{ "metadata": { "name": "", "signature": "sha256:ea21ebd4e0ef19922cb616b1d26a4cd9f05ffebf771ebadd7459d866ac991994" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Vent solaire (corrig\u00e9)\n", "\n", "*Auteur: [Aymeric SPIGA](http://www.lmd.jussieu.fr/~aslmd)*\n", "\n", "*Enonc\u00e9: Roch Smets -- Donn\u00e9es: Ga\u00ebtan Lechat, Karine Issautier, Sylvain Beaumont*\n", "\n", "La sonde [ULYSSE](https://fr.wikipedia.org/wiki/Ulysses_%28sonde_spatiale%29) a \u00e9t\u00e9 lanc\u00e9e en 1990. Elle est la premi\u00e8re \u00e0 avoir explor\u00e9 le vent solaire au del\u00e0 de 1 UA (Unit\u00e9 Astronomique). Ses mesures ont permis d'\u00e9tudier (via les caract\u00e9ristiques thermodynamiques) et de mieux comprendre la nature de son expansion dans le milieu interplan\u00e9taire. L'objet de ce probl\u00e8me est d'essayer de comprendre si l'expansion du vent solaire est un processus plut\u00f4t isotherme, plut\u00f4t adiabatique, ou autre. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Commen\u00e7ons par charger les donn\u00e9es au format `ASCII` en utilisant la fonction `loadtxt`. Cette fonction est dans la librairie `numpy` que l'on doit donc importer. Par ailleurs, comme nous allons utiliser `curve_fit` et faire des figures, importons \u00e9galement les librairies `scipy.optimize` et `matplotlib`. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import scipy.optimize as sciopt\n", "import matplotlib.pyplot as mpl\n", "# (ligne ci-dessous seulement pour cette page)\n", "%matplotlib inline " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "D\u00e9sormais, nous pouvons utiliser la fonction `loadtxt` avec l'option `unpack=True` afin de pouvoir remplir directement les trois variables d'int\u00e9r\u00eat avec le contenu du fichier `ulysse_first.txt`\n", "\n", "* distance h\u00e9liocentrique $r$ stock\u00e9e en colonne 1 en unit\u00e9 astronomique (UA)\n", "* densit\u00e9 $\\rho$ stock\u00e9e en colonne 2 en cm$^{-3}$\n", "* pression $P$ en colonne 3 en K cm$^{-3}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "dist,dens,press = np.loadtxt(\"ulysse_first.txt\",unpack=True)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons imm\u00e9diatement v\u00e9rifier la quantit\u00e9 de points collect\u00e9s par ULYSSE que nous venons de charger, ainsi que, par exemple, les valeurs minimum et maximum de chacune des variables" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print dist.shape,dens.shape,press.shape\n", "print dist.min(),dens.min(),press.min()\n", "print dist.max(),dens.max(),press.max()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(7687,) (7687,) (7687,)\n", "1.3382 0.32141 43079.0\n", "2.2947 17.7816 2242364.6\n" ] } ], "prompt_number": 33 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous allons convertir la pression $P$ en megaPascal en multipliant par la constante de Boltzmann les valeurs en cm$^{-3}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.constants as scicst\n", "press = scicst.k * press" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons par ailleurs faire une figure, par exemple $\\rho$ en fonction de $r$. Nous allons repr\u00e9senter les mesures par des points