{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Gross-Pitaevskii equation with external magnetic field"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We solve the 2D Gross-Pitaevskii equation with a magnetic field.\n",
"This is similar to the\n",
"previous example (Gross-Pitaevskii equation in one dimension),\n",
"but with an extra term for the magnetic field.\n",
"We reproduce here the results of https://arxiv.org/pdf/1611.02045.pdf Fig. 10"
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n Energy log10(ΔE) log10(Δρ) Δtime\n",
"--- --------------- --------- --------- ------\n",
" 1 +30.40743520513 -1.42 5.13s\n",
" 2 +23.95051791622 0.81 -0.77 10.6ms\n",
" 3 +21.65829285710 0.36 -0.37 10.4ms\n",
" 4 +19.79805467132 0.27 -0.28 10.5ms\n",
" 5 +18.34725768879 0.16 -0.49 10.4ms\n",
" 6 +13.44183896546 0.69 -0.45 10.4ms\n",
" 7 +10.03875646258 0.53 -0.45 10.4ms\n",
" 8 +9.224587654307 -0.09 -0.71 8.44ms\n",
" 9 +8.915536203565 -0.51 -0.95 8.51ms\n",
" 10 +8.748496019147 -0.78 -1.01 8.41ms\n",
" 11 +8.624414735914 -0.91 -0.98 8.36ms\n",
" 12 +8.496505081782 -0.89 -0.98 8.36ms\n",
" 13 +8.403619841622 -1.03 -1.06 6.37ms\n",
" 14 +8.318072596839 -1.07 -1.07 6.37ms\n",
" 15 +8.220172203342 -1.01 -1.01 6.49ms\n",
" 16 +8.174244157943 -1.34 -1.06 6.54ms\n",
" 17 +8.122124893775 -1.28 -1.05 6.39ms\n",
" 18 +8.057408145205 -1.19 -0.78 49.5ms\n",
" 19 +8.016103387287 -1.38 -1.00 6.91ms\n",
" 20 +7.976589050989 -1.40 -1.14 6.66ms\n",
" 21 +7.942160965503 -1.46 -1.22 6.51ms\n",
" 22 +7.912519223739 -1.53 -1.09 8.39ms\n",
" 23 +7.885169958563 -1.56 -1.19 6.38ms\n",
" 24 +7.857929374049 -1.56 -1.18 6.41ms\n",
" 25 +7.838054375681 -1.70 -1.18 6.45ms\n",
" 26 +7.813489391633 -1.61 -1.27 6.36ms\n",
" 27 +7.807638907214 -2.23 -1.26 6.36ms\n",
" 28 +7.794523541314 -1.88 -1.35 6.37ms\n",
" 29 +7.786136511033 -2.08 -1.36 6.35ms\n",
" 30 +7.770365002571 -1.80 -1.12 8.48ms\n",
" 31 +7.763995631407 -2.20 -1.24 6.40ms\n",
" 32 +7.749705060282 -1.84 -1.31 6.39ms\n",
" 33 +7.742339367976 -2.13 -1.34 6.43ms\n",
" 34 +7.731506958657 -1.97 -1.14 8.37ms\n",
" 35 +7.722796413393 -2.06 -1.40 6.37ms\n",
" 36 +7.720441219131 -2.63 -1.28 33.1ms\n",
" 37 +7.710635638641 -2.01 -1.42 6.79ms\n",
" 38 +7.707967460885 -2.57 -1.27 6.41ms\n",
" 39 +7.699905369066 -2.09 -1.48 6.39ms\n",
" 40 +7.699751183325 -3.81 -1.34 6.40ms\n",
" 41 +7.692279641004 -2.13 -1.47 6.36ms\n",
" 42 +7.686639013682 -2.25 -1.34 8.35ms\n",
" 43 +7.683328563494 -2.48 -1.43 6.37ms\n",
" 44 +7.681589036952 -2.76 -1.46 6.40ms\n",
