619 lines
257 KiB
Text
619 lines
257 KiB
Text
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "e47f1fd3-c09d-43cb-80c8-64f42e8161a4",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1000"
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]
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},
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"using SpiDy\n",
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"using NPZ\n",
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"using DataFrames\n",
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"using CSV\n",
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"using ProgressMeter\n",
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"using Random\n",
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"using Statistics\n",
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"using LinearAlgebra\n",
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"using Plots\n",
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"\n",
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"########################\n",
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"########################\n",
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"\n",
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"Δt = .2\n",
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"N = 1000\n",
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"tspan = (0., N*Δt)\n",
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"saveat = (0:1:N)*Δt\n",
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"\n",
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"matrix = IsoCoupling(1)\n",
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"\n",
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"T = .01\n",
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"noise = ClassicalNoise(T);\n",
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"\n",
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"theta = pi * 3/8\n",
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"\n",
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"s0 = [0, 1, cos(theta)]\n",
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"s0 = s0 ./ norm(s0)\n",
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"\n",
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"J0 = 1.\n",
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"JH = Nchain(1, J0)\n",
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"\n",
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"nruns = 1000"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "6e3cdf02-c243-4622-a52a-a6d7f987c68d",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Starting...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:03:04\u001b[39mm\n"
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]
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}
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],
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"source": [
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"α = 10. # 0.16\n",
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"ω0 = 7. # 1.4\n",
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"Γ = 5. # 0.5\n",
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"\n",
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"J = LorentzianSD(α, ω0, Γ) # coloring the noise\n",
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"\n",
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"println(\"Starting...\")\n",
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"progress = Progress(nruns);\n",
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"\n",
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"sols_ohm = zeros(nruns, length(saveat), 3)\n",
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"\n",
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"Threads.@threads for i in 1:nruns\n",
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" bfields = [bfield(N, Δt, J, noise),\n",
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" bfield(N, Δt, J, noise),\n",
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" bfield(N, Δt, J, noise)];\n",
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" sol = diffeqsolver(s0, tspan, J, bfields, matrix; JH=JH, saveat=saveat);\n",
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" sols_ohm[i, :, :] = transpose(sol[:, :])\n",
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" next!(progress)\n",
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"end\n",
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"\n",
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"solavg_ohm = mean(sols_ohm, dims=1)[1, :, :];\n",
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"solstd_ohm = std(sols_ohm, dims=1)[1, :, :];"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"id": "3422af78-2f32-468c-a8a3-a0732a836fd1",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
|