rouges pour bien souligner qu'il s'agit d'une succession de mesures ponctuelles." ] }, { "cell_type": "code", "collapsed": false, "input": [ "mpl.plot(dist,dens,'r.',label=\"mesures ULYSSE\") # commande principale\n", "mpl.xlabel(u'distance h\u00e9liocentrique(UA)') # titre axe abscisses\n", "mpl.ylabel(u'densit\u00e9 (cm$^{-3}$)') # titre axe ordonn\u00e9es\n", "mpl.legend() # affichage de la l\u00e9gende" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 35, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 35 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ce n'est pas par hasard que nous avons trac\u00e9 $\\rho$ en fonction de $r$. Nous pouvons nous demander si nous ne pouvons pas deviner physiquement comment est suppos\u00e9 varier $\\rho$ en fonction de $r$. Si l'on raisonne sur l'expansion d'une coquille d'\u00e9paisseur $e$ infinitesimale et situ\u00e9e \u00e0 une distance $r$ du Soleil, c'est-\u00e0-dire dans un \u00e9coulement stationnaire \u00e0 g\u00e9om\u00e9trie sph\u00e9rique, le volume de la coquille est $4 \\pi r^2 e$ et la densit\u00e9 est donc proportionnelle \u00e0 $r^{-2}$. Cela est-il compatible avec les donn\u00e9es observ\u00e9es par Ulysse ?\n", "\n", "Pour le savoir, nous allons effectuer une r\u00e9gression d'une fonction param\u00e9trique sur les points de donn\u00e9es. Soit une fonction param\u00e9trique $f_{a,b} : x \\rightarrow f_{a,b}(x)$ de $x$ d\u00e9finie par les deux param\u00e8tres $a$ et $b$. L'exemple le plus simple est celui de la r\u00e9gression lin\u00e9aire o\u00f9 $f_{a,b}(x) = a \\, x + b$. Le principe de la r\u00e9gression est que l'on doit trouver les deux param\u00e8tres $(a_{opt},b_{opt})$ tels que les valeurs de la fonction $f_{a,b}(x_i)$ en chacune des abscisses de mesure $x_i$ soient les plus proches possibles des ordonn\u00e9es de mesure $y_i$.\n", "\n", "Traduisons cela \u00e0 la situation pratique de ULYSSE. Nous disposons d'une s\u00e9rie de mesures de distance h\u00e9liocentrique $r_i$ et de densit\u00e9 $\\rho_i$ (donc $x_i \\equiv r_i$ et $y_i \\equiv \\rho_i$). Nous souhaitons v\u00e9rifier que ces mesures suivent la loi pr\u00e9dite par la th\u00e9orie physique $\\rho = a \\, r^{-2}$ avec $a$ une constante de proportionalit\u00e9. La fonction de r\u00e9gression que nous allons choisir est donc $$ f_{a,b} : x \\rightarrow a\\, x^b $$ et nous souhaitons d\u00e9terminer $(a_{opt},b_{opt})$ tels que les valeurs de $f_{a,b}$ prises en $r_i$ soient le plus proche possible de $\\rho_i$. Si nous trouvons $b_{opt}=-2$, nous aurons valid\u00e9 les consid\u00e9rations th\u00e9oriques par les observations d'Ulysse.\n", "\n", "Commen\u00e7ons donc par d\u00e9finir ladite fonction param\u00e9trique $f_{a,b}$ que nous appellerons en Python `regf` (pour fonction de r\u00e9gression)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def regf(x,a,b):\n", " return a * (x**b)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 36 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour illustrer le principe de fonction param\u00e9trique $f_{a,b}$, dessinons `regf` pour des valeurs diff\u00e9rentes de `a` et `b`" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.linspace(-6,6,100)\n", "a = 1 ; b = 2 ; mpl.plot(x,regf(x,a,b),label='$x^2$ (a=%i et b=%i)' % (a,b))\n", "a = 3 ; b = 2 ; mpl.plot(x,regf(x,a,b),label='$3x^2$ (a=%i et b=%i)' % (a,b))\n", "a = 1 ; b = 3 ; mpl.plot(x,regf(x,a,b),label='$x^3$ (a=%i et b=%i)' % (a,b))\n", "mpl.legend()\n", "mpl.xlabel('$x$') ; mpl.ylabel('$y$')\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 37, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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nueOyO5jUexLd23avwYCrxpJGLZaenc47O99h0XeLOHDiALfE3MIvev2Cn4b/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\nQmCC\n", "text": [ "" ] } ], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maintenant que $f_{a,b}$ est d\u00e9finie par la fonction Python `regf`, nous pouvons employer la fonction `curve_fit` qui va faire la r\u00e9gression dont nous parlions pr\u00e9c\u00e9demment, c'est-\u00e0-dire nous donner les param\u00e8tres optimaux $(a_{opt},b_{opt})$ tels que les valeurs $f_{a,b}(r_i)$ soient les plus proches possibles de $\\rho_i$. Cette fonction prend en argument\n", "\n", "* la fonction param\u00e9trique $f_{a,b}$ utilis\u00e9e pour la r\u00e9gression\n", "* les abscisses de mesure $x_i$\n", "* les ordonn\u00e9es de mesure $y_i$\n", "\n", "et donne en sortie\n", "\n", "* un tableau contenant les param\u00e8tres optimaux (ici au nombre de deux $a_{opt}$ et $b_{opt}$) de la fonction de r\u00e9gression $f_{a,b}$\n", "* la matrice de covariance \u00e9valuant l'optimalit\u00e9 des param\u00e8tres $a_{opt}$ et $b_{opt}$\n", "\n", "L'appel \u00e0 la fonction `curve_fit` s'\u00e9crit donc dans notre cas" ] }, { "cell_type": "code", "collapsed": false, "input": [ "param,cov = sciopt.curve_fit(regf,dist,dens)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 38 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Voyons les param\u00e8tres obtenus par `curve_fit`" ] }, { "cell_type": "code", "collapsed": false, "input": [ "a_opt = param[0]\n", "b_opt = param[1]\n", "print u'r\u00e9sultat a=%.3f et b=%.3f' % (a_opt,b_opt)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "r\u00e9sultat a=23.838 et b=-6.804\n" ] } ], "prompt_number": 39 }, { "cell_type": "markdown", "metadata": {}, "source": [ "(NB: ici il y a deux param\u00e8tres, mais il pourrait y en avoir plus en fonction de la fonction param\u00e9trique utilis\u00e9e qui pourrait \u00eatre \u00e0 3,4 ... param\u00e8tres !)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Au vu du r\u00e9sultat obtenu pour $b$, il est clair que nous n'avons pas $\\rho$ proportionnel \u00e0 $r$ d'apr\u00e8s les donn\u00e9es ULYSSE ! Ajoutons la fonction $f_{a,b}$ pour les param\u00e8tres optimaux $a_{opt}$ et $b_{opt}$ \u00e0 la figure pr\u00e9c\u00e9demment produite avec les mesures ULYSSE" ] }, { "cell_type": "code", "collapsed": false, "input": [ "mpl.plot(dist,dens,'r.',label=\"mesures ULYSSE\") \n", "mpl.xlabel(u'distance h\u00e9liocentrique(UA)')\n", "mpl.ylabel(u'densit\u00e9 (cm$^{-3}$)')\n", "# ajout de la fonction optimale obtenue avec curve_fit\n", "zelab = 'curvefit $f(x) = a x^b$ avec $b=%4.2f$' % (b_opt)\n", "mpl.plot(dist,regf(dist,a_opt,b_opt),label=zelab)\n", "mpl.