ba0d-4783-8a3d-888902277b75 # ╠═ea758628-8a57-481f-9d8f-edda66f30e42 # ╠═00ebaf5f-0258-4daf-840e-6f01b3bdd352 # ╠═e3160714-e504-48bd-898b-fdfcb07856ba # ╠═81e1c4e1-89bf-4888-bf65-ce021c7a574b # ╠═5589b059-d8c8-43fa-8916-c2a5d1a36a1d # ╠═fede4fd1-acb3-4b2e-b2bc-2e3703e7762d # ╠═9e5c5ea0-850a-4dbf-b89b-33ae234bbce6 # ╠═4312153d-d1c3-4c04-8f49-0681ebe49931 # ╠═56d8ea14-6fb7-4aed-a098-58c99a00d98f # ╠═510a8bb6-c36f-427a-8a1f-09520ba8e372 # ╠═4435eb0e-92b9-4e2b-b010-ea30d33cca7f # ╟─02bb3de1-ac52-4c41-881f-6cbefa0f14d6 # 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╠═f6b50ef9-94d9-4f80-b778-ef00f3635279 # ╠═16db9976-fc91-4010-98fd-8d4cda6117d8 # ╠═5c79d594-a3a0-472e-a4cc-0c78df3ecf9d # ╠═91e05e7f-70bd-4ded-9a1e-f62602386a40 # ╠═8ca87124-d990-422b-a9ce-eda1fceb4cb9 # ╠═f75e6776-e2a7-4a54-9bf9-e674d778bc66 # ╠═4a182660-f8ba-4a4b-a40b-73389459cad4 # ╟─00000000-0000-0000-0000-000000000001 # ╟─00000000-0000-0000-0000-000000000002