{ "cells": [ { "attachments": { "disp.png": { "image/png": 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" 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} }, "cell_type": "markdown", "metadata": {}, "source": [ "# Etude préliminaire\n", "\n", "On procède tout d'abord à une étude simple pour se familiariser avec les notions de relations de dispersions et de gap pour un système mécanique donné.\n", "L'étude se portera sur deux grands cas, d'abord sur des chaines atomiques puis sur des chaines masses-ressorts. On pourra y notifier des signatures topologique dans certaines conditions.\n", "\n", "## Chaine atomique et diatomique\n", "\n", "Considérons une chaîne de N atomes atomes de même masse. Soit $x_n$ la position du $n-ieme$ atome déplacé de sa position d'équilibre $x_n^0=na$, $a$ représente la distance entre deux atomes et $\\gamma$ est le terme de couplage entre chaque atomes.\n", "On appellera $u_n = x_n-x_n^0$ le déplacement de l'atome à partir de la position d'équilibre.\n", "On applique les conditions de périodicité : $x_0=x_N$.\n", "\n", "L'équation du mouvement de l'atome $n$ se réduit à :\n", "\n", "\\begin{align}\n", "m \\omega^2 u_n = \\gamma (2 - e^{i k a} - e^{- i k a} ) u_n\n", "\\end{align}\n", "\\begin{align}\n", "\\omega = 2 \\sqrt{\\frac{ \\gamma}{m}} | \\sin ( \\frac{k a}{2} ) |\n", "\\end{align}\n", "On veut à présent savoir quelles sont les parties de ce spectre qui correspondent réellement aux modes de vibration.\\\\\n", "Les modes $k$ et $k + 2 \\pi / a$ décrivent la même vibration collective puisque:\n", "\n", "\\begin{align*}\n", "u_n^k = e^{ i k n a - i \\omega t}\n", "\\end{align*}\n", "\\begin{align*}\n", "u_n^{k + \\frac{2 \\pi}{a} }= e^{i k n a - i \\omega t} e^{ i \\frac{2 \\pi}{a} n a }\n", "\\end{align*}\n", "\n", "Seul l'intervalle de base de longueur $2 \\pi / a$ comporte les modes indépendants dont le nombre est :\n", "\n", "\\begin{align*}\n", "\\frac{2 \\pi}{a} \\frac{1}{2 \\pi / L} = \\frac{L}{a} = N\n", "\\end{align*}\n", "\n", "Ce sont les N degrés de liberté. La relation de dispersion montre qu'il y a une distribution des pulsations comprises entre 0 et $\\omega_M = 2 \\sqrt{\\frac{\\gamma}{m}}$.Dans la figure ci-dessous $\\omega$ représente la pulsation et $ka$ le nombre d'onde. On y aperçoit pas de gap.\n", "\n", "![disp.png](attachment:disp.png)\n", "\n", "\n", "### Chaîne linéaire diatomique\n", "\n", "Soit un cristal unidimensionnel de longueur $ L = N a $ (a : maille élémentaire). La maille élémentaire contient deux types atomes : A de masse $m_1$ et B de masse $m_2$ (on supposera $m_1 < m_2$ ). On appelle $u_n$ le déplacement du $n-ieme$ atome A et $ \\nu_n $ celui du $n-ieme$ atome B par rapport à leur position d'équilibre. A l'équilibre les atomes A et B sont équidistants.\n", "\n", "#### Résolution par la mécanique classique\n", "\n", "On cherche des solutions sous la forme d'ondes de propagation :\n", "\n", "\\begin{align*}\n", "u_n = U e^{-i \\omega t} e^{i n k a}\n", "\\end{align*}\n", "\\begin{align*}\n", "\\nu_n = Ve^{- i \\omega t} e^{i n k a}\n", "\\end{align*}\n", "\n", "Qui conduisent à un système homogène de deux équations couplées : \n", "\n", "\\begin{equation}\n", "\\begin{pmatrix}\n", "2 C - m_1 \\omega^2 & - C ( 1 + e^{ - i k a})\\\\\n", "- C ( 1 + e^{ i k a }) & 2 C - m_2 \\omega^2\n", "\\end{pmatrix}\n", "\\begin{pmatrix}\n", "U \\\\\n", "V\n", "\\end{pmatrix}\n", "= 0\n", "\\label{mat}\n", "\\end{equation}\n", "\\begin{align*}\n", "\\Rightarrow \\omega^2 = C \\frac{m_1 +m_2}{m_1 m_2}[1 \\pm (1 - \\frac{4 m_1 m_2}{(m_1 + m_2)^2} \\sin^2(\\frac{ka}{2})^\\frac{1}{2}]\n", "\\end{align*}\n", "\n", "Voici trois relations de dispersions que nous avons plotté pour différentes valeurs de $m_2$.