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 40, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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/PnBb8+awYoUVKxlj4i7adRCnAD8Aj4rIJhFZKSKrRGQT8E9c7+fB4V681igp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\nIicBvwMGxDstEfYP4GZVVRERIPwBthJ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"text": [ "" ] } ], "prompt_number": 40 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous constatons que la fonction `curve_fit` a fait ce qu'elle a pu pour rapprocher le plus possible la fonction param\u00e9trique $f_{a,b}$ des points de mesure ULYSSE, mais que le r\u00e9sultat n'est pas tr\u00e8s concluant. La fonction optimale obtenue (ligne bleue) est particuli\u00e8rement \u00e9loign\u00e9e des mesures (ligne rouge) et ce, particuli\u00e8rement \u00e0 $r>1.8$ UA et $r<1.2$ UA.\n", "\n", "Nous remarquons que pour les distances $r<1.5$ UA, plus proche du Soleil, les points de mesure sont extr\u00eamement dispers\u00e9s ce qui pourrait traduire par exemple\n", "\n", " 1. une variabilit\u00e9 plus grande de la densit\u00e9 \n", " 2. une moins bonne pr\u00e9cision de l'instrument\n", "\n", "Ainsi, la dispersion des mesures effectu\u00e9es en $r<1.5$ UA ne para\u00eet pas propice \u00e0 v\u00e9rifier une loi physique type $\\rho = a r^{-2}$ obtenue par un raisonnement g\u00e9om\u00e9trique sur une situation moyenne.\n", "\n", "Nous allons donc restreindre l'analyse aux donn\u00e9es obtenues pour $r>1.5$ UA. Pour cela, il suffit d'employer la fonction `where` de `numpy` qui permet de s\u00e9lectionner une partie d'un tableau v\u00e9rifiant une condition particuli\u00e8re, pour l'utiliser ensuite pour d\u00e9finir un nouveau tableau." ] }, { "cell_type": "code", "collapsed": false, "input": [ "w = np.where(dist > 1.5)\n", "dist2 = dist[w]\n", "dens2 = dens[w]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 41 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons appliquer de nouveau `curve_fit' comme pr\u00e9c\u00e9demment. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "param,cov = sciopt.curve_fit(regf,dist2,dens2)\n", "a_opt = param[0]\n", "b_opt = param[1]\n", "print u'r\u00e9sultat a=%.3f et b=%.3f' % (a_opt,b_opt)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "r\u00e9sultat a=2.481 et b=-1.976\n" ] } ], "prompt_number": 42 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cette fois, en ayant restreint les mesures de $\\rho$ au cas o\u00f9 $r>1.5$ UA, nous trouvons $b \\simeq -2$ comme pr\u00e9vu th\u00e9oriquement. Nous pouvons reprendre le graphique pr\u00e9c\u00e9demment effectu\u00e9 pour constater cette fois la bien meilleure performance de `curvefit`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "mpl.plot(dist2,dens2,'r.',label=\"mesures ULYSSE\") \n", "mpl.xlabel(u'distance h\u00e9liocentrique(UA)')\n", "mpl.ylabel(u'densit\u00e9 (cm$^{-3}$)')\n", "# ajout de la fonction optimale obtenue avec curve_fit\n", "zelab = 'curvefit $f(x) = a x^b$ avec $b=%4.2f$' % (b_opt)\n", "mpl.plot(dist2,regf(dist2,a_opt,b_opt),label=zelab)\n", "mpl.