" 45 +7.679111709509 -2.61 -1.46 6.35ms\n",
" 46 +7.675881512906 -2.49 -1.56 6.34ms\n",
" 47 +7.671921382044 -2.40 -1.32 8.30ms\n",
" 48 +7.669112597370 -2.55 -1.68 6.32ms\n",
" 49 +7.668966744259 -3.84 -1.45 6.38ms\n",
" 50 +7.666071357831 -2.54 -1.77 6.37ms\n",
" 51 +7.662929783659 -2.50 -1.36 8.33ms\n",
" 52 +7.660899070272 -2.69 -1.59 6.42ms\n",
" 53 +7.658443827569 -2.61 -1.73 6.38ms\n",
" 54 +7.656117400000 -2.63 -1.60 6.37ms\n",
" 55 +7.654093412043 -2.69 -1.36 8.37ms\n",
" 56 +7.652194642305 -2.72 -1.50 110ms\n",
" 57 +7.652008351222 -3.73 -1.49 8.56ms\n",
" 58 +7.650008522980 -2.70 -1.62 8.11ms\n",
" 59 +7.648742068357 -2.90 -1.57 8.22ms\n",
" 60 +7.646056039246 -2.57 -1.17 10.6ms\n",
" 61 +7.644011513007 -2.69 -1.67 8.26ms\n",
" 62 +7.643283208520 -3.14 -1.64 8.36ms\n",
" 63 +7.640607721221 -2.57 -1.42 8.26ms\n",
" 64 +7.638793894247 -2.74 -1.52 10.8ms\n",
" 65 +7.637288344953 -2.82 -1.68 8.28ms\n",
" 66 +7.635702379870 -2.80 -1.56 10.6ms\n",
" 67 +7.635635896940 -4.18 -1.71 8.31ms\n",
" 68 +7.635506725063 -3.89 -1.54 8.11ms\n",
" 69 +7.634244756424 -2.90 -1.58 10.9ms\n",
" 70 +7.632347478761 -2.72 -1.80 8.37ms\n",
" 71 +7.630822064931 -2.82 -1.64 551ms\n",
" 72 +7.629498567770 -2.88 -1.89 6.59ms\n",
" 73 +7.628177859889 -2.88 -1.46 8.70ms\n",
" 74 +7.627243957282 -3.03 -1.77 6.52ms\n",
" 75 +7.626306735581 -3.03 -1.88 6.41ms\n",
" 76 +7.625576061958 -3.14 -2.04 6.42ms\n",
" 77 +7.625056631662 -3.28 -1.92 6.51ms\n",
" 78 +7.624463816544 -3.23 -1.47 8.58ms\n",
" 79 +7.623792793674 -3.17 -1.49 8.51ms\n",
" 80 +7.623104801284 -3.16 -2.03 7.46ms\n",
" 81 +7.622682516599 -3.37 -1.78 8.59ms\n",
" 82 +7.622354999403 -3.48 -1.78 8.00ms\n",
" 83 +7.622139013520 -3.67 -2.04 7.96ms\n",
" 84 +7.621749301055 -3.41 -2.09 7.95ms\n",
" 85 +7.621549590557 -3.70 -2.02 7.91ms\n",
" 86 +7.621384635449 -3.78 -2.06 8.03ms\n",
" 87 +7.621052695397 -3.48 -2.09 8.10ms\n",
" 88 +7.620835760113 -3.66 -1.91 8.07ms\n",
" 89 +7.620682807220 -3.82 -1.81 8.14ms\n",
" 90 +7.620619929810 -4.20 -2.19 8.09ms\n",
" 91 +7.620223192538 -3.40 -2.11 8.24ms\n",
" 92 +7.620096760435 -3.90 -2.18 8.03ms\n",
" 93 +7.619835935341 -3.58 -1.90 10.6ms\n",
" 94 +7.619748661897 -4.06 -1.93 6.99ms\n",
" 95 +7.619590529046 -3.80 -2.29 6.94ms\n",
" 96 +7.619471623799 -3.92 -2.09 7.00ms\n",
" 97 +7.619262466071 -3.68 -1.92 9.29ms\n",
" 98 +7.619157128193 -3.98 -2.08 7.04ms\n",
" 99 +7.619016316774 -3.85 -2.06 7.01ms\n",
" 100 +7.618741575751 -3.56 -2.02 7.11ms\n",
" 101 +7.618538029263 -3.69 -1.90 9.34ms\n",