\n", "\n", "![disptot.png](attachment:disptot.png)\n", "\n", "Ici on remarque bien le cas d'un conducteur devenant un isolant lorsque qu'on change $m_2$. Dans le premier graphique a)$m_1$ et $m_2$ sont égales, ensuite dans b) $m_2 = 2$ et enfin dans c) $m_2 = 5$. On s'aperçoit clairement de l'ouverture d'un gap lorsque le rapport des masses est différent de 1.\n", "Le but de cette partie était de nous intéresser aux différentes relations de dispersions pouvant être observées sur des chaines monoatomiques et diatomiques infinie, nous allons à présent étudier le cas de chaines finies, afin de nous intéresser aux modes de bords visibles dans certaines configurations du système." ] }, { "attachments": { "Chaine2m3r.png": { "image/png": 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62Tam3BxRbldQbhE2zZCx9n3y1sZmlyLX/V6iceijM/tjAoqXLcpKOTEx7uEtc8MrKqQzGnu2N60e+aqlJu68M9g1BC5WrizsPjS0jd11s21Mubmj3Ci3ZmyaIWO12iNPS2fjGdWyaBXmDGVkJWU7SCu+z6T4lXHdJf5PkCe33eOllqKefbZ2883seOtKL9ScOcXcU4S2sbuutY0pt0QoN8qtGZtmyFgKWE0PB9Xb1nja/iziLxS1+8iW7JeRUgaqP6VvhIot406ybY8QeW5oadPt5Zl88EHQjWe/kEROnAhetJEm+4d2F21jd91pG1NuKVBulFsDm2bIWFoEtcDZwdX0tumVtYPMtn34UsxZSQ6d2pu9869Vk5igpqJq9Zc6apVHQ6++tyZ7LV1lYiJYpX7+eTuEu02bajNnFu1MibSN3cX/CeK/bUy5pUa5UW5Xs2mGjLVuz+MHP9tjB1db/fZPlZ3tILOYMCf6QWt2PmgHaSnDxcS4VufhdRf/J4h+RHwIS2zlymDXEKSzYEHtF7+wt4uBtrG7Vh+QIf9tY8otC8qthWqWm00zZCxFYwVkO7ja+r3LW8WvFGLCnFz+63j2hV4ZKOaMuiOfvvPqe2vsIJUXhp+Kf0H2n9iV8Udc5dSpoAN/+LAdIimzCaNIBz3FxHTaxhGtPiBDntvGlFtGlFsL1Sw3m2bIWL8c/PHZ8c/s4GpeOpyhtbsWtwpzhhb6jOcs2bBvRcxCoJ+esT8ck0cNxfyYdm5iCxfWli61t5HO00/X5rc83id/tI3d5d02ptyyo9yaqWa52TRDxmo8DW5oz8dvNr2QeDoKc+f/ctoOmlnx1sL4B7QVn4EUJTMeiBRzqQHDSzfOOnCgduONtYsX7RDpTEzUpk+vDQ3ZYbfRNnaXa9uYcvOCcmummuVm0wwZK+bUrh+d2f/ckLcVu0feuEuLmh00o58V3yVqa9WOn8Ssmnw1eTnmHGsuWp0Crp7+TD9nEJ4zp7auw1fmqYhNm2qzZ9vb3Ubb2F2ubWPKzRfKrZkKlptNMxXPWH+OPa/G+b+c9rhjYEyYM5TTFcbtIJW2rbKM2+Db/gnyzLsPZDy+I7B5c3B8E3zRJ+j69fZ2V9E2dpdf25hy84tya1DBcrNppuIZS++6Fg47aGbx6z/wsmOgflDbt2fwDy+/ne3ClspA8esKWtBbrda09dXk5SW//aEdtLZ+7/Kml+1M5tZbi3wVsN6zc2dBPkRpG7vLr21MuflFuTWoYLnZNFPxjHW83Tn422ZbR1o4lG/soIXhY4NZViyUBdtmoLbt0Bht86gxcOjF3Ue22EE6w8PBmWbglyb9gQF7u0toGyeSU9uYcusEyu1qFSw3m2YqnrEUOOK3sCp9e+jKOPwg0Q9al+HCli4ZKMuCfvKLIy7N2D0fv5n1VChz5wZX84Bf/f3BJoyuaruI0jYO5dc2ptw6gXK7WgXLzaaZimes+NPny2v712btykzZf2LXhn0r7KCFz7NdgKxtT04GDr2YekF3iYny0Zn98S9pG4cPBxf8n5iwQ/gyORkcOHbggB12A21jdy6rTJK1bUy5dQjldrUKlptNMxXPWPvanT5fiWTLQQ+H2+z5+M22h31e/ut4TGu3LZcMtOvw66kvU6WYqBRvB61pTWJV66tKtbdoUe2JJ+xt+LVmTXdP3tN2EaVtHMqpbUy5dQ7lVqeC5WbTTMUzVvwVAMQxWLQ1GHv+tJCi+ldpL2ypvBhzqQEjy5/TNo+GHt4y195Kany8du21wfmm0QkXLwYv74kTdpg72sbuXD63JFPbmHLrKMqtTgXLzaaZimesttHnk/Njz7z7gB1k8JvRX+86/LodtJaleTt8bLBtq+zouUOpz7e7fWzjtg9fsoNY+itaHTDcxssvB3uHoHMWLAhWr7uEtrG7PNrGlFunUW5XVLDcbJqpeMZqG33iD81wp2VdS7wdtKbFSAuTHSTk0ipz3OrcVPwVqeo9N7RUYc4OErnjjmDeR+cMDgYH6ncJbWN3ebSNKbdOo9zqVK3cbJqpeMZyiT56TePP/OFC4ekjh6uCO0axprRG0rZT+u3fvnE5QrUp99/ttf1rYy560NLZs0FrfTzrS404k5PBZWu7tP2i7VxM2zjU8bYx5ZYDyq1O1crNppmKZyzF3tGTu+2ghVU7fnLyiyN2kJbeey3QdtCa3ubUF3l1zEAxZ/6NtyH2Ugb1FPUGDr1oB+7WrQta6+i0hQtrK1fa2/mibeyu421jyi0flNsVVSs3m2YqnrFc3vX4q1060nuvJcAOWtt9ZEvqA1wdf8/UkdG9QhRb0/Rsb7uNk03nYWioWyehdpmLaRsb7r9byrYx5ZYPyu2KqpWbTTNkrLa5wbERGs9xUVZISn2Aq2MGSn287jPvPuDSihOXY0CiTp0Ktlxwnp583Hhj7VjLq1J0Dm1jd51tG1NueaLcplSt3GyaqXjGcmkvKWApZtlBWo75Wukk9QbyFW8tdNnanXplwrEVJ2la0P39HOKUn3vv7co1a11WA2gbG46rTJKmbUy55Ylym1K1crNphozVduHI0lsyLl4+63hlKD3ysa0pT1vnuKC7b3iO0CqCwpMdtKOM5f7gwKJFXTzIuXI042vez53LREbb2Ohs25hyyxPlNqVq5WbTTMUzlhaOtkeTKhcrHdtBKmcuHV++/T47aKftVZlacfzGPR+/mW5lItGmbvdF1po1q7vXnaiWY8dq06fb2zlyWQ2gbWw4rjJJmrYx5ZYnym1K1crNppmKZyyXhUMJXVHMDlJRAFcMt4N23N/sepPffL349R/YQSytTLifqTakFyHRPL5h34oElzU4dap2zTXBcc7IzQ035L+PiMuyTdvY6GDbmHLLH+VWvXKzaabKGcvlMpNGsimsQaJYs3bXYpemaISWPy2FdhDrk/NjKU4i4v78hpZ1/bODtvr7g9MhIk/z5+e/jwhtY3eOvQEjWduYcssf5TalUuVm00yVM5Z7blj99k+PX/jIDpLb53wOWVm/d7njAQ71tKA7lkrStGQk3edj+NjghnZXsPrOokXdOoVMdT3/fP77iLhMZLSNpbNtY8otf5TblEqVm00zZCw7iKW3re1BsDG2j210P7h68/t97/5pkx04S7SgJ8rsRqLnl2Sn3L311tqOHfY28jEyUrvpJns7F7SN3SVdEUrWNqbc8ke5TalUudk0U+WMpRygt9wOYqXLPSG9H+7nBdEPSnGdzrHTI+4L+mNb5yc9iUjS48P1/I8O/MgO2rrhhi5enb6iLl6sff/79nYu3Ccy2sadbRtTbvmj3KZUqtxsmqlyxnLvzWQ8+CLRwQ5aBBNMl1ckWtCfefeBpCcRSfT8xsOOZxAeH8959oGV75XU3Kc/2sYdbBtTbt1CuVWs3GyaqXLGOnRqr2Nv5mC2gy+UmdwXYr1/id5vY8/Hb7p3v/S3JD2JSIpzSbuuHh04kHMXHdYtt9R27rS3O4+2sbsOto0pt26h3CpWbjbNVDljufdmMh58ocykpGwH7aTrdg46XDIz9Op7a9z7akai5zdc28KbNnHK6e5YsCC4MHBe3FcWaRt3sG1MuXUL5VaxcrNppuIZy3HZynjwhd71z79McHIUx2Mo6g0cenHPx2/aQTspAtNrya87q1/Jaf1m5crakiX2djHMmzfPLIf333+/vauZo0ePzpgxwzxydHTU3ltn1apV1113nb5qx0Xz9NO1pUvt7c6jbeyug23j0pWb7l+2bNns2bPNl3RDdWe/ViiUW8XKzSyQYscOypaxlADco8Yjb9zltJrYzC8THrD65LZ7kh7okWhlQo9MehIRPX+Cg8On6Ke8MuIw2S1cGBzYXCR2KZzSNDwZ+kiwD5o2bWhoyN47Rd8VTvpi7y2a/v7a3Xfb253nvrJI2zjFWpBr27hc5abHm9WYiPi41h2UW8XKzS6LVc5YelndNyRrKUzagQwpnyU68dqanQ8m/VlamfjozH47aEcx33EVJ/Tc0FL3QjIU859xuXJCN87OF88shLfffrv+bzVZnzt3TpO7VqzNw+ozllajdY++pDuDJypsxtq5szZnjr3deZr4aBs76mDbWOX2crJfptNMjaQrN93Qnf39/UePHjUPC6NYfUkWAuU2pTrlZpZDsWMHZctYWw6ucw+86/Y8fujUXjtIKOlSpQCUtNuZaGVCAc5xd8iQnj/BiaSnfDV52al0Ne8U7Gw9ZiHUxK3/NbNr4rZfqNPX16evKk41ZqzZs2cvW7bMfFfwRGSsKbSN3XWwbax3PMc9r12YGkldbo1MC7lwWwwptynVKTcthIYdOyhbxkr0zmmdwD1K19PylLQ7uvn9vqSxes3OB90X9BS/0vLt9yUqJMPpu4o66WseNxO6Zn/7hTpm1xCtPTdO+vUfEsETFTZjHTiQ56VqNePTNnbUwbZx6cqtkWkkFy5j5XtEJ+XmrkPlpoXQsGMHXctYeksUhpQ0U2ftppSx3N+5d/+0KelucYZCRtKt3fpZSbudykyJDlh1PAVwSM+f4sV/Yfip9s2/mTNrBevqm4VQ87hZt9a0br9whb6k++fNm6fb8ZN+8ESFzVjHjuWZsWgbu+tg21jldviwvV0Mpka8lJthHtPX12fHBUG5TalOuWkhNOzYQRcy1p6P31y+/b7Vb/9UeUjvzWNb5yt8pLuoZKNE6XX05G6nVnwDvXl6C+3AjdLkq++tsQM3CU6qPkWZKVHDNsWJ3WTbhy+1P/OK5p3cr0gfzyyEZh43e9SavT1CZp+PrVu36nZvZ6wcT0dJ29hdB9vGpS43OXfuXPB0DU/SfflmLMrNXYfKzSyHYscOcs1YlyYuKJroxa0/QlJ3vjD8lMKWl5il53ffWU9RKWk6NhTjkrYu9S19v3vUDtwk7Uvpb0m0o2LSDGc4ndvtmmuKPOmb+X3ZsmXmS6K5W/fMmDHDDHs4Y01M6Pezt+vQNm5Lk3ivto1VbuM+39bsTI14KTfR9+oBeh47Lg6V2/e+Z2/Xodza6tFy03Jo2LGD/DLWmUvHn9x2z/axjY1ZSvfoY9tLzFr99k/d06ve46Tp2FDxaHG3AzdJF1wtH0l/N72A7g1b/T7p/vaz458p7NtBK1oEC3b1NLMQmnl8dHRUt7V6bb4kkb09ejhjydW/G21jRz3cNi7e0mhqxEu5bd261Xx70x3nu49yq1K5aVE07NhBx4vT/EJ/9/fXaWmLOfmElsI1Ox9M19usp3fi4uWzduAgaTo2ho8NJl1FmPzm60feuMsOHCgDrXhroR24+c3or907yYpK6Xp48nDb8+F+//tF7mOJOUwp3BU33P3WDHs4Y01OhpM+bWM7cNPDbWOV28SEvV0Mpkayl1t4rqxWxdhlKrcrfSzKzQ7c9Gi5aVE07NhBHhlrxj/8p//zwpy2LRYtmnpdEmXVRkpy9pYb5ZhEmczQqknS1qjor1PSsoN29GokXZlI9FupKpI+f0iLe5t3s9g7iIg5blyTu26bFWWz+63RwxlLL/vUpE/buEJt45KWWxiwmh6WWAh62af2x6LcKlJuWhoNO3aQR8b6r//4n//u779rFMd4bf/apC3HiKQdwueGlh49d8gOnG05uC7pLn6ipVBvoR20k2LNYF+Sk4hoeU1aSCElufjLIHw747/UhoftoBhMYYTzeP1etGaKN7vfGr2dsaZP1yJN27hCbePCZ6wU5dYDAUsotynVKbdgIZ5ixw7yyFiGHcfS36a3yj2INEraIVSkc7paxdWUTtzf71Ciren6rZJmIMWmF5yvZK7fP3XG+uT8mNao7KCBVuYGlt1W2BP22PGVXXHNhdXC3W+NHs5YH3xw8M6bNOO3XeejbVyvt9vGBT4/lh0nLLfeCFiicvvRf6fcpCLlpmXSsGMHxcpYoria7mgISdEhVCB4+4+v2oGzdXsed09LoUTJTI9Membbk18ccTpj4ZRdh19PUUghVZRebTuoo19b8evy7T0w6ZttFkbk3IY9nLF27hy97385tmZpG4d6u238T6Uqt54JWKJyW/hPlJtUpNy0WP7bf/dv9L8dOyhcxvr8y2NPbrvHDhLSp377fReuNvLpO0mjjCgjp1h29eYp0tlBO3pw0gx0aeKC+0uX6JdptPn9vsZfT++dsldQaUW9XmEkNpl9byXc/dZozFhm/bspfSTYBxWBPmudL+5B2zjU223j//u/g4sTF4kpjXTlZo46bIVyc0e5pRBfbv9w94z/ueC/aTm0YweFy1iiRKy/0w6S0Hcl7RAqKiUN1KIk17SLE2/Px2+657ltH76UosHmvqKj3yRFIYUUpx7bOr++