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 43, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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DiNCgNgtVHRT521JVSwMpLUURYTwwLEmeV1S1TyTVURRxqe8K7FTdWDOtZ+JE\nN3rwFAVElcOGDfA//5O+zIZhGA1MWq6z2UJVZ4pI1yTZMrMae409uAY93SmdVN1Yp0yJekONHp26\nN5RnzPZTVpZanYZhGHki3UCCZ4hIWeT41yLytIgc2QByKTBQROaJyFQR6ZnyJ+u7ZiGs5x9GNr2h\nUq3TMAwjT6TrOvtrVd0gIoNxC/MeAP6afbF4G+ikqkcQXTWeGvVteK+8Elatgl69YPDg+NNMRx3l\n/vbpA+PHp1+PH3OdNQyjkZPuNJS33/bJwH2q+pyI/G+WZUJVN/qOp4nIXSLSOszzaty4cbXH1dXV\nVFdX18+byD+N9fnn7m/YdNYTT2RvIZ25zhqG0UDU1NRQU1NT73LSXcH9PLAMGAocCWwFZkdGAOlV\n7GwWU+J4Q7XDeUppZL+MSaraNSRfXW+oHj2cLaG4GN56K33PIs9bqazMGZz9XksNhbnOGoaRIzL1\nhkp3ZHEG8G3g96q6VkT2A9J23xGRx4DjgLYishS4nkioc1W9Bzgd+KGI7AS2AGelXPjHH0ejxQ4c\nCMuWpSfcxImup19Y6BbdZVtJhI0iLDaUYRiNnHRHFk2B04CuRBWNquqN2RctJXnqjiwKCqKRY4cO\nhenTMyu8oXr7YeVabCjDMHJErmJDPQN8D9iB2wBpE7A54ScamqABusg3WCpOc18m/9qJN9901woL\n4dpr6y1mbfn/+Y87Li2F3//eHXtG9XPOsd35DMNolKSrLPZX1TNV9VZVvd1LDSJZqkybBmecET1v\n0SJ6HBZifOxYp1BEnDJ5993oPf+CvC1b3LVdu+Db386OrIsWwfbt7njjxugCvIbez8K2ijUMo56k\nqyz+LSKHN4gk9eGFF6JurkdEbO3xXFoXLXIKAGDnTujXL3rPsx00FP7ye/eO2ica2mZhmysZhlFP\n0jVwHwtcJCKfAN6qNFXV/CuQ115zf7t0gbZtoU0buOwy+PTTcGOyx6GHOiVTWem8n0pKor1/cCOQ\nf/0rOzJWVjq5Cgvdim/PPjFxIhx5JDRp4qaisu0+awZ0wzDqSboG7q6RQ8UXjkNVl2RTqFQRkVjp\nRZyB2xs5tG0Lq1e7Y78x+Ywz4NVX4bDDYM4cd7+yEr780h136ODcb3fvjt5btKj+DXg8o7m3jmP9\n+rr3soEZ0A3DiJArA/dnuNHFhREFsRuoSrfSBqGw0HlBeYqiosJN9UBsj7q8HLp2hf793ajDu3+E\nb6nIqlXCqQolAAAgAElEQVSxZX/5Zd3pm0zsAPF6+A8+GFUUpaXZ7/3bCnHDMOpJusriLmAAcE7k\nfFPkWv4oLHRTR/37x14XcUbk9u3hH/+IbSi9OfzVq12+Fi3g/vuj93fujI4qwIX+CDbgmdgBJk6E\nbt2i001ej99TcACbN8PIkfGVkBmrDcPIB6qacgLe8f+NHM9Lp4xsJtxYwqX27aPHwTRqlMbQvHnd\nPCNHxp6XlqqWlKgOHaq6dq3W4aSTXL6+fcPvx+O442LlCsp91FHx5VaNzT9yZOr1GoZhqKpr9tNv\nb9MdWWwXkULvREQqcVNR+WfXrtg1Fh5hRt2tW+vm274dqiIzagUFblSyfTvU1DgbQrAXX1npbCLp\nTu0Ep6L80WuPPx5WrnTHZWXRdRh+/PlTtTfZaMQwjHqSrrL4E/A0UCUiNwOv4bZazT9ffummj/y0\nb183rtPYseGNbEkJHHywO/ZPQe3Y4cJ+BKeapk9301gzZrj9LFKlstIlTyYvem2LFm5Kbf/93Xm8\njZCaNXN/Cwpcw59K4z9lSnTK7KKLUpfVMAwjQlrKQlUnAFcBNwPLgRGq2nij3jVpUnf+f9Gi8Lw3\n3BDdhKh169jV3/7V1h7p7Gfh79kvXuwU24wZzl3WWxS4ebO79s477rxtW1i+vO5oYE0k8O7u3U4B\npGIvyWQ0YhiG4SPVPbiv8J363WYjhgP9Q/ZFS04d11k/BQWuEfeMx926uemn1avrjkDAuctu3OhS\nGEF31qFDXePepw+89FLi6aj99ovuqldV5byt+vZ1ysxbH+KnY0c3BeZ5ZY0Y4dZljB0L990XzVdY\n6L5PorrHjoWHHnIjpJYt4f33bY9vw9iHaWjX2VKgJXAU8EOgA7A/8P9wocobH7t3x7rRemsnwhQF\nOEUSVBSFEfNMmN3jiSecAkmmKCC2Z9+3b3RzpjLf9uX+uk44Ab76Knpv6lTn5hscFZ1wQvK6Fy2K\nRuHdtKnx7PHtH21deKHZVAyjkZPSCm5VHQcgIjOBIzWyOZGIXA9MbTDpskFhIRx+ePKggmvX1r1W\nVgbf/KbrmQftHl6Y8VRo1syVX1oKd90V7dl/9FE0TtVLL8Ef/+jyPvNMrDvtjh0u3Lp/LUhBAdx2\nW/K6/TKGTaflC/8e5m3aRJXjkUdC586pbwRlG0cZRm5Ix3UKWAg09Z03BRZm4oaVjQSoFhXFd5n1\np+HDnatpQUHde/36ub9hLrVh7qtB99dkNG0aK4dHq1bR6x07umvNmsWXf+3a2GsdOiSve+1a1TZt\n0pM3F1RURGWqqoq6IXvHqboGp/u/MIx9HHLkOvsI8IaIjBORG4DZwMNZ01yZEG9aKcgrr7ge++6A\np295Ofzzn25qaODAup974gnX8+/fPzpF4vXWW7Z0IwbvetBFtUcPV/62bdHyZsyI3vdGOwUFcOCB\n7po3ZRTklltcWX73YG+FeiLKy+GYY9xxothQuXav9bzACgud0b6oyHmE+Ud4/hhd8bC4V4aRG9LV\nLji7xeXAZUCfTDRUthKpjCi85Izh4amwULVJE7cgLlE+r+e6dq1qZWXd68EFc/6RA8SOakaNUj3r\nrLrlt24dXnfHjqpjxkTLbNZMdciQ1BYErl3ryk6UN9c99LKy5P8n/ygsHql8N8MwaiHDkUXeGvps\npLSURTaSv0EKW8Htn1oZMcIpIE9JVFVFlUlZmeqSJbENdFGRu7ZkiVs5Hqx73rzY/OlM1XTv7pRM\n27au/DAyXZGeKWHPt6wsdloxFWVhGEZaZKos