PN_breakdown.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "890cc0be-c601-4ed0-8d4d-cefd72e9fdb2",
   "metadata": {},
   "outputs": [],
   "source": [
    "using PostNewtonian\n",
    "using LaTeXStrings\n",
    "using Plots\n",
    "plotlyjs();\n",
    "\n",
    "q = 10\n",
    "M₁ = q/(1+q)\n",
    "M₂ = 1/(1+q)\n",
    "χ⃗₁ = [0., 0., 0.]\n",
    "χ⃗₂ = [0., 0., 0.]\n",
    "Ωᵢ = 0.02\n",
    "\n",
    "cutoffFrequency=0.1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "0c4548c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 0.0PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mTerminating forwards evolution because the PN parameter 𝑣 has reached 𝑣ₑ=1.0.  This is ideal.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 0.5PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mTerminating forwards evolution because the PN parameter 𝑣 has reached 𝑣ₑ=1.0.  This is ideal.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 1.0PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mTerminating forwards evolution because 𝑣 is decreasing:\n",
      "\u001b[36m\u001b[1m│ \u001b[22m\u001b[39mThis is only unusual if 𝑣 ≲ 1/2; the current value is\n",
      "\u001b[36m\u001b[1m└ \u001b[22m\u001b[39m∂ₜ𝑣=-1.3485583897489948e-12.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 1.5PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mTerminating evolution because the time-step size has become very small:\n",
      "\u001b[36m\u001b[1m│ \u001b[22m\u001b[39m|dt=1.1167527014939859e-8| < √ϵ=1.4901161193847656e-8\n",
      "\u001b[36m\u001b[1m└ \u001b[22m\u001b[39mThis is only unexpected for 𝑣 ≲ 1/2; the current value is 𝑣=0.8129825414185575.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 2.0PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mTerminating evolution because the time-step size has become very small:\n",
      "\u001b[36m\u001b[1m│ \u001b[22m\u001b[39m|dt=1.3775926692635376e-8| < √ϵ=1.4901161193847656e-8\n",
      "\u001b[36m\u001b[1m└ \u001b[22m\u001b[39mThis is only unexpected for 𝑣 ≲ 1/2; the current value is 𝑣=0.5040169872046328.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 2.5PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mTerminating forwards evolution because 𝑣 is decreasing:\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mThis is only unusual if 𝑣 ≲ 1/2; the current value is\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m∂ₜ𝑣=-2.188047811306525e-8.\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ PostNewtonian ~/.julia/dev/PostNewtonian/src/utilities/termination_criteria.jl:160\u001b[39m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 3.0PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mTerminating evolution because the time-step size has become very small:\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m|dt=1.0036855882813982e-8| < √ϵ=1.4901161193847656e-8\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mThis is only unexpected for 𝑣 ≲ 1/2; the current value is 𝑣=0.456973041591987.\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ PostNewtonian ~/.julia/dev/PostNewtonian/src/utilities/termination_criteria.jl:121\u001b[39m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 3.5PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mTerminating evolution because the time-step size has become very small:\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m|dt=7.037635000506215e-9| < √ϵ=1.4901161193847656e-8\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mThis is only unexpected for 𝑣 ≲ 1/2; the current value is 𝑣=0.4569747135055055.\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ PostNewtonian ~/.julia/dev/PostNewtonian/src/utilities/termination_criteria.jl:121\u001b[39m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 4.0PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mTerminating evolution because the time-step size has become very small:\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m|dt=2.1404097875475635e-9| < √ϵ=1.4901161193847656e-8\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mThis is only unexpected for 𝑣 ≲ 1/2; the current value is 𝑣=0.43785147929214663.\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ PostNewtonian ~/.julia/dev/PostNewtonian/src/utilities/termination_criteria.jl:121\u001b[39m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 4.5PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mTerminating evolution because the time-step size has become very small:\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m|dt=1.440224574078872e-8| < √ϵ=1.4901161193847656e-8\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mThis is only unexpected for 𝑣 ≲ 1/2; the current value is 𝑣=0.4378505038226452.\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ PostNewtonian ~/.julia/dev/PostNewtonian/src/utilities/termination_criteria.jl:121\u001b[39m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Working on 5.0PN\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mTerminating evolution because the time-step size has become very small:\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m|dt=3.9868485800012685e-9| < √ϵ=1.4901161193847656e-8\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mThis is only unexpected for 𝑣 ≲ 1/2; the current value is 𝑣=0.4280535206558848.\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ PostNewtonian ~/.julia/dev/PostNewtonian/src/utilities/termination_criteria.jl:121\u001b[39m\n"
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       ");\n",
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       "    </script>\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Φₑ = 0.0\n",
    "p = plot()\n",
    "for PNOrder ∈ 0//2 : 1//2 : 10//2\n",
    "    flush(stdout); flush(stderr); println(\"Working on $(float(PNOrder))PN\")\n",
    "    inspiral = orbital_evolution(M₁, M₂, χ⃗₁, χ⃗₂, Ωᵢ; PNOrder, quiet=false)\n",
    "    Φₑ = max(Φₑ, inspiral[:Φ, end])\n",
    "    plot!(\n",
    "        p, inspiral[:Φ], inspiral[:v],\n",
    "        leg=:topleft, linewidth=2, xlabel=L\"v\", ylabel=L\"\\Phi\",\n",
    "        label=\"$(float(PNOrder))PN\"\n",
    "    )\n",
    "end\n",
    "xlabel!(p, L\"\\Phi\")\n",
    "ylabel!(p, L\"v\")\n",
    "xlims!(p, -10, Φₑ+10)\n",
    "hline!(p, [PostNewtonian.v(Ω=cutoffFrequency)], line=(3, :dash), label=\"cutoffFrequency\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "da51af0e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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