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"Starting...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:52\u001b[39m\n"
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]
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}
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],
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"source": [
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"α = 0.16\n",
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"ω0 = 1.4\n",
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"Γ = 0.5\n",
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"\n",
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"J = LorentzianSD(α, ω0, Γ) # coloring the noise\n",
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"\n",
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"println(\"Starting...\")\n",
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"progress = Progress(nruns);\n",
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"\n",
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"sols_col = zeros(nruns, length(saveat), 3)\n",
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"\n",
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"Threads.@threads for i in 1:nruns\n",
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" bfields = [bfield(N, Δt, J, noise),\n",
|
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" bfield(N, Δt, J, noise),\n",
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" bfield(N, Δt, J, noise)];\n",
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" sol = diffeqsolver(s0, tspan, J, bfields, matrix; JH=JH, saveat=saveat);\n",
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" sols_col[i, :, :] = transpose(sol[:, :])\n",
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" next!(progress)\n",
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"end\n",
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"\n",
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"solavg_col = mean(sols_col, dims=1)[1, :, :];\n",
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"solstd_col = std(sols_col, dims=1)[1, :, :];"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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||
"id": "e4ad51fc-0dc7-4106-99e4-2b29e54b1930",
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"metadata": {},
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"outputs": [],
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"source": [
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"using HypothesisTests\n",
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"using LaTeXStrings"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"id": "d16b97dd-b9f5-415c-b388-2b1f3344be45",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"\"/work/benstem/SpiDySims/runs/std_66_5.png\""
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]
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},
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"execution_count": 17,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"plot(saveat, solstd_ohm[:, 1], label=L\"\\Delta x\", lw=1)\n",
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"plot!(saveat, solstd_ohm[:, 2], label=L\"\\Delta y\", lw=1)\n",
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"plot!(legend=:topright, xlabel=\"Time\", ylabel=\"Standard Deviation\")\n",
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"\n",
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"axis = twinx()\n",
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"plot!(axis, saveat, solavg_col[:, 3], label=L\"s_z\", ls=:dash)\n",
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"hline!(axis, [0], label=\"\", ls=:dash)\n",
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"plot!(axis, legend=:bottomright, ylabel=L\"$s_z$ Spin Component\")\n",
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"\n",
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"savefig(\"./std_66_5.png\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"id": "a06addc4-47b2-4467-8148-3e68f3eae702",
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"metadata": {},
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]
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},
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"execution_count": 18,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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||
"plot(saveat, solstd_col[:, 1], label=L\"\\Delta s_x\")\n",
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||
"plot!(saveat, solstd_col[:, 2], label=L\"\\Delta s_y\")\n",
|
||
"\n",
|
||
"axis = twinx()\n",
|
||
"plot!(axis, saveat, solavg_col[:, 3], label=L\"s_z\", ls=:dash)"
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||
]
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||
},
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{
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"cell_type": "code",