0p2G2nfo0yf2vF+/WOOpZ5z+5BMXBHDs2Oj0jQjc\neGN0mmj3bjfF4kXA3bAhugDQY+dOZ9wdPDi68M7Pdde5NRpBUpmq+fhjJ+Pq1dC9e/g008SJUS+t\nfBmJ+/WL3bwqlZ0ObXW6YeSEdPez2DcoKop1a4VohFqPVatcA//VV3DAAU5BuNGO+/ud70TzlpW5\n9RWffBK9tmMHvPFGbJlr1kQX3QURcV5Un38eez2VBtWTC5wb7ze+UTfkuheZNlcUF9e1z7zwgvPY\nAmeL2LzZKYBEyssL6AjRUO+GYWSdPX5kISiC0o2P+Sl3sowO9S90585oA+SxYoVbXOftyOc3WvvX\ndIBr2J9/PnYk8fHHdesJ2/bVo7Awetyzp9v1z1NY3r3evZ1bbyLGjo3trUN4yPXgZxq6t35knOU5\n3lqXLVucM8C55yYuxwzchpET0tr8qLEhIjqRs7iLS5nFsaF5TucJ7uBndGRZdisP7qgXxNtfw/O+\natbMNWz+xXb+zZnKypxSqahw3lE9esDbb0PTps5zqEMHN1XkeX916ABDhtTdCTCIf8Mlj9JS+Oyz\n+D32eJs0QfbWNQwf7mJVFRUl9mjr0AGWJfjfeWHemzVL/izqi63pMPYCMl3BnXcjdX0SIUbS2Ryt\nLdiY0E59MffrYrplbuguKqrr6ZQslZfXvdamTewaiJKS+OUGvbQqKmIN6u3bJw6l7k9Dhya2gCUy\ndmfLa8rzYvLWuMRL8+alVl625BozxpV10kkN990NI4+QoYE7X438g8BK4L0Eef4IfAjMI46Lbpiy\nCKZdiD7JKUnb8u9zr86nu+5OtfFv2zY9ZREveQv2CgvrX5a/AfMavQ4d6uYLehkFG8i1a1W7dVMd\nNKhuo5lNr6nu3ZN/7xEjUisrW3IlUgi59hgzjAZgT1MWxwJ94ikLYDgwNXLcD3g9Tr66jUsKK7q3\n0kTvYUzStvc8HtF3OCJcgVRUqBYX17+Bb9ky9rxPn8zKKS2NdYsNc7P1UnBk4V8fMmJE7HqOYKOZ\nyrqGRL1zP6mMzlLd4Km+6y08mT13Z8+9OZt1GEYjYI9SFk5euiZQFncDZ/rOFwDtQvLVbVz8O82l\nkdZQrn/g8uRtF0/pf+iX+ggk1VRS4qakhgxxDX8mZXTrFm2khwxx18IUmkjsgj7/verqWEVTUZF+\n45jqbn7JRmctWsRfF5JtwpRrcGSRynoVw2jk7G3KYgow0Hc+AzgqJF94IxMW/ymDtJZWeic/SZp1\nILP0Jap1FwlWfydKFRWxc/f++EiZpubNk4+yvMYwqEj8tpDy8vQbRv/zHzq07khjzBinUFIZWeRq\nYV7Hjq4+b1qsZcu6K+TDYnkZxh5GpsqiMbvOBq31mtKnevSou6AujNatk2YpZz0/5U8R51yXNlDK\n/VxCIVEPnn8ziBN4mUJ21+Zsw2qeZzg7KUxQQ4RvfCO64K5tW7f3RlWVc9UtKXHeUemyZUtiL6Oy\nMudq2qNH7HXV2PhM69Y5d2GPVNxq/ZtBvfoq/Pe/0Z36PI+iFSvcQsFkzJ2bPE+qciXCiwS8a5d7\n3ps21d0F0VvT0rw5zJqVfh2GsQfTWBflLQM6+c47Rq7VYZzvuBqoXrAABg1yFwoLY9c/+NmwISPB\nStnEJTzIJTxYe20HRUxlOFdwO4s5CIA1tOFknq/z+fu5hPP5GyX4FqTNnu3+duzoGi1vQ6SwhWvZ\nwmv4wtZ/BPGCHJaXx4YWv+giePrp2Lxjx8Y+86+/jipCby1Er16py7lli3OJjbdhk6d83n03quQy\nWZznLcLs2xc+/DCqyPyKr6zMuTpv3+724Jg82dxnjUZPTU0NNTU19S8ok+FINhKJp6H8Bu7+JDJw\nhwX+a9Ika1NR9UnvcaiO4OmkWcdyt24uaOkCC/qngLKZwp7TqFF1r4fFpfKuB+NWhU0Rhc39L1kS\naxgeNCg92RNN+QTr6907fRvLmDFRr7SSktipKP8UXHDazNxnjT0QMpyGSvsD2UjAY7g9vLcDS4GL\ngR8AP/Dl+TPwEc519sg45YQ3LjNnNkyDm4W0gZb6v/wqadYbuVYXcVB26hVxzyRow5g3L/X9QLxy\n/NFiw9xavbl/fwo23mFrP8LqAqf0E621CJaVqveUn3h7iECsQvQb5A87zLyi9iZS9eDbC8hUWezx\nK7hDpW/I6ZsGoobjGMY/+ZqmcfMMYhZn8Tin8w/aszK9CsKm5BJN08XDW7neogUMGOD2+/BPxTRr\nFhsKBaBTJxc/y1v5DG6q6JlnwlfBe/t2eKvbvT3IPfwrqVu1giefdP/v3r3h5Zej8vjzVVbGX+Fd\nVBT/ORQXuzhg5eVw9tmurvJyePNN28t8byJR1IK9jH17BbdI+tNOGbrY5jLtQnQmg/RS/qytWR03\n67G8on/kx7qM/dKrI7jGI5VUUBC7Gj04FZPs8yNHRntxYd5QFRVuOs6/WC84WvCPBILTdoMGRXuG\n/nz+8oIy+1fRhyUvv3/KK96K+SD7UI91j2YfWnBJhiOLtD/QmBKJfuDJUvv2rhEI2z/Cv7FRY0k+\nZfg1xTqNb+vF3K+lrI/7kSN5S2/iGp1P9/AMiTZ6SjXNnBl9C8eMSZ6/c+fweps1i24dG7RD9OsX\n+wP23wtbR+I15GH1hzUGwU2ogsmbBgtOeaVis7AQIXsG+9CCS1MW6Sb/KuZgYxHcrW7mzOyE42jg\ntJ0i/RdD9f9xl1axIn57zRK9jDv05ebDdQf1/F5Nm0Z7z6mM7oI75BUVuTUh/fpFe9+p2DSSpZEj\nY88LC52NJdgYBFerhyXPwH7wwdFrQeN3PDwbjohbbJmNBX02WjHqgSmLYIrn1eMlv+HSv+IY6i6K\n69YtPUNwI0u7Qd+mt17LjXoo7yXMfhJT9W7Gpj6ltf/+6QdV9KdWrWKnkrzeXX2/d+fOdd+HsFhX\nicKieMkbPQW/ZypTUWGeX/Vd0BcMz2IYaWDKIpiSTbH4lYW/sfJiAnmulGVlySOj1keOfKahQ3U5\n7fVevq/fYUrCrFWs0Iu5X59ipG7AZ+vI5ojLH4+pPuU0a5b4f1ZVpXrBBbGxoBKlykonU1h4kkSN\n9Zgx0XcrVe+uVPC/r/G8v