OfzV5GUtmnYFaOHC2vPPT91dFGZ+j0zQZjav3/3WMInKMWNFPki6TJ+1d99tbzugbWzokUnXtQrUNr7/n8tUbmYH+VaKlbEotysqUm73/Op//Pv/+D0th/YuB0XMWFoK07VYtGQkzVgXL59NuvOdPLntnktJzp9mHDq1V4uvHbSTbmXCfadIPX+KVZx6r4ysqi/gDftW6J8drFxZW7LE3kaeEr7ytI0NPTjppFygtjHl1i2U2xUVKbdrb/gPSfNMETNWiqhkHPxsz/qEJ/aQFAdfpDu/2fELH8U0ISOUV1JkoDU7H3RsASZq7TalMPfY1vkq4zOXjutlX7tr8VeTl+3XNm2qzXW4zhq8S95BpG0svd02pty6hXK7oiLlZtNMr2esb//2zSNv3PXdB7YzvawptsL+MuEJZPWLOV2otYGSuPuBISqnFBlo3Z7HFTTtIJYiUbpSr3fyiyP6ifpVlfqvOvtLvpejx3duvbW2Y4e97Ya2sfR225hy6xbK7YqKlJtNM72esSRdl0UxM8WBG1pwj9edmbctZfyk28VD7tczV2pO9FsZyu+OZ2HRn5BiZcXVxYt5XpkY37nhhqRXMUoxdxu0jYvSNqbcuoVyu6Ii5WbTTAkyVrpeYoqtvKLMO3pytx04SLQwRbgnm3QZyP0VeDTzyVrauP76ol2ysPzGx1N81tI2Fn3spZiUi9I2Fsotf5RbnYqUm00zJchYY6dH3BuPIfeEUU/f0v6qq3VSr4iI3nvH3Qm1oHe0DtOtrCRwyy1FO2dP+aXdZkTbuLfbxkK55Y9yu1oVys2mmRJkLHMqETtw9pvRX+8+ssUOnCmX6BvtwMHIp+9sCPeESEjf6NgzS5eBlE1ddnJM9/Ims2hRbU2mE+4hsfXrgzOTJUfbON2k7P4KdLxtTLnlj3K7WhXKzaaZEmQsSXTeWEPLU4o96bRK4X5yM0m3PmFsObjOJQVevHw23SG+J784otfNDlrT8q2l3A46pL+fY53ydu+96c6TRNu459vGlFv+KLerVaHcbJopR8Z6ZWTVyKfv2IGbFN8iChwuuSSUblk3tLhrJcYOWlO4TJeBLk1cUIS3g9a0suJ+PreUTp2qXXutvY18TJ9eG0uzFwJt455vG1Nu+aPcrlaFcrNpphwZa9fh1ze/32cHbhTAU2znlkR7+em3SrRmUG+/2zUEsqxMaPGN7g/bIMvzJzBrVrDLAvJx7FhwlFNatI3tIIkCtY2FcssT5dagCuVm00w5MtbRc4fW7HzQDtykzlh6S9w336Zb1g39US7hxjGwN6W/pe2mbkW91CsrCbCPSJ7S7h1i0Da2gyQK1DYWyi1PlFuDKpSbTTPlyFhfTV5e8tsftm3J1Fvx1sLPvzxmB0ko9+iNsYN2lH6UgewgIS3xLieFU4Zz3PDcSMG07UbxLM+fAPuI5Cnt3iEGbWM7SKhAbWPKLU+UW4MqlJtNM+XIWLJ8+30nvzhiBw5cWjhNaclwP/hi7a7F6ZZ10fLhsqk4RQWGXhh+qu3fsn1so8sKR1ZmH5HJSTtER914Y+3wYXs7OdrGdpBQgdrGlFueKLcGVSg3m2ZKk7HW712e6P1+bOv8S8kvAiCDSQ6+SJ3kDP2S9RdCaipLw/a1/WvbbhTP8vzJ3HprbXDqkmroqKGh2s0329up0Da2g4QK1DYWyi0flFszVSg3m2ZKk7GUexK1c9IdrSB6V9wPvsh47o1n3n3gzKXjdtDCq++tcTzZWqPtYxsHDr1oBy1kWVlJ5tlnawsW2NvonIceqj39tL2dFm3jFArUNhbKLR+UWzNVKDebZkqTsQ6d2qu33A4cpM5YWqrcT1iS+qcYWko+OrPfDlrYkOpyToZLik+3+2QaZ88G2y8mJuwQnTA5GRzilGHLhUHbOIVitY0ptxxQbq2VvtxsmilNxvrz11+6n+gi9RGhoqXK8eALx0MbYvxm9NdtSyv1pndRgGu7UTzL8yd22221zZvtbXTCjh212bPt7QxoG6dQrLaxUG6dRrm1Vvpys2mmNBlLlIsdzyOinKQMbgfJOR58oQVo+fb77CCVt//4atuUnXrTu+gb224UT3e5qJTWreNwp85auNDLQfu0jVPQbF6gtrFQbp1GubVW+nKzaaZMGUsLh+Oltk9+cST1hZZE+cwlv2t5bdsliqe3v+1SomR58fJZO0jIpfmXsSGczNmztWuuqV28aIfwa2Ii2Dx04oQdZkDbOIXCtY0pt46i3GKVvtxsmilTxtpycJ3jttWM6Uff69LaUQBfv3e5HaSi3/O5oaV20ELGlYklv/1h/Ebxxa//oO1Wc5/uvTf7LqJo7tlnPfYtaBsnVbi2sVBunUO5xSp9udk0U6aMpUzzgtulAJRw22aXGK++t8algbnn4zdf27/WDlJRUcUvJYnWb5pSNcaUrtKVQpgd5OODD4K9RNkV17vJydrMmcGR5J7QNk6qcG1jodw6hHJrp/TlZtNMmTKWcqtjsnbZUhtj+9hG/bOD1hTSHftqrbSNOIpHWkrsIJX4ZmnGVaKU7rwzuPoE/Nq8OTglkj+0jVMoXNtYKLdOoNzaKX252TRTpoz17d++0Wv61eRlO24tY8ZSAHe5FuZr+9emPiYiFH/sRsZykg37VsTs9Kdiy+PqaRE7d9Zuusnehi+33OL3IDLaxilojaVYbWOh3DqBcmun9OVm00yZMpY4bl59+4+vtj2qM4bjdQAU810W1nj6i2LOPnfwsz3uh4E0pdWjmBOiuOw22BGzZ9cGBuxtZDc8HGy58Iq2cQqqJq0X2UGD7rSNhXLzi3JzUPpys2mmZBnrlZFVLq2jjMvHpYkLLgduxL/BjhShDp3aawcNMpaTKGApZtlBg+zPn5LvTnvV3XGH9+1BtI1TKGLbWCg3vyg3N+UuN5tmSpaxHM/V9pvRX7c9A2w8Le5tt+NqtaPtOdbaiv9VtcKR8VIA+2Mvirnr8Ovup6Tz7JZbai9nWk+CNTgYbAzqwAWAaRsnVdC2sVBuvlBuzspdbjbNlCxjjZ0ecdkUrZivsG8Hqax4a2Hb/KSQnu6CBvXi+0yqJcUgO0jlk/NjMWe3y94QTm94OLhePUc8ZaS5ftas4HzTHUDbOKmCto2FcvOCckui3OVm00zJMpbjidH6fvdozFvrwuUZMh4TYYye3B1z+Eb2sHjx8tmYbdKvvrdm+Fj3Ls6/YEHtF7+wt5HO6tXBgWOdoSmMtnEixW0bC+WWHeWWRLnLzaaZkmUsid/Ea2TP4G2X4ywn260Xv834heGnsq9MLH79B/ZWAz2/+2XY/TtxIjhR8rGU56BDcCLv66/PfknaVmgbJ1XctrFQbhlRbgmVu9xsmilfxtJS+FG7qyC5LEPx2q5SfP7lMceLEsSL78wpLOoH2UFaWiNpdZ43Lw3hTJ54onb33fY2klq4sLZkib3dAbSNkyp021gotywot4TKXW42zZQvYyn6tA2/et0znt217e54iiYKKHaQzcNb5l7+67gdXC37HyJKpcr7dnA1L8+fycREsH9Df78dwt3AQLCHTYevRqdJn7ZxIsVtGwvllhrllly5y82mmfJlLCXftudGc9neHO/MpePx50/Tr/HKyCo7yGbVjp+0