diff --git a/.gitignore b/.gitignore
index e29e31c..96d2aab 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,4 +1,4 @@
-exports
+exports/
 
 # Profiling
 *.mem
diff --git a/Manifest.toml b/Manifest.toml
index c289b4a..7870e28 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -25,9 +25,9 @@ uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 
 [[deps.ArrayInterface]]
 deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
-git-tree-sha1 = "c933ce606f6535a7c7b98e1d86d5d1014f730596"
+git-tree-sha1 = "81f0cb60dc994ca17f68d9fb7c942a5ae70d9ee4"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "5.0.7"
+version = "5.0.8"
 
 [[deps.Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
@@ -54,9 +54,15 @@ version = "0.4.2"
 
 [[deps.CUDA]]
 deps = ["AbstractFFTs", "Adapt", "BFloat16s", "CEnum", "CompilerSupportLibraries_jll", "ExprTools", "GPUArrays", "GPUCompiler", "LLVM", "LazyArtifacts", "Libdl", "LinearAlgebra", "Logging", "Printf", "Random", "Random123", "RandomNumbers", "Reexport", "Requires", "SparseArrays", "SpecialFunctions", "TimerOutputs"]
-git-tree-sha1 = "ba75320aaa092b3e17c020a2d8b9e0a572dbfa6a"
+git-tree-sha1 = "19fb33957a5f85efb3cc10e70cf4dd4e30174ac9"
 uuid = "052768ef-5323-5732-b1bb-66c8b64840ba"
-version = "3.9.0"
+version = "3.10.0"
+
+[[deps.Calculus]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
+uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
+version = "0.5.1"
 
 [[deps.CellListMap]]
 deps = ["DocStringExtensions", "LinearAlgebra", "Parameters", "ProgressMeter", "Random", "Setfield", "StaticArrays"]
@@ -66,9 +72,9 @@ version = "0.7.13"
 
 [[deps.ChainRules]]
 deps = ["ChainRulesCore", "Compat", "IrrationalConstants", "LinearAlgebra", "Random", "RealDot", "SparseArrays", "Statistics"]
-git-tree-sha1 = "cd313dab8ec7be4a6438573d34018a032f8bebce"
+git-tree-sha1 = "de68815ccf15c7d3e3e3338f0bd3a8a0528f9b9f"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "1.28.3"
+version = "1.33.0"
 
 [[deps.ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
@@ -78,9 +84,9 @@ version = "1.14.0"
 
 [[deps.ChangesOfVariables]]
 deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
-git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1"
+git-tree-sha1 = "1e315e3f4b0b7ce40feded39c73049692126cf53"
 uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
-version = "0.1.2"
+version = "0.1.3"
 
 [[deps.CircularArrayBuffers]]
 deps = ["Adapt"]
@@ -96,9 +102,9 @@ version = "0.7.0"
 
 [[deps.ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
-git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
+git-tree-sha1 = "a985dc37e357a3b22b260a5def99f3530fb415d3"
 uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
-version = "0.11.0"
+version = "0.11.2"
 
 [[deps.ColorVectorSpace]]
 deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
@@ -158,9 +164,9 @@ version = "1.10.0"
 
 [[deps.DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "3daef5523dd2e769dad2365274f760ff5f282c7d"
+git-tree-sha1 = "cc1a8e22627f33c789ab60b36a9132ac050bbf75"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.18.11"
+version = "0.18.12"
 
 [[deps.DataValueInterfaces]]
 git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
@@ -199,9 +205,9 @@ uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[deps.Distributions]]
 deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
-git-tree-sha1 = "221ff6c6c9ede484e9f8be4974697187c06eb06b"
+git-tree-sha1 = "8a6b49396a4058771c5c072239b2e0a76e2e898c"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
-version = "0.25.55"
+version = "0.25.58"
 
 [[deps.DocStringExtensions]]
 deps = ["LibGit2"]
@@ -213,6 +219,12 @@ version = "0.8.6"
 deps = ["ArgTools", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 
+[[deps.DualNumbers]]
+deps = ["Calculus", "NaNMath", "SpecialFunctions"]
+git-tree-sha1 = "5837a837389fccf076445fce071c8ddaea35a566"
+uuid = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
+version = "0.6.8"
+
 [[deps.EarCut_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
@@ -227,9 +239,9 @@ version = "1.2.9"
 
 [[deps.EllipsisNotation]]
 deps = ["ArrayInterface"]
-git-tree-sha1 = "d064b0340db45d48893e7604ec95e7a2dc9da904"
+git-tree-sha1 = "010c3f9692344e56d05793311dfe554b0d351d79"
 uuid = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
-version = "1.5.0"
+version = "1.5.1"
 
 [[deps.ExprTools]]
 git-tree-sha1 = "56559bbef6ca5ea0c0818fa5c90320398a6fbf8d"
@@ -238,9 +250,9 @@ version = "0.1.8"
 