" 102 +7.618387688675 -3.82 -2.16 6.90ms\n",
" 103 +7.618312103968 -4.12 -2.03 6.85ms\n",
" 104 +7.618124879712 -3.73 -2.27 6.87ms\n",
" 105 +7.617851225696 -3.56 -1.64 8.65ms\n",
" 106 +7.617639407998 -3.67 -1.89 6.45ms\n",
" 107 +7.617459118068 -3.74 -1.76 6.35ms\n",
" 108 +7.617161560088 -3.53 -2.10 6.41ms\n",
" 109 +7.616775347856 -3.41 -1.56 8.35ms\n",
" 110 +7.616596136718 -3.75 -1.73 6.39ms\n",
" 111 +7.616187590718 -3.39 -1.87 6.48ms\n",
" 112 +7.615872640753 -3.50 -2.05 6.50ms\n",
" 113 +7.615407741996 -3.33 -1.50 9.26ms\n",
" 114 +7.614931825532 -3.32 -1.54 9.32ms\n",
" 115 +7.614920210061 -4.93 -1.84 7.11ms\n",
" 116 +7.614803369590 -3.93 -1.95 7.37ms\n",
" 117 +7.614572942469 -3.64 -1.72 6.99ms\n",
" 118 +7.614449504529 -3.91 -1.87 6.74ms\n",
" 119 +7.614103057224 -3.46 -1.87 7.69ms\n",
" 120 +7.613940183063 -3.79 -2.02 6.50ms\n",
" 121 +7.613501569257 -3.36 -1.79 6.45ms\n",
" 122 +7.613434390333 -4.17 -1.79 6.67ms\n",
" 123 +7.612945672758 -3.31 -1.98 6.49ms\n",
" 124 +7.612546821629 -3.40 -1.70 8.63ms\n",
" 125 +7.611997559739 -3.26 -2.05 23.2ms\n",
" 126 +7.611333048058 -3.18 -1.64 8.87ms\n",
" 127 +7.610942149066 -3.41 -1.75 8.46ms\n",
" 128 +7.610788638182 -3.81 -1.99 6.51ms\n",
" 129 +7.610477920726 -3.51 -1.81 8.45ms\n",
" 130 +7.610284001260 -3.71 -1.93 8.40ms\n",
" 131 +7.610263135250 -4.68 -1.78 6.47ms\n",
" 132 +7.609959375595 -3.52 -2.14 6.43ms\n",
" 133 +7.609915086966 -4.35 -1.48 6.45ms\n",
" 134 +7.609599466041 -3.50 -1.78 6.37ms\n",
" 135 +7.609174677972 -3.37 -1.84 8.36ms\n",
" 136 +7.608677873783 -3.30 -1.93 6.52ms\n",
" 137 +7.608437035874 -3.62 -1.98 6.58ms\n",
" 138 +7.608298119723 -3.86 -2.01 6.48ms\n",
" 139 +7.607990735010 -3.51 -1.76 8.44ms\n",
" 140 +7.607660477391 -3.48 -2.03 6.47ms\n",
" 141 +7.607445773850 -3.67 -2.09 8.54ms\n",
" 142 +7.607270337122 -3.76 -1.87 6.47ms\n",
" 143 +7.607186400597 -4.08 -2.12 6.43ms\n",
" 144 +7.606946753872 -3.62 -1.80 9.01ms\n",
" 145 +7.606722581589 -3.65 -1.88 8.59ms\n",
" 146 +7.606624294590 -4.01 -2.04 6.48ms\n",
" 147 +7.606394872724 -3.64 -1.90 8.42ms\n",
" 148 +7.606334516054 -4.22 -2.08 6.76ms\n",
" 149 +7.606243060616 -4.04 -1.95 6.47ms\n",
" 150 +7.606209479334 -4.47 -2.20 6.43ms\n",
" 151 +7.606017073368 -3.72 -2.09 6.41ms\n",
" 152 +7.605956753803 -4.22 -2.24 6.43ms\n",
" 153 +7.605849161817 -3.97 -2.07 6.51ms\n",
" 154 +7.605732581268 -3.93 -2.04 6.38ms\n",
" 155 +7.605616680147 -3.94 -2.14 8.45ms\n",
" 156 +7.605533361457 -4.08 -2.32 6.43ms\n",
" 157 +7.605405414760 -3.89 -2.06 8.40ms\n",