OvjC8dpS8bS60OoIkZh4l58DB4IOPJswEjl1KrhGys6ddtgxtI2TKnTbWCi3FCi3VMpdbjbNlC9jxUdjI3uf05ytxA6a8bg/Xau4rZiY8TS4xuAfXm560jk9f8xKQK5Wrw7O39OBw6FL6447akvTn+vZHW3jpArdNjYot6Qot7RKXG42zZQvYykZxHd3lGof2zrfDjLQ6kLMefq3ffiSr/3pVFdasbCDOlo+tJTYQQb7Pnmr6UnnfD2/B5ru58ypPf20HSLemjXBmbtz+YykbZxU0dvGQrklQrllUOJys2mmfBlL9LbF5FNf0UFJf+z0iB00yL6/Xmj3kS1N60orEzEHTbhrdSo2xf81Ox+0g647cSLYhDE8bIdoxWzr6djBTRG0jZPqgbaxUG6OKLdsSlxuNs2UMmOt37v84Gd77KCBrz7nloPrYnYMzH5wR0jPo2ezgzqK5zEHZbhrdVmoVj+3awYGgp0eNPujlVOnatOne7+ORwxNVbSNE9GqV9Hbxgbl1hblllmJy82mmVJmLOXWmCVg7PSIl+iw5+M3tXzYQQOtbbTaDJzUmUvHlze7GqivlQmttWjVR//b8RXDxwY3duus062sXBlcp2K8ANtTCkgvyy235H8aSdrGifRG29ig3GJQbj6UuNxsmillxjr42Z4Xhp+ygwZaOLxEh6PnDsXsGPjktntiKiGRVl3NgUMvNu2CpqDftnGtRTnV18qKTwsXBnuYskNuo7vvrs33sAqbFG3jRHqmbWxQbq1Qbj6UuNxsmillxmr1shptD0x1dGniQtP2kuHlFG2hx7bObzwA9ZWRVb5WJlSWjYcEd/+MiE1pur/tttqiRXYIY+nS4FiwblxvjrZxIr3UNhbKrSnKjXJrx6aZUmYsiTlkwGN75pE37ppsdgTH+b+c9nKKtlDTDKQ7tdZiB9loaVNR2cEVHldWPBsfD86UuHq1HWLNmtrMmcHeId1A2zipXmobC+UWQblRbg5smilrxlqz88FW+cNje0Y/pelxp1pA/W7rVaJvzEC/HPxxq7OrJaWlWcu0HVwRc1Rt92mC07yvyQ56EW64oTbmZ7UyBdrGSfVS29ig3EKUG+XmxqaZsmYshZJdLc7Vpjdv5NN37CAbvU9Nz73ha1tySH9L47Uz4w+vTUS/8IaG65M/8sZdhThbTytm3l+50g6rSTP+9OldnPEN2saJ9Fjb2KDchHKj3JzZNFPWjKWI2uokaR7fPK00NLZ/RPfHXE48hbHTI5H+cPx6RlLHL3wUabyphuMPEi4EM+8/9JAdVo1mfP35ehG6jbZxIr3XNjYoN8qNcnNm00xZM5ZevtVv/9QOrubxxVUQbrppfPP7fTEHZaSgRBXpD2tBf27I29UblKgi143SS6QXyg6K7OLFYOfTCs77q1cXZMYX2saJ9GTb2KDcCoByS6Rb5WbTTFkz1rd/++bhLXObtjo97q+n52naTNIi6L0PGVkmtLKiGrADHx7bOr/+iu4HP2tzyaoCGR8PLv0xd25VTuSjP/Pee4PLdxRjxhfaxon0atvYoNy6jXJLpFvlZtNMWTOWPPPuA3px7aCO3/319FZ9NXnZDq7QO5r9guERes6j5w7ZgdfDLoy1uxbXF6fWLbS2ZAfFNzlZW7IkWNH84AN7T1kdPly7+ebgrEXdOG68FdrGiWiK79W2sUG5dRXllki3ys2mmRJnLC0KjVt5//z1l4/4uApSqOmZQvSONgavjCL94fV7lzdt5Kb26ntr6l+umHZ0cfX3B4f86P+yGhwM/sB1PlcivaBtnFQPt41DlFuXUG5JdaXcbJopccYa+fSdxoaq9wCrRSES6htTsxcKQPV/jsf1FSPSuCr6UU6taMV65sxgJbtI650eTE4GV+248cbaSMsLXHQXbeNEerttHKLcuoRyS6Qr5WbTTIkzVtPziCg3eDkNbkgBK5LktOirAOzAHz1tfTpc8tsf+m2VaRGs/7X10p25dNwOesv4eHCZi1mzakND9p5eNzwcbLC4887aWT8H2nQCbeNEytA2Nii3bqDcEulKudk0U+KMJVoaLk1csIMpeqH9NiEj0Ue8H3ZhTH7ztXKVaahqNcLjLoGGnlnPb645oBLyeFhHdwwMBKuhixYFR0L1Ln2ALVkSbLDY1OTS9IVC2ziRyJp0r7aNQ5Rbvii3RLpSbjbNlDtjrdvz+OjJ3XYwZfAPL/ttQtZHH2Pg0ItND8fI7l92//zg1NVA9Uc1Flh2K95aaJZsBcdW+1T2Ek33P/tZMPUXfsZsbnAwOOHhvff2xOcWbeNEytM2DlFuOaLcEulKudk0U+6M9fYfX9189YUFNv7+V75OHxJas/PBsdPfbbZ/Yfgpv33O0LYPXzJ/zmv71zY2irPTWsvw1PnrVFp+u33dNDQUbMiYM6e2c6e9p/gOHAiOjdeMv2OHvacX0DZ2V7a2cYhyywvl5q4r5WbTTLkz1ifnxyL9mOeGlvq6YHhIuaf+8gVaPvz2OUN6WrPu8mSzi1xmt++Tt8xay4Z9KzqR4bpmcrK2fn2wc+5ttwXzaZGZ6f6GG4KTSvfafsS0jRMpW9s4RLnlgnJLJP9yW3+FHTvovYwlkYNClVHqj+H0QkuGlg9zWz/r4U6e3Ew/aOPvfxX+OL+0VqSXS2H/sa3zfR0AXCCa+p99NphPNasW8HChXp7uDdrGiZSzbRyi3DqMckukJ8qtJzNW/REKX01e7sT+eqYPabYfa3H0u0U84syl48r4nduWrBLasG/F2l2L7bh8NJ9qVr3xxuDEzc8/3/19L8bHgxPw3HJLT0/3Bm3jRErbNq5HuXUM5ZZIT5RbT2Ys5frwZLVa/jqUHvS0ZgVCS6RWL8ydvej8X05rQexQFRXL4GBt/vzatdfWFizozr4jw8PBDrb6BbQ+PTAQrPf3PtrG7kreNo6g3DqAcnPXE+XWkxnrq8nLemXNktfYXPVFGdkkOWVw72sS6KCzZ4MtGjffbA8p6u/v7ElxtB6/aVNwiLt+3E03BReaLfA5eFKgbZxI+dvGEZSbV5RbIsUvt57MWKIF0ZxwTAHZ7FXn3eQ3X2sdYsvBdaXad7VSDh8OtmVoHfeaa4LtGkuXBmvex3yczvjEieCpfvGLYAuFnvyOO4KPmbFyBnHaxolUqG0cQbn5QLklUvxy69WMpVxs2kuK+QpD9l7fjp47pDDXuQyOnExOBtsyNEfPmRPstGE+A+bPr61cWdu8OfiS/ukTQp8H4XX4tXKsoe40X9XD9OAFC4Jv1Ldff33wVPoU0Zd6ef8PF7SNkUyKctMNym0K5VYyvZqxZPvYxl8O/rhDTSyU2cWLwZ4c69cHs7ZWuzV9ayqfPj3YjVcL6rRpG/7xn4Mb+njQnfqSHqCHLVkS7Fqrb+z6Tr65o22M9BzLTUPKbQrlViY9nLGADrlt8e/sLUyhbYzOodwiKLcy6Xj0sWfsSnLOLqC7mPQb0TZGh1BujSi30qC9BEQx6QO5odxQYmQsIIpJH8gN5YYSI2MBUUz6QG4oN5QYGQuIYtIHckO5ocTIWEAUkz6QG8oNJUbGAqKY9IHcUG4oMTIWEMWkD+SGckOJkbGAKCZ9IDeUG0qMjAVEMekDuaHcUGJkLCCKSR/IDeWGEiNjAVFM+kBuKDeUGBkLiGLSB3JDuaHEyFhAFJM+kBvKDSVGxgKimPSB3FBuKDEyFhDFpA/khnJDiZGxgCgmfSA3lBtKjIwFRDHpA7mh3FBiZCwgikkfyA3lhhIjYwFRTPpAbig3lBgZC4hi0gdyQ7mhxMhYQBSTPpAbyg0lRsYCopj0gdxQbigxMhYQxaQP5IZyQ4mRsYAoJn0gN5QbSoyMBUQx6QO5odxQYmQsIIpJH8gN5YYSI2MBUUz6QG4oN5QYGQuIYtIHckO5ocTIWEAUkz6QG8oNJUbGAqKY9IHcUG4oMTIWEMWkD+SGckOJkbGAKCZ9IDeUG0qMjAVEMekDuaHcUGJkLCCKSR/IDeWGEiNjAVFM+kBuKDeUGBkLiGLSB3JDuaHEyFhAFJM+kBvKDSVGxgKimPSB3FBuKDEyFhDFpA/khnJDiZGxgCgmfSA3lBtKjIwFRDHpA7mh3FBiZCwgikkfyA3lhhIjYwFRTPpAbig3lBgZC4hi0gdyQ7mhxMhYQBSTPpAbyg0lRsYCopj0gdxQbigxMhYQxaQP5IZyQ4mRsYAoJn0gN5QbSoyMBUQx6QO5odxQYmQsIIpJH8gN5YYSI2MBUUz6QG4oN5QYGQuIYtIHckO5ocTIWEAUkz6QG8oNJUbGAqKY9IHcUG4oMTIWEMWkD+SGckOJkbGAKCZ9IDeUG0qMjAVEMekDuaHcUGJkLCCKSR/IDeWGEiNjAVFM+kBuKDeUGBkLiGLSB3JDuaHEyFhAFJM+kBvKDSVGxgKimPSB3FBuKDEyFhDFpA/khnJDiZGxgCgmfSA3lBtKjIwFRP2//j/ZWwA6jHJDiZGxAAAA/CNjAQAA+EfGAgAA8I+MBQAA4B8ZCwAAwD8yFgAAgH9kLAAAAP/IWAAAAP6RsQAAAPwjYwEAAPhHxgIAAPCPjIXq2rp167Rp06677rpz587Zu64wX5o9e7YdXzE6Onr77bfrS6tWrbJ3AUhl2bJlKiUVlB3XMV/S/2aoCu3r6zOlJzNmzLj//vsbyxYoGjIWKk2Tdf1UbmjuVvDS/Upa9q4pylVTM3yAjAVkdPToUVNNkUIbGhrSnapBPcDcY+o0QqtAxCwUHBkLlWZmcwlnczFZqn71Wl8N05joBhkLyM7UmorLjqc0toqVtzQcHR01w76+Pj0g8higgMhYqLp58+Zpsg4TVbhuHU7oovVsfQwokOm2+VRgcgeyO3funFl7CQuqv79fQ90Z36MyqzpNtzMCxUHGQtWFocpEqPvvv1+3NYObrxr10z0ZC/DIhKpwt0gTuSJbDxuZDjQZCwVHxgK+22AR7ggSsw5NxgL8MhsHtXpjisslOZlHzps3z46BQiJjAd9tsDC7uvf19dkvNEPGAvwaHR1VTYkpwPrN9K3Mnj1bj+zv77djoJDIWEDAbLAQhS17VwtkLMA7s41edMPe1Zo5tUrbUgW6jowFBExykvgNhULGArwzmwul7YbCo0ePmnaX2YESKDIyFvDdbu/hfiH2C82QsQC/wmMJRTditgBq/cdsJaQA0RPIWIA9fYNm7aYnboggYwEehXtDDg0NhWGraS85DFgu2xOBIiBjoeoixxK2Pe8OGQvwyBRUWHGt2lQELPQiMhaqLrJ5QlO52duj1QYLMhbgS9g51g1zj1nnqb9HCFjoUWQsVJoJTIpZdjwlvNN0tiLIWIAvTfeANHeG574iYKF3kbFQXWHLqvEAJdPcCoNUeP6eRpwFEUgnspk+FDa3TGGGna2m4s9mB3QXGQvVFbPrlTkBj5hhTMaK2XMLQIxWu15JfW3GVJ+QsVBkZCwAAAD/yFgAAAD+kbEAAAD8I2MBAAD4R8YCAADwj4wFAADgHxkLAADAPzIWAACAf2QsAAAA/8hYAAAA/pGxAAAA/CNjAQAA+EfGAgAA8I+MBQAA4B8ZCwAAwD8yFgAAgH9kLAAAAP/IWAAAAP6RsQAAAPwjYwEAAPhHxgIAAPCPjAUAAOAfGQsAAMA/MhYAAIBvtdr/B5Y+T8ZpHSUyAAAAAElFTkSuQmCC" 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Chaine finie de masses-ressorts\n", "\n", "Nous allons à présent nous intéresser au cas d'une chaîne finie de masses-ressorts, ce système simple nous permettra d'illustrer signatures typiques des isolants topologiques.\n", "Ce chapitre sera divisé en deux parties : \n", "\n", "- Premièrement nous résoudrons analytiquement un système simple.\n", "\n", "- Puis à l'aide d'une simulation numérique nous étudierons différents les effets de bord associés à différentes configurations d'une chaine finie\n", "\n", "### Chaîne : 2 masses 3 ressorts couplés\n", "\n", "Tout d'abord, on part du système le plus simple possible afin de bien assimilé les bases de cette partie. On choisit une chaine masses-ressorts avec des mur aux bords du système. (Par la suite un enlèvera ces murs). On se base sur la position des masses et non sur leurs déplacements.\n", "\n", "![Chaine2m3r.png](attachment:Chaine2m3r.png)\n", "\n", "Sur la figure\\ref{c1} les masses et ressort sont à leur positions d'équilibre. M1 et M2 seront noté $m_1$ et $m_2$ par la suite, de même pour k1, k2 et k3 qui seront $k_1$, $k_2$ et $k_3$, les $k$ représentent la constante de raideur du ressort, $x_1$ et $x_2$ représentent respectivement la position des masses $m_1$ et $m_2$.