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"execution_count": 19,
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"id": "bc1686fd-d86d-42b0-9d87-bcb911526d00",
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"metadata": {},
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"outputs": [
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{
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2287.6,1445.03 2289.63,1445.06 2291.67,1445.1 \"/>\n",
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"<path clip-path=\"url(#clip130)\" d=\"M2012.55 250.738 L2280.81 250.738 L2280.81 95.2176 L2012.55 95.2176 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
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"<polyline clip-path=\"url(#clip130)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2012.55,250.738 2280.81,250.738 2280.81,95.2176 2012.55,95.2176 2012.55,250.738 \"/>\n",
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"<polyline clip-path=\"url(#clip130)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"2036.53,147.058 2180.42,147.058 \"/>\n",
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]
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},
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
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||
"source": [
|
||
"plot(saveat, solavg_ohm[:, 3])\n",
|
||
"plot!(saveat, solavg_col[:, 3])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"id": "59ac92d9-6a78-402b-91ae-3f5fd22cc6ff",
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"metadata": {},
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"outputs": [],
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"source": [
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||
"projected_ohm = zeros(nruns, length(saveat), 2)\n",
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"\n",
|
||
"normalized_avg = [normalize(vec(row)) for row in eachrow(solavg_ohm)]\n",
|
||
"\n",
|
||
"Threads.@threads for i in 1:length(saveat)\n",
|
||
" n = normalized_avg[i, :][1]\n",
|
||
"\n",
|
||
" u = normalize(cross(n, [0,0,1]))\n",
|
||
" v = cross(u, n)\n",
|
||
"\n",
|
||
" for j in 1:nruns\n",
|
||
" b = sols_ohm[j, i, :]\n",
|
||
" proj = dot(b, n) * n\n",
|
||
" b_ort = b - proj\n",
|
||
"\n",
|
||
" projected_ohm[j, i, 1] = dot(u,b)\n",
|
||
" projected_ohm[j, i, 2] = dot(v,b)\n",
|
||
" end\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"id": "f1661b24-42b1-4f59-989a-54dc3ed03bf8",
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"metadata": {},
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"outputs": [],
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"source": [
|
||
"projected_col = zeros(nruns, length(saveat), 2)\n",
|
||
"\n",
|
||
"normalized_avg = [normalize(vec(row)) for row in eachrow(solavg_col)]\n",
|
||
"\n",
|
||
"Threads.@threads for i in 1:length(saveat)\n",
|
||
" n = normalized_avg[i, :][1]\n",
|
||
"\n",
|
||
" u = normalize(cross(n, [0,0,1]))\n",
|
||
" v = cross(u, n)\n",
|
||
"\n",
|
||
" for j in 1:nruns\n",
|
||
" b = sols_col[j, i, :]\n",
|
||
" proj = dot(b, n) * n\n",
|
||
" b_ort = b - proj\n",
|
||
"\n",
|
||
" projected_col[j, i, 1] = dot(u,b)\n",
|
||
" projected_col[j, i, 2] = dot(v,b)\n",
|
||
" end\n",
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||
"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"id": "e5b9609e-f467-4bd7-9b51-9a4c1f175738",
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"metadata": {},
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"outputs": [],
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"source": [
|
||
"JB_ohm = zeros(N)\n",
|
||
"for i in 1:N\n",
|
||
" JB_ohm[i] = HypothesisTests.JarqueBeraTest(projected_ohm[:, i, 1]).JB\n",
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||
"end"
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]
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},
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{
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"cell_type": "code",
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"id": "51ccaeb8-2b3d-4630-afc3-2640142c4d54",
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"metadata": {},
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"outputs": [],
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"source": [
|
||
"JB_col = zeros(N)\n",
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||
"for i in 1:N\n",
|
||
" JB_col[i] = HypothesisTests.JarqueBeraTest(projected_col[:, i, 1]).JB\n",
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"end"
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]
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},
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{
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]
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},
|
||