3I9+rDRzh6DKQt/Ki2tO90RbDz8ysIfmXXQINeQ+D8fHHmkmlq2rKss\nqqry49o7dGjdMOlduoTnFdEdFOprDNCr+Y32Yl7ConvwX/05t+l0hug2kozowlKLFtHjsBAkmaRk\nU2Lp2KVEXGMYpoASuerGc8lt3rx+MaaaN3flFBbGVzz+EZM/ZlhDNeT+79q2rSmMRowpC+/H42+U\nveOZM93L6zeG+nuEwakCf2/T+0Fmo9GqqorWmYknUtj3TDV16pQ1w/1mmukUvqM/4K+6P0sTZv8G\nC/Qy7tBpfFs3E2g8S0pcQ+YpsT59orGjsiBn3FRUFA20GPYsg9dmzgyfriosdI19WIDBVL9DJlNS\n/o5MvM/7vXv87/eoUbHyduuWneCIwWeWq5he2WAfGxWZsgj+iGfOrOvd4DUQwVW+/oVkvXrVnZtu\n0ybzcOTxph9Smf5IVmZDNaT1+PxaWukTnKaXcJ924POE2dsWr9VzZKI+xAXORuI1MKnYEeqTioud\n63T79tFORWFh+N4i1dVOJq/xDY5YRoyIfTdKSty7FW9UIRLNn86UlL9B8xwwmjeP38AffLCrq6go\nqow9T7B4zyVVxRXWuAafS/v2qZXVGNjHPNZMWQRThw51n1I89zh/z6u4OP1wFIlSvDUJ9bGDNFRq\nYI+vTTTXqQzTy/mD9uT9pB85jpf1f/mV/pv+9ffaipdSUbyDBqkecEC4Ih06tG4Zo0Ylfpb+NT6p\nNE5Bj61OnZxSOu64+D3hYIenQ4fwkPReSqR4goQ1rsGw+sl2Y0z2fXPZ0/c6AmGRhvdCTFkEUzrD\n4KCrZocOdXuZ8XrciRqbli2j9o7gZjpenUVFmceDKi+v33RWI0q7EJ1DH72l1wQ9vv0HST/SllU6\nir/rX/ihfsAh2d9fJJjiNf5NmsTea9XKNTaJbCbeO5PqAjD/KKWsrO60kmrdBjY4cvX/HoLytG+f\nfDrKP3XlKYu2baMeZkHvw0zCrnih6/2/tXjfL5sEn1cmsu9B7LvKwptG6NMn+iPq1Su9F2rt2ujL\n7vWw2rWLvjwdOsTfqCfZdJJ/dbC/F3nBBa7MIUNcfelM/7Rv717otWuzt71rY0jFxc6uEqKAV9Na\nn+QUvZQ/a3fmJy2qHV/omTymdzNWF/CN+iuTVP8/3gLCZBtY+Teg8hrJioq6Pdsw24dns2jd2r3/\nFRV1dzYMG7l6HZbgdwm6GYeNyv3lFxTU/R/51yaVl2fWoAenHz3FG7zXEFNF/g5b0MNtL7Np7LvK\n4oILXAPjNbqZrsJcssTN2Xq9qqB7Yti6jd69wxtrT0H07Ru1kwR7kcGX38uXLPXsGVtO2Ar0xpCa\nN6/rkdaA6TM66t84Vy/hPj2Aj5J+pDWrdQRP6+38TN/kqOTTXNXVqduKBg1K3SZVVFS38fY3VomC\nHIbJ49nj4i1s7NgxucNGcFTePU4EAH/yK6eKirqjE3+De9BB4aOYYBDKNm2i73pDhuMYMyY6XRwW\nIHIvW9ey7yqLhvpHBt0Tgz/Mpk1jRyRe6tkzVmn5RxD+lzD48vu9tZo1C5/28P94/IRFeg1LBQW5\nVSyNIWxKQYHuBl1CZ32IC/Ri7teDWZjSR4/iTf0p/6d/Z5QuO3F0eo4F9bFJHX989H+brh3pqKPc\n58KmosCNRAYNSvxdgkb3VL53cNotODrxd478ytFvVA9TjN6UULzfUTYIc2jw4//NFBXt8Vvq7rvK\nIpUFSpkQdE8M/hiWLHE9Ev91vxHRI95+1GHGdv/oJswjKJ4dJp1tWDP16sokDR+eu7rqmdZQrs9y\nsl7FLTqYV1XYlfRjLdmg32aa3si1OoMTYhcr1ieJuMYx0/U93ruZaf0dOsSOBFL5TNB25n9X/YsT\n/WtqvLq8UUaYUhoxwo1sEgWCrC/BZx/8DQc7WGHTdPkkzWmyfVdZeNM3no9+tvCmlzwbhr+XNnWq\nyxPsLYX1OBLNhSbCUyb+XliYskhlisBLBxwQNdwHU9icfH28o7zpkGw0nvHkTWWUlG40Ym9EGUi7\nu3bTRS1664OM1ku4T3vw35SKK2eNDmOqjuM6ncowXU3r1ORI1JtP1tPv0CFzRQPOk6k+n/dPlY4Z\nk7mrd1mZKyf4eW/kky1bQrDeoDIKdrC89TWNBf+ILAXHnn1XWTRUtMigDcM/reCtiA3aK8J6PPHW\ndqSK/0UNexGCL3KiBrRDh9yMLPwxk1JprBMppVx6exUUuP9zcKRWWBj7/49jj9hOkb7FkfonfqTn\nMCEl24mXjuQt/X/cpQ8yWt+np+6kHjs9FhTUz17UsWNmDXxJiXt2/oa0vmtmwj7vTV1lawra710W\n9jsN+83UN75XNvH/flIY9ey7yiJXxFsR6zUc8Qxv9VVm/nUaYdNswRFBvFAi3ggp3o8y2GB7UVL9\nDVCqP3C/nMn2ivDqincvnSm2bKbgc82SHLsQnU93fZjz9VL+rH15I+WPV7FCh/OcXsc4fZaTdTnt\n43t51WfRZ/B/loriiTdNlI0IwsHkjSz81woKMu/tr13r3tmwqMTB32BQBtWoW3GTJq4DGebV5ifb\n3lX+32ZpadLnYMqiofE3+n7FUR8PrFRINs0WnC4Im0Zp2jR5gL5g4zh0aOyoaN4815tK5hIalLM+\n3lrl5YkVXFhqKAN+nOmphkpfUaH/Yqj+L7/Sk3lW2/FFyh+vYoUOK5ul1zS/Q5/gNF1Mt9RdhwsL\n64boT5SCnYhgp8kf1j2TFPa+eZ2R4PWw3r7nllxQEP1unk0n1QY7zFPRrxDjRV2Ot0Yknh0zU4LP\nKMnqeVMWuSSXG6Ukq8s/yiksrDs15vdVVw2f8ikrix3ue0PxsLoTufjGC9m9dm3iMObxVsx7026p\njE68lOkCx2SpEUYP3g36KZ30SU7Rq/mNDmNqwn1MgqkJW7U//9ZL+bPexyU6hz7pBYKsqqr7f/Vv\nhqVa/+dWXFx3ZONNOcWzZfgXEMbbaMt/vVOn+OtcvPfX35ny/6biORL47RpB5eB/R6uq6t+OBH/z\npiwakbJoTHijnOJi92Pxv4hhhriwOeB585IPxT3iGa3D/NODnxs61I1yPOUgEg3yGCzPP0JZsiQ1\nW0vv3rERhOuTEo2gevbMTh0NmfyL/vr10y9po9MZor/jf/RMHtNvsCClYorYrj/jdv0tV+p4LtSp\nDNO3OFKXsr9+/a2T6nYemjSJ/b9n47u0bRudVvM6MmPG1LVnVVa6NRz1rc8/aghbVe6NeOP9nrzk\nKQL/bzJserC+oVGCbtpBhR0gU2Uh7rN7JiKie7L8WWHdOhg7Fu69F8rLYehQmDEDWrWCefOgS5fY\n/BdeCI88EnttxAiYPDn1OiWw1/vw4fDoo67+TGQGmDULjjsOnnsOxo+PvQfQogVs2RIrQ1ER7NgB\nvXrBgQe6z3XvDqtWJa6/qAiaN4cNG1KT119feTm8+SZ06+Z+mo2dkSPhrbfg889Tyv41JcznEOZx\nBHPpTRO+pi2rWUk7VhZ3ZOWO1qyiipW040sqKS35mnbbl9LO5XCp6QbadWtO1bqFtPtibu31ZmzL\n7DsUFcFHH8Hxx8Pmze792b49PK9I/f4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"text": [ "" ] } ], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consid\u00e9rons d\u00e9sormais la possibilit\u00e9 que l'expansion du vent solaire soit un processus isotherme. La pression $P$ et la densit\u00e9 $\\rho$ doivent alors v\u00e9rifier $ P / \\rho = \\alpha $ avec $\\alpha$ une constante, ce qui indique que $P$ doit suivre une loi en $r^{-2}$ comme $\\rho$. V\u00e9rifions cela en appliquant la m\u00eame m\u00e9thode que pr\u00e9c\u00e9demment et en se restreignant au domaine $r > 1.5$ UA." ] }, { "cell_type": "code", "collapsed": false, "input": [ "press2 = press[w]\n", "param,covp = sciopt.curve_fit(regf,dist2,press2)\n", "a_opt = param[0]\n", "b_opt = param[1]\n", "print u'r\u00e9sultat a=%5.2e et b=%.3f' % (a_opt,b_opt)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "r\u00e9sultat a=9.77e-18 et b=-2.510\n" ] } ], "prompt_number": 44 }, { "cell_type": "code", "collapsed": false, "input": [ "mpl.plot(dist2,press2,'r.',label=\"mesures ULYSSE\") \n", "mpl.xlabel(u'distance h\u00e9liocentrique(UA)')\n", "mpl.ylabel(u'pression (MPa)')\n", "# ajout de la fonction optimale obtenue avec curve_fit\n", "zelab = 'curvefit $f(x) = a x^b$ avec $b=%4.2f$' % (b_opt)\n", "mpl.plot(dist2,regf(dist2,a_opt,b_opt),label=zelab)\n", "mpl.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 45, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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CiK5aRd2EEN8UQjyE4BO43QEsE0KshvTlf1YJ+7AINmFaWys9exIS5GciYMaM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\nRM4NmJq5KciURuX2gnXp4s00pVaNchLygwcHbps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"text": [ "" ] } ], "prompt_number": 45 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le recours \u00e0 `curve_fit` semble fonctionner correctement, avec une fonction obtenue qui approche raisonnablement la tendance dessin\u00e9e par les mesures (impression visuelle qu'il s'agirait de confirmer en \u00e9tudiant plus pr\u00e9cis\u00e9ment les sorties de `curve_fit`, ce que nous ne ferons pas ici). Nous trouvons que $b = -2.5$, ce qui nous indique une loi en $r^{-5/2}$ pour $P$ et non une loi en $r^{-2}$. Nous concluons que l'expansion du vent solaire n'est pas un processus isotherme, m\u00eame si elle s'en rapproche.\n", "\n", "Pour une expansion adiabatique, la pression devrait \u00e9voluer comme $n^{\\gamma}$, soit $r^{-2 \\gamma} = r^{-10/3}$. C'est encore moins le cas. L'expansion du vent solaire n'est donc pour s\u00fbr pas adiabatique. Il faut donc identifier la source du chauffage du vent solaire... ce qui est encore un sujet de recherche active !" ] } ], "metadata": {} } ] }