 [[deps.FileIO]]
 deps = ["Pkg", "Requires", "UUIDs"]
-git-tree-sha1 = "80ced645013a5dbdc52cf70329399c35ce007fae"
+git-tree-sha1 = "9267e5f50b0e12fdfd5a2455534345c4cf2c7f7a"
 uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
-version = "1.13.0"
+version = "1.14.0"
 
 [[deps.FillArrays]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
@@ -262,9 +274,9 @@ version = "0.12.10"
 
 [[deps.ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "34e6147e7686a101c245f12dba43b743c7afda96"
+git-tree-sha1 = "2f18915445b248731ec5db4e4a17e451020bf21e"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.27"
+version = "0.10.30"
 
 [[deps.FreeType]]
 deps = ["CEnum", "FreeType2_jll"]
@@ -301,9 +313,9 @@ version = "8.3.2"
 
 [[deps.GPUCompiler]]
 deps = ["ExprTools", "InteractiveUtils", "LLVM", "Libdl", "Logging", "TimerOutputs", "UUIDs"]
-git-tree-sha1 = "556190e1e0ea3e37d83059fc9aa576f1e2104375"
+git-tree-sha1 = "d8c5999631e1dc18d767883f621639c838f8e632"
 uuid = "61eb1bfa-7361-4325-ad38-22787b887f55"
-version = "0.14.1"
+version = "0.15.2"
 
 [[deps.GeometryBasics]]
 deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
@@ -311,11 +323,17 @@ git-tree-sha1 = "83ea630384a13fc4f002b77690bc0afeb4255ac9"
 uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
 version = "0.4.2"
 
+[[deps.HypergeometricFunctions]]
+deps = ["DualNumbers", "LinearAlgebra", "SpecialFunctions", "Test"]
+git-tree-sha1 = "cb7099a0109939f16a4d3b572ba8396b1f6c7c31"
+uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
+version = "0.3.10"
+
 [[deps.IRTools]]
 deps = ["InteractiveUtils", "MacroTools", "Test"]
-git-tree-sha1 = "7f43342f8d5fd30ead0ba1b49ab1a3af3b787d24"
+git-tree-sha1 = "af14a478780ca78d5eb9908b263023096c2b9d64"
 uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
-version = "0.4.5"
+version = "0.4.6"
 
 [[deps.IfElse]]
 git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
@@ -340,15 +358,15 @@ version = "0.5.4"
 
 [[deps.Intervals]]
 deps = ["Dates", "Printf", "RecipesBase", "Serialization", "TimeZones"]
-git-tree-sha1 = "323a38ed1952d30586d0fe03412cde9399d3618b"
+git-tree-sha1 = "b993074580045d1551d30990dc0fa5ba6feef92b"
 uuid = "d8418881-c3e1-53bb-8760-2df7ec849ed5"
-version = "1.5.0"
+version = "1.6.0"
 
 [[deps.InverseFunctions]]
 deps = ["Test"]
-git-tree-sha1 = "91b5dcf362c5add98049e6c29ee756910b03051d"
+git-tree-sha1 = "336cc738f03e069ef2cac55a104eb823455dca75"
 uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
-version = "0.1.3"
+version = "0.1.4"
 
 [[deps.IrrationalConstants]]
 git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
@@ -385,15 +403,15 @@ version = "0.8.4"
 
 [[deps.LLVM]]
 deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Printf", "Unicode"]
-git-tree-sha1 = "c9b86064be5ae0f63e50816a5a90b08c474507ae"
+git-tree-sha1 = "c8d47589611803a0f3b4813d9e267cd4e3dbcefb"
 uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
-version = "4.9.1"
+version = "4.11.1"
 
 [[deps.LLVMExtra_jll]]
-deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg"]
-git-tree-sha1 = "5558ad3c8972d602451efe9d81c78ec14ef4f5ef"
+deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "Pkg", "TOML"]
+git-tree-sha1 = "771bfe376249626d3ca12bcd58ba243d3f961576"
 uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
-version = "0.0.14+2"
+version = "0.0.16+0"
 
 [[deps.LaTeXStrings]]
 git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
@@ -429,9 +447,9 @@ uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
 [[deps.LogExpFunctions]]
 deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
-git-tree-sha1 = "44a7b7bb7dd1afe12bac119df6a7e540fa2c96bc"
+git-tree-sha1 = "09e4b894ce6a976c354a69041a04748180d43637"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
-version = "0.3.13"
+version = "0.3.15"
 
 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
@@ -482,9 +500,9 @@ uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 
 [[deps.NNlib]]
 deps = ["Adapt", "ChainRulesCore", "Compat", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
-git-tree-sha1 = "a59a614b8b4ea6dc1dcec8c6514e251f13ccbe10"
+git-tree-sha1 = "f89de462a7bc3243f95834e75751d70b3a33e59d"
 uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
-version = "0.8.4"
+version = "0.8.5"
 
