diff --git a/examples/chemistry/fokker_planck.jl b/examples/chemistry/fokker_planck.jl index 450ef110..c1737f74 100644 --- a/examples/chemistry/fokker_planck.jl +++ b/examples/chemistry/fokker_planck.jl @@ -5,8 +5,11 @@ # gradient of (some potential) Ψ. # Load libraries. -using Catlab, CombinatorialSpaces, Decapodes -using GLMakie, LinearAlgebra, MLStyle, MultiScaleArrays, OrdinaryDiffEq +using Catlab, CombinatorialSpaces, Decapodes, DiagrammaticEquations +using CairoMakie, ComponentArrays, LinearAlgebra, MLStyle, MultiScaleArrays, OrdinaryDiffEq +using GeometryBasics: Point3 +Point3D = Point3{Float64} +using Arpack # Specify physics. Fokker_Planck = @decapode begin @@ -15,56 +18,58 @@ Fokker_Planck = @decapode begin ∂ₜ(ρ) == ∘(⋆,d,⋆)(d(Ψ)∧ρ) + β⁻¹*Δ(ρ) end -Fokker_Planck = expand_operators(Fokker_Planck) -infer_types!(Fokker_Planck) -resolve_overloads!(Fokker_Planck) - # Specify domain. -s′ = loadmesh(Icosphere(4)) -s = EmbeddedDeltaDualComplex2D{Bool, Float64, Point3D}(s′) -subdivide_duals!(s, Barycenter()) - -# Specify initial conditions. -Ψ = map(point(s)) do (x,y,z) - abs(y) -end -ρ = fill(1/nv(s), nv(s)) -constants_and_parameters = (β⁻¹ = -0.001,) -u₀ = construct(PhysicsState, [VectorForm(Ψ), VectorForm(ρ)], Float64[], [:Ψ, :ρ]) +s = loadmesh(Icosphere(6)); +sd = EmbeddedDeltaDualComplex2D{Bool, Float64, Point3D}(s); +subdivide_duals!(sd, Barycenter()); # Compile. -function generate(sd, my_symbol; hodge=GeometricHodge()) - op = @match my_symbol begin - _ => default_dec_generate(sd, my_symbol) - end - return (args...) -> op(args...) -end sim = eval(gensim(Fokker_Planck)) -fₘ = sim(s, generate) +fₘ = sim(sd, nothing) + +# Specify initial conditions. +# Ψ must be a smooth function. Choose an interesting eigenfunction. +Δ0 = Δ(0,sd) +Ψ = real.(eigs(Δ0, nev=32, which=:LR)[2][:,32]) +# We require that ρ integrated over the surface is 1, since it is a PDF. +# On a sphere where ρ(x,y,z) is proportional to the x-coordinate, that means divide by 2π. +ρ = map(point(sd)) do (x,y,z) + abs(x) +end / 2π + +constants_and_parameters = (β⁻¹ = 1e-2,) +u₀ = ComponentArray(Ψ=Ψ, ρ=ρ) # Run. -tₑ = 1.0 +tₑ = 20.0 prob = ODEProblem(fₘ, u₀, (0, tₑ), constants_and_parameters) -soln = solve(prob, Tsit5()) +soln = solve(prob, Tsit5(), progress=true, progress_steps=1) -findnode(soln(0), :ρ) -findnode(soln(tₑ), :ρ) +# Verify that the PDF is still a PDF. +s0 = dec_hodge_star(0,sd); +@info sum(s0 * soln(0).ρ) +@info sum(s0 * soln(tₑ).ρ) # ρ integrates to 1 +@info any(soln(tₑ).ρ .≤ 0) # ρ is nonzero # Save solution data. @save "fokker_planck.jld2" soln # Create GIF -begin -frames = 800 -# Initial frame -fig = GLMakie.Figure(resolution = (800, 800)) -p1 = GLMakie.mesh(fig[1,1], s′, color=findnode(soln(0), :ρ), colormap=:jet, colorrange=extrema(findnode(soln(0), :ρ))) -Colorbar(fig[1,2], colormap=:jet, colorrange=extrema(findnode(soln(0), :U))) - -# Animation -record(fig, "fokker_planck.gif", range(0.0, tₑ; length=frames); framerate = 30) do t - p1.plot.color = findnode(soln(t), :ρ) -end +function save_gif(file_name, soln) + time = Observable(0.0) + fig = Figure() + Label(fig[1, 1, Top()], @lift("ρ at $($time)"), padding = (0, 0, 5, 0)) + ax = LScene(fig[1,1], scenekw=(lights=[],)) + msh = CairoMakie.mesh!(ax, s, + color=@lift(soln($time).ρ), + colorrange=(0,1), + colormap=:jet) + Colorbar(fig[1,2], msh) + frames = range(0.0, tₑ; length=21) + record(fig, file_name, frames; framerate = 10) do t + time[] = t + end end +save_gif("fokker_planck.gif", soln)