" 158 +7.605357463386 -4.32 -2.32 6.46ms\n",
" 159 +7.605273662135 -4.08 -2.23 8.36ms\n",
" 160 +7.605254958895 -4.73 -2.33 6.35ms\n",
" 161 +7.605219392203 -4.45 -2.19 35.6ms\n",
" 162 +7.605169221727 -4.30 -2.40 9.13ms\n",
" 163 +7.605118997533 -4.30 -2.29 6.58ms\n",
" 164 +7.605058881814 -4.22 -2.25 8.52ms\n",
" 165 +7.604978183226 -4.09 -2.05 8.41ms\n",
" 166 +7.604956030375 -4.65 -2.47 6.39ms\n",
" 167 +7.604935142828 -4.68 -2.34 6.39ms\n",
" 168 +7.604905768199 -4.53 -2.58 6.40ms\n",
" 169 +7.604879814290 -4.59 -2.20 6.40ms\n",
" 170 +7.604824251203 -4.26 -2.56 6.40ms\n",
" 171 +7.604776894693 -4.32 -2.20 6.50ms\n",
" 172 +7.604692221918 -4.07 -2.13 8.37ms\n",
" 173 +7.604630748127 -4.21 -2.25 6.45ms\n",
" 174 +7.604560924221 -4.16 -2.00 8.35ms\n",
" 175 +7.604472760627 -4.05 -2.50 6.46ms\n",
" 176 +7.604411805435 -4.21 -2.23 6.40ms\n",
" 177 +7.604327627764 -4.07 -2.05 8.38ms\n",
" 178 +7.604249904082 -4.11 -1.81 8.51ms\n",
" 179 +7.604190588420 -4.23 -2.05 8.40ms\n",
" 180 +7.604085709147 -3.98 -1.61 8.36ms\n",
" 181 +7.604065857909 -4.70 -2.15 6.35ms\n",
" 182 +7.603960120423 -3.98 -1.57 8.40ms\n",
" 183 +7.603908442865 -4.29 -2.20 6.35ms\n",
" 184 +7.603826087998 -4.08 -2.23 6.47ms\n",
" 185 +7.603800245040 -4.59 -2.32 6.36ms\n",
" 186 +7.603712066841 -4.05 -2.33 6.37ms\n",
" 187 +7.603651682821 -4.22 -2.07 8.41ms\n",
" 188 +7.603604458943 -4.33 -2.34 6.40ms\n",
" 189 +7.603553427850 -4.29 -2.32 20.2ms\n",
" 190 +7.603493610866 -4.22 -2.19 6.53ms\n",
" 191 +7.603454734658 -4.41 -2.26 6.45ms\n",
" 192 +7.603401976902 -4.28 -2.12 6.43ms\n",
" 193 +7.603347386849 -4.26 -2.33 8.40ms\n",
" 194 +7.603309883062 -4.43 -2.05 6.40ms\n",
" 195 +7.603262659122 -4.33 -2.17 6.39ms\n",
" 196 +7.603258057164 -5.34 -2.11 6.41ms\n",
" 197 +7.603186603127 -4.15 -2.50 6.43ms\n",
" 198 +7.603176662550 -5.00 -2.44 6.41ms\n",
" 199 +7.603108292370 -4.17 -2.14 6.42ms\n",
" 200 +7.603080127346 -4.55 -2.33 6.35ms\n",
" 201 +7.603023836162 -4.25 -2.42 6.37ms\n",
" 202 +7.602952786680 -4.15 -2.16 8.35ms\n",
" 203 +7.602892316555 -4.22 -2.09 8.39ms\n",
" 204 +7.602869888511 -4.65 -2.48 6.40ms\n",
" 205 +7.602798119397 -4.14 -1.91 8.41ms\n",
" 206 +7.602757954926 -4.40 -2.10 8.37ms\n",
" 207 +7.602702504457 -4.26 -1.88 8.36ms\n",
" 208 +7.602680883115 -4.67 -2.60 6.40ms\n",
" 209 +7.602641580782 -4.41 -1.90 8.42ms\n",
" 210 +7.602636048556 -5.26 -2.16 6.36ms\n",
" 211 +7.602593017411 -4.37 -1.88 8.36ms\n",
" 212 +7.602568702238 -4.61 -2.38 16.8ms\n",
" 213 +7.602545915393 -4.64 -2.50 6.50ms\n",
" 214 +7.602531577161 -4.84 -2.59 6.50ms\n",