"execution_count": 30,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"plot(saveat, JB_ohm, title=\"JB Test for Ohmic and Non-Ohmic Coupling\", label=\"Ohmic\", linewidth=2, xlabel=\"Time\", ylabel=\"JB Test\", legend=:topleft, ylimits=(0, 200))\n",
|
||
"plot!(saveat, JB_col, label=\"Non-Ohmic\", linewidth=2)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 25,
|
||
"id": "ad2674ba-9711-4feb-96ab-a39d88b27ce5",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"ename": "LoadError",
|
||
"evalue": "BoundsError: attempt to access 1000-element Vector{Float64} at index [1:1001]",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"BoundsError: attempt to access 1000-element Vector{Float64} at index [1:1001]",
|
||
"",
|
||
"Stacktrace:",
|
||
" [1] throw_boundserror(A::Vector{Float64}, I::Tuple{UnitRange{Int64}})",
|
||
" @ Base ./abstractarray.jl:691",
|
||
" [2] checkbounds",
|
||
" @ ./abstractarray.jl:656 [inlined]",
|
||
" [3] getindex(A::Vector{Float64}, I::UnitRange{Int64})",
|
||
" @ Base ./array.jl:867",
|
||
" [4] gr_draw_segments(series::Plots.Series, x::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, y::Vector{Float64}, z::Nothing, fillrange::Nothing, clims::Tuple{Float64, Float64})",
|
||
" @ Plots ~/.julia/packages/Plots/ju9dp/src/backends/gr.jl:1825",
|
||
" [5] gr_add_series(sp::Plots.Subplot{Plots.GRBackend}, series::Plots.Series)",
|
||
" @ Plots ~/.julia/packages/Plots/ju9dp/src/backends/gr.jl:1742",
|
||
" [6] gr_display(sp::Plots.Subplot{Plots.GRBackend}, w::Measures.AbsoluteLength, h::Measures.AbsoluteLength, vp_canvas::Plots.GRViewport{Float64})",
|
||
" @ Plots ~/.julia/packages/Plots/ju9dp/src/backends/gr.jl:964",
|
||
" [7] (::Plots.var\"#537#538\"{Int64, Int64, Plots.GRViewport{Float64}})(sp::Plots.Subplot{Plots.GRBackend})",
|
||
" @ Plots ~/.julia/packages/Plots/ju9dp/src/backends/gr.jl:688",
|
||
" [8] foreach(f::Plots.var\"#537#538\"{Int64, Int64, Plots.GRViewport{Float64}}, itr::Vector{Plots.Subplot})",
|
||
" @ Base ./abstractarray.jl:2712",
|
||
" [9] gr_display(plt::Plots.Plot{Plots.GRBackend}, dpi_factor::Float64)",
|
||
" @ Plots ~/.julia/packages/Plots/ju9dp/src/backends/gr.jl:688",
|
||
" [10] #578",
|
||
" @ ~/.julia/packages/Plots/ju9dp/src/backends/gr.jl:2062 [inlined]",
|
||
" [11] withenv(::Plots.var\"#578#579\"{Plots.Plot{Plots.GRBackend}, Float64}, ::Pair{String, String}, ::Vararg{Pair{String, String}})",
|
||
" @ Base ./env.jl:172",
|
||
" [12] _show(io::IOStream, #unused#::MIME{Symbol(\"image/png\")}, plt::Plots.Plot{Plots.GRBackend})",
|
||
" @ Plots ~/.julia/packages/Plots/ju9dp/src/backends/gr.jl:2057",
|
||
" [13] #invokelatest#2",
|
||
" @ ./essentials.jl:716 [inlined]",
|
||
" [14] invokelatest",
|
||
" @ ./essentials.jl:714 [inlined]",
|
||
" [15] show",
|
||
" @ ~/.julia/packages/Plots/ju9dp/src/output.jl:232 [inlined]",
|
||
" [16] #345",
|
||
" @ ~/.julia/packages/Plots/ju9dp/src/output.jl:6 [inlined]",
|
||
" [17] open(::Plots.var\"#345#346\"{Plots.Plot{Plots.GRBackend}}, ::String, ::Vararg{String}; kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})",
|
||
" @ Base ./io.jl:330",
|
||
" [18] open",
|
||
" @ ./io.jl:328 [inlined]",
|
||
" [19] png(plt::Plots.Plot{Plots.GRBackend}, fn::String)",
|
||
" @ Plots ~/.julia/packages/Plots/ju9dp/src/output.jl:6",
|
||
" [20] savefig(plt::Plots.Plot{Plots.GRBackend}, fn::String)",
|
||
" @ Plots ~/.julia/packages/Plots/ju9dp/src/output.jl:149",
|
||
" [21] savefig(fn::String)",
|
||
" @ Plots ~/.julia/packages/Plots/ju9dp/src/output.jl:154",
|
||
" [22] top-level scope",
|
||
" @ In[25]:6"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"right_axis = twinx()\n",
|
||
"\n",
|
||
"plot!(right_axis, saveat, solavg_ohm[:, 3], label=\"Ohmic\", ls=:dash, ylabel=L\"S_z\", ylimits=(-1.5, 1.5))\n",
|
||
"plot!(right_axis, saveat, solavg_col[:, 3], label=\"Non-Ohmic\", ls=:dash)\n",
|
||
"\n",
|
||
"savefig(\"./67_5.png\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 26,
|
||
"id": "a1c77edf-652b-42ea-8bc0-445749a22a2c",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"Jarque-Bera normality test\n",
|
||
"--------------------------\n",
|
||
"Population details:\n",
|
||
" parameter of interest: skewness and kurtosis\n",
|
||
" value under h_0: \"0 and 3\"\n",
|
||
" point estimate: \"-0.09472173866793361 and 3.1398692030437387\"\n",
|
||
"\n",
|
||
"Test summary:\n",
|
||
" outcome with 95% confidence: fail to reject h_0\n",
|
||
" one-sided p-value: 0.3150\n",
|
||
"\n",
|
||
"Details:\n",
|
||
" number of observations: 1000\n",
|
||
" JB statistic: 2.31051\n"
|
||
]
|
||
},
|
||
"execution_count": 26,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"HypothesisTests.JarqueBeraTest(projected_col[:, 125, 1])"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "48b2963f-d070-46c9-a077-fe4aad09155a",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Julia 1.7.3",
|
||
"language": "julia",
|
||
"name": "julia-1.7"
|
||
},
|
||
"language_info": {
|
||
"file_extension": ".jl",
|
||
"mimetype": "application/julia",
|
||
"name": "julia",
|
||
"version": "1.7.3"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|