 [[deps.NNlibCUDA]]
 deps = ["CUDA", "LinearAlgebra", "NNlib", "Random", "Statistics"]
@@ -521,9 +539,9 @@ version = "1.4.1"
 
 [[deps.PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
-git-tree-sha1 = "3114946c67ef9925204cc024a73c9e679cebe0d7"
+git-tree-sha1 = "027185efff6be268abbaf30cfd53ca9b59e3c857"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.11.8"
+version = "0.11.10"
 
 [[deps.Parameters]]
 deps = ["OrderedCollections", "UnPack"]
@@ -682,15 +700,15 @@ uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [[deps.SpecialFunctions]]
 deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
-git-tree-sha1 = "5ba658aeecaaf96923dce0da9e703bd1fe7666f9"
+git-tree-sha1 = "bc40f042cfcc56230f781d92db71f0e21496dffd"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "2.1.4"
+version = "2.1.5"
 
 [[deps.Static]]
 deps = ["IfElse"]
-git-tree-sha1 = "91181e5820a400d1171db4382aa36e7fd19bee27"
+git-tree-sha1 = "3a2a99b067090deb096edecec1dc291c5b4b31cb"
 uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
-version = "0.6.3"
+version = "0.6.5"
 
 [[deps.StaticArrays]]
 deps = ["LinearAlgebra", "Random", "Statistics"]
@@ -715,16 +733,16 @@ uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 version = "0.33.16"
 
 [[deps.StatsFuns]]
-deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
-git-tree-sha1 = "5950925ff997ed6fb3e985dcce8eb1ba42a0bbe7"
+deps = ["ChainRulesCore", "HypergeometricFunctions", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "5783b877201a82fc0014cbf381e7e6eb130473a4"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.18"
+version = "1.0.1"
 
 [[deps.StructArrays]]
 deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
-git-tree-sha1 = "8f705dd141733d79aa2932143af6c6e0b6cea8df"
+git-tree-sha1 = "e75d82493681dfd884a357952bbd7ab0608e1dc3"
 uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
-version = "0.6.6"
+version = "0.6.7"
 
 [[deps.SuiteSparse]]
 deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
@@ -768,9 +786,9 @@ version = "1.7.3"
 
 [[deps.TimerOutputs]]
 deps = ["ExprTools", "Printf"]
-git-tree-sha1 = "11db03dd5bbc0d2b57a570d228a0f34538c586b1"
+git-tree-sha1 = "7638550aaea1c9a1e86817a231ef0faa9aca79bd"
 uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
-version = "0.5.17"
+version = "0.5.19"
 
 [[deps.TranscodingStreams]]
 deps = ["Random", "Test"]
@@ -792,9 +810,9 @@ uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
 [[deps.UnicodePlots]]
 deps = ["ColorTypes", "Contour", "Crayons", "Dates", "FileIO", "FreeTypeAbstraction", "LinearAlgebra", "MarchingCubes", "NaNMath", "Printf", "SparseArrays", "StaticArrays", "StatsBase", "Unitful"]
-git-tree-sha1 = "30cdd71bd78478ba19835466c6e2a52ad776d800"
+git-tree-sha1 = "4b18663db312f47f9729935066a377e5c6a9bdfb"
 uuid = "b8865327-cd53-5732-bb35-84acbb429228"
-version = "2.11.1"
+version = "2.11.2"
 
 [[deps.Unitful]]
 deps = ["ConstructionBase", "Dates", "LinearAlgebra", "Random"]
@@ -814,9 +832,9 @@ uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 
 [[deps.Zygote]]
 deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SparseArrays", "SpecialFunctions", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "9c65b4b9d4547c4d16fc3f73e3f6ebee08730c76"
+git-tree-sha1 = "a49267a2e5f113c7afe93843deea7461c0f6b206"
 uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
-version = "0.6.39"
+version = "0.6.40"
 
 [[deps.ZygoteRules]]
 deps = ["MacroTools"]
diff --git a/analysis/mean_squared_displacement.jl b/analysis/mean_squared_displacement.jl
index 4d0eeb8..689ab4e 100644
--- a/analysis/mean_squared_displacement.jl
+++ b/analysis/mean_squared_displacement.jl
@@ -95,7 +95,7 @@ function mean_squared_displacement(;
 
     mean_sq_displacements = zeros(Float64, (length(ts), n_v₀s))
 
-    @simd for v₀_ind in 1:n_v₀s
+    for v₀_ind in 1:n_v₀s
         for sim_ind in 1:n_simulations
             sim_dir = sim_dirs[sim_ind, v₀_ind]