" 215 +7.602507699482 -4.62 -2.16 8.37ms\n",
" 216 +7.602481657301 -4.58 -2.53 6.41ms\n",
" 217 +7.602467523383 -4.85 -2.62 8.35ms\n",
" 218 +7.602455183466 -4.91 -2.77 6.38ms\n",
" 219 +7.602443143956 -4.92 -2.58 6.37ms\n",
" 220 +7.602435066949 -5.09 -2.70 6.40ms\n",
" 221 +7.602421769265 -4.88 -2.31 8.36ms\n",
" 222 +7.602409128020 -4.90 -2.51 6.36ms\n",
" 223 +7.602400843571 -5.08 -2.55 6.40ms\n",
" 224 +7.602389229286 -4.94 -2.49 6.37ms\n",
" 225 +7.602387043233 -5.66 -2.32 6.36ms\n",
" 226 +7.602368903040 -4.74 -2.73 6.40ms\n",
" 227 +7.602363952066 -5.31 -2.52 6.37ms\n",
" 228 +7.602347700196 -4.79 -2.68 6.36ms\n",
" 229 +7.602347647311 -7.28 -2.67 6.40ms\n",
" 230 +7.602340583817 -5.15 -2.61 6.37ms\n",
" 231 +7.602335299557 -5.28 -2.37 6.43ms\n",
" 232 +7.602325884138 -5.03 -2.73 15.4ms\n",
" 233 +7.602312260251 -4.87 -2.54 6.47ms\n",
" 234 +7.602284879580 -4.56 -2.32 8.46ms\n",
" 235 +7.602273325539 -4.94 -2.49 6.40ms\n",
" 236 +7.602256291123 -4.77 -2.42 8.37ms\n",
" 237 +7.602244110998 -4.91 -2.57 6.50ms\n",
" 238 +7.602241928492 -5.66 -2.40 6.41ms\n",
" 239 +7.602231087326 -4.96 -2.59 6.44ms\n",
" 240 +7.602216406811 -4.83 -2.40 8.41ms\n",
" 241 +7.602211965176 -5.35 -2.32 6.37ms\n",
" 242 +7.602183452543 -4.54 -2.06 8.41ms\n",
" 243 +7.602163667876 -4.70 -2.44 6.38ms\n",
" 244 +7.602159106577 -5.34 -2.27 6.41ms\n",
" 245 +7.602149565301 -5.02 -2.65 6.40ms\n",
" 246 +7.602136424664 -4.88 -2.09 6.36ms\n",
" 247 +7.602103794698 -4.49 -2.56 14.1ms\n",
" 248 +7.602056252331 -4.32 -2.52 6.43ms\n",
" 249 +7.602007354953 -4.31 -2.00 8.43ms\n",
" 250 +7.601999037657 -5.08 -2.47 6.41ms\n",
" 251 +7.601983945660 -4.82 -2.75 6.42ms\n",
" 252 +7.601957317728 -4.57 -2.06 8.44ms\n",
" 253 +7.601955496522 -5.74 -2.58 6.38ms\n",
" 254 +7.601933641044 -4.66 -2.46 6.41ms\n",
" 255 +7.601905930048 -4.56 -2.03 8.39ms\n",
" 256 +7.601904477951 -5.84 -2.21 6.37ms\n",
" 257 +7.601880420025 -4.62 -2.42 6.39ms\n",
" 258 +7.601849609637 -4.51 -2.39 8.34ms\n",
" 259 +7.601841919401 -5.11 -2.63 13.4ms\n",
" 260 +7.601836127776 -5.24 -2.74 6.48ms\n",
" 261 +7.601798428020 -4.42 -2.41 6.43ms\n",
" 262 +7.601777636959 -4.68 -2.43 8.41ms\n",
" 263 +7.601765855334 -4.93 -2.69 6.39ms\n",
" 264 +7.601765004666 -6.07 -2.55 6.36ms\n",
" 265 +7.601745832932 -4.72 -2.54 6.40ms\n",
" 266 +7.601729146111 -4.78 -2.75 6.36ms\n",
" 267 +7.601728352895 -6.10 -2.35 6.40ms\n",
" 268 +7.601713890767 -4.84 -2.53 6.36ms\n",
" 269 +7.601711807614 -5.68 -2.65 12.5ms\n",
" 270 +7.601691572412 -4.69 -2.31 8.42ms\n",