\n", "\n", "On applique à présent la dynamique au système étudié, on obtient donc les équations du mouvement :\n", "\n", "\\begin{align*}\n", "m_1 \\ddot{x}_1 = -(k_1 + k_2).x_1 + k_2 . x_2 \\\\\n", "m_2 \\ddot{x}_2 = k_2 . x_1 -(k_2 + k_3) . x_2\n", "\\end{align*}\n", "\n", "En divisant par la masse on retrouve les relations suivantes :\n", "\n", "\\begin{align}\n", "\\ddot{x}_1 = \\frac{-(k_1+k_2)}{m_1} . x_1 + \\frac{k_2}{m_1} . x_2 \\\\\n", "\\ddot{x}_2 = \\frac{k_2}{m_2} . x_1 + \\frac{-(k_2 + k_3)}{m_2} . x_2\n", "\\end{align}\n", "\n", "On simplifie les équations en prenant $m_1=m_2=m$ et $k_1=k_2=k_3=k$.\n", "\n", "Un peu à présent écrire le système sous forme vectorielle en prenant : $\\frac{d^2 \\vec{X}}{dt^2} = A.\\vec{X}$.\n", "\n", "On obtient donc : \n", "\n", "\\begin{equation}\n", "A =\n", "\\begin{pmatrix}\n", "-2.\\frac{k}{m} & \\frac{k}{m} \\\\\n", "\\frac{k}{m} & -2.\\frac{k}{m}\n", "\\end{pmatrix}\n", "\\Rightarrow \\vec{X} = \n", "\\begin{pmatrix}\n", "x_1(t) \\\\\n", "x_2(t)\n", "\\end{pmatrix}\n", "\\end{equation}\n", "\n", "On recherche une solution de la forme $\\vec{X} = \\vec{X}_0 . e^{\\omega t}$\n", "\n", "On dérive deux fois par rapport au temps et en remplaçant dans l'équation vectorielle on obtient:\n", "\n", "\\begin{align*}\n", "\\omega^2 . \\vec{X}_0 . e^{\\omega t} = A . \\vec{X}_0 . e^{\\omega t} \\rightarrow \\omega^2 . \\vec{X}_0 = A . \\vec{X}_0\n", "\\end{align*}\\\\\n", "On pose $\\lambda = \\omega^2$, on a donc un problème aux valeurs propres $A . \\vec{X}_0 = \\lambda \\vec{X}_0$, $\\lambda$ représentant les valeurs propres de $A$ et $\\vec{X}_0$ vecteur propre de A.\\\\\n", "Les valeurs propres sont déterminables grâce à la relation : \\\\\n", "$det(A - \\lambda . Id) = 0$\n", "\\begin{equation}\n", "\\begin{vmatrix}\n", "-2.\\frac{k}{m}-\\lambda & \\frac{k}{m} \\\\\n", "\\frac{k}{m} & -2.\\frac{k}{m} - \\lambda\n", "\\end{vmatrix}\n", " = 0\n", "\\end{equation}\n", "\n", "D'où : $\\lambda^2 + 4.\\frac{k}{m}.\\lambda + 3.\\frac{k^2}{m^2} = 0$\n", "\n", "Les valeurs propres de A sont donc :\n", "\n", "\\begin{equation}\n", "\\lbrace\n", "\\begin{matrix}\n", "\\lambda_1 = - \\frac{k}{m} \\\\\n", "\\lambda_2 = - \\frac{3k}{m}\n", "\\end{matrix}\n", "\\end{equation}\n", "\n", "Pour déterminer les vecteurs propres on résout $ A . \\vec{X}_1 = \\lambda_1 . \\vec{X}_1 $ et $ A . \\vec{X}_2 = \\lambda_2 . \\vec{X}_2 $\n", "\n", "On obtient alors :\n", "\n", "- $\\vec{X}_1 = (1,1)$ le vecteur propre associé à la valeur propre $\\lambda_1 = - \\frac{k}{m}$ \n", "\n", "- $\\vec{X}_2 = (1, -1) $ le vecteur propre associé à la valeur propre $\\lambda_2 = - \\frac{3k}{m}$ \n", "\n", "Ces vecteurs propres traduisent des oscillations dans la chaine, $\\vec{X}_1$ représente un mouvement des masses en phase, et $\\vec{X}_2$ représente un mouvement des masses en opposition de phase.\n", "\n", "### Chaine N Masses N-1 Ressorts couplés sans murs\n", "\n", "On s'intéresse à présent au cas d'une chaine composée de 4 masses et de 3 ressort sans murs.\n", "\n", "![c4m3r.png](attachment:c4m3r.png)\n", "\n", "Comme dans la partie précédente, on résout le problème et on obtient les équations du mouvement, elles seront un peu différentes en raison des conditions aux bords qui ont changées :\n", "\n", "\\begin{align*}\n", "m_1 \\ddot{x}_1 = -k_1 . x_1 + k_1 . x_2 \\\\\n", "m_2 \\ddot{x}_2 = k_1 . x_1 - k_1 . x_2 - k_2 . x_2 + k_2 . x_3 \\\\\n", "m_3 \\ddot{x}_3 = k_2 . x_2 - k_2 . x_3 - k_3 . x_2 + k_3 . x_4 \\\\\n", "m_4 \\ddot{x}_4 = k_3 . x_3 - k_3 . x_4\n", "\\end{align*}\n", "\n", "On se retrouve donc avec une matrice tridiagonale de forme :\n", "\n", "\\begin{equation}\n", "A = \n", "\\begin{pmatrix}\n", "\\frac{k_1}{m_1} & -\\frac{k_1}{m_1} & 0 & 0 \\\\\n", "-\\frac{k_1}{m_2} & \\frac{k_1 +k_2}{m_2} & -\\frac{k_2}{m_2} & 0 \\\\\n", "0 & -\\frac{k_2}{m_3} & \\frac{k_2 + k_3}{m_3} & -\\frac{k_3}{m_3} \\\\\n", "0 & 0 &-\\frac{k_3}{m_4} & \\frac{k_3}{m_4}\n", "\\end{pmatrix}\n", "\\end{equation}\n", "\n", "On peut donc généraliser cette matrice pour un système à $N$ masses et $N-1$ ressorts, ainsi on pourra l'utiliser numériquement et étudier les différents comportement liés à la chaine masses ressort.