" 271 +7.601680963730 -4.97 -2.52 8.43ms\n",
" 272 +7.601670755084 -4.99 -2.72 6.37ms\n",
" 273 +7.601661389244 -5.03 -2.99 6.38ms\n",
" 274 +7.601655351278 -5.22 -2.78 6.40ms\n",
" 275 +7.601643319234 -4.92 -2.36 8.43ms\n",
" 276 +7.601640834184 -5.60 -2.70 6.39ms\n",
" 277 +7.601631195656 -5.02 -2.85 6.41ms\n",
" 278 +7.601628357278 -5.55 -2.38 6.39ms\n",
" 279 +7.601624482075 -5.41 -2.67 13.1ms\n",
" 280 +7.601613495006 -4.96 -2.24 8.50ms\n",
" 281 +7.601607406166 -5.22 -2.57 6.53ms\n",
" 282 +7.601603498329 -5.41 -2.66 6.45ms\n",
" 283 +7.601601220497 -5.64 -2.69 6.42ms\n",
" 284 +7.601588704595 -4.90 -3.06 6.38ms\n",
" 285 +7.601575252569 -4.87 -2.40 8.41ms\n",
" 286 +7.601574907551 -6.46 -2.69 6.40ms\n",
" 287 +7.601565714989 -5.04 -2.39 8.45ms\n",
" 288 +7.601561034040 -5.33 -2.83 6.35ms\n",
" 289 +7.601551447881 -5.02 -2.29 14.6ms\n",
" 290 +7.601551061891 -6.41 -2.50 6.41ms\n",
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]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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",
"text/html": [
"\n",
"\n"
],
"image/svg+xml": [
"\n",
"\n"
]
},
"metadata": {},
"execution_count": 1
}
],
"cell_type": "code",
"source": [
"using DFTK\n",
"using StaticArrays\n",
"using Plots\n",
"\n",
"# Unit cell. Having one of the lattice vectors as zero means a 2D system\n",
"a = 15\n",
"lattice = a .* [[1 0 0.]; [0 1 0]; [0 0 0]];\n",
"\n",
"# Confining scalar potential, and magnetic vector potential\n",
"pot(x, y, z) = ((x - a/2)^2 + (y - a/2)^2)/2\n",
"ω = .6\n",
"Apot(x, y, z) = ω * @SVector [y - a/2, -(x - a/2), 0]\n",
"Apot(X) = Apot(X...);\n",
"\n",
"\n",
"# Parameters\n",
"Ecut = 20 # Increase this for production\n",
"η = 500\n",
"C = η/2\n",
"α = 2\n",
"n_electrons = 1; # Increase this for fun\n",
"\n",
"# Collect all the terms, build and run the model\n",
"terms = [Kinetic(),\n",
" ExternalFromReal(X -> pot(X...)),\n",
" LocalNonlinearity(ρ -> C * ρ^α),\n",
" Magnetic(Apot),\n",
"]\n",
"model = Model(lattice; n_electrons, terms, spin_polarization=:spinless) # spinless electrons\n",
"basis = PlaneWaveBasis(model; Ecut, kgrid=(1, 1, 1))\n",
"scfres = direct_minimization(basis, tol=1e-5) # Reduce tol for production\n",
"heatmap(scfres.ρ[:, :, 1, 1], c=:blues)"
],
"metadata": {},
"execution_count": 1
}
],
"nbformat_minor": 3,
"metadata": {
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.4"
},
"kernelspec": {
"name": "julia-1.11",
"display_name": "Julia 1.11.4",
"language": "julia"
}
},
"nbformat": 4
}