\n", "Soit une chaine finie de $N$ masses et $N-1$ ressorts, on prend une masse quelconque à la position $x_n$ et ses deux plus proches voisins, c'est à dire les masses située en $x_{n-1}$ et $x_{n+1}$\n", "\n", "![cNm.png](attachment:cNm.png)\n", "\n", "Comme précédemment on en déduit de la matrice A une matrice tridiagonale de taille $N*N$:\n", "\n", "\\begin{equation}\n", "A = \n", "\\begin{pmatrix}\n", "\\frac{k_1}{m_1} & -\\frac{k_1}{m_1} & 0 & . & . & . & . & . & . & 0 \\\\\n", "-\\frac{k_1}{m_2} & \\frac{k_1 + k_2}{m_2} & -\\frac{k_2}{m_2} & . & & & & & & .\\\\\n", "0 & \\ast & \\ast & \\ast & . & & & & & .\\\\\n", ". & . & \\ast & \\ast & \\ast & . & & & & . \\\\\n", ". & & . & -\\frac{k_{n-2}}{m_{n-1}} & \\frac{k_{n-2} + k_{n-1}}{m_{n-1}} & -\\frac{k_{n-1}}{m_n} & . & & & .\\\\\n", ". & & & . & -\\frac{k_{n-1}}{m_{n}} & \\frac{k_{n-1} + k_{n}}{m_{n}} & -\\frac{k_{n}}{m_{n+1}} & . & & .\\\\\n", ". & & & & . & -\\frac{k_{n}}{m_{n+1}} & \\frac{k_{n} + k_{n+1}}{m_{n+1}} & -\\frac{k_{n+1}}{m_{n+2}} & . & .\\\\\n", ". & & & & & . & \\ast & \\ast & \\ast & 0 \\\\\n", ". & & & & & & . & -\\frac{k_{N-2}}{m_{N-1}} & \\frac{k_{N-2} + k_{N-1}}{m_{N-1}} & -\\frac{k_{N-1}}{m_N} \\\\\n", "0 & . & . & . & . & . & . & 0 & -\\frac{k_{N-1}}{m_N} & \\frac{k_{N-1}}{m_N}\n", "\\end{pmatrix}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulation Numérique\n", "\n", "Maintenant que nous avons tous les outils nécessaire pour le système masses-ressorts nous pouvons faire des simulations numériques. Le code que nous avons écris est programmé en python. Le but de la simulation du système consiste à étudier le changement des états propres d'une chaine de masses-ressorts pour différents rapports de $\\frac{m_1}{m_2}$ on retrouvera des résultats similaires à ceux de la chaine diatomique, c'est à dire l'ouverture et la fermeture d'un gap. Les chaines étudiées étant finies, nous remarquerons par la suite la présence d'effets de bords selon certaines conditions.\n", "\n", "On va étudier ce système dans deux grand cas, dans la premier cas on aura un nombre de masses $N$ pair, et dans le deuxième cas $N$ sera impair." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cas N pair\n", "\n", "On prend $ N = 50$ et on plot le spectre de la matrice :" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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6qwCsAoB58+ZFLA4BxvY539bVCwD5KRC9z/kgeyYsdTIsyyZKBk5Ue6IaLR1TZWbWTPZI839aSudpdwL4Jpwo/WY4Qh6Kqo4AWJHreO1REVmmqlt866wBsAYAWltb+QQwDl5PNc5bsONF8n6BDhPusMogbn/0SRH3JkpKqLPi4bOCMU+a/9Ools7NAIYBPAjgIQBDAP4y6kFyFtDTAN5XYvmID69t438L1n05qthLUi5BnnyQBRNmzYRZMlHsmqi2R5qWTlIeeVY8fHZDbJ40/6eRInxVHQDweRGZ4vHlQxGRFgAnVLVPRBoBXAXga/GLWrts3HkIn31kE/73h84rsG38b8EWe0nKH9GXGsmHRfhhkUmUqMWkpRM3wk4qK8VUZJx21gy7Ic4WUYc4vAzAdwBMATBPRM4DcJOq/kXIZqcDuDfn408A8JCqPl5ugWsFr8jf9lA7unoGcdtD7QU3ud+fL+bD+5cFWS2lLreduMJID78Qdp6WLaJaOv8I4L0AegBAVTcBeHfYBqq6WVXPV9XlqrpMVb9SXlGzj7crYu8LUufNdSL48+aeEmrbFHtJyr8s6EWqIAsmbuplFBvGpKVT6bRMU4/paWfN8MWrbBG10RaqutsZCyXPSPLFqT28mTbeRljvC1I7ewcBAPuOHMfsaY0AgrJuir0k5V9W/EWqOBF+2HeVtnTiRqZJNbaasl7YeyUph6gR/u6craMi0iAifwPgZYPlyjxuNH/rA7/Buu3d+MIPXypohPW+IOWN8L2evN+fL9Yg618W1GgbJ8LP4kDhSTW2ZiUPn2SLqBH+pwDcBWAOgDcA/DtKyNIho7je/KQ6wbZ9/Wie5ETqJ0beCuyK+IaL5uHVA/244SLnPQWvJ++dL9YHvb/RLagRLk6EHxZFR/Gao/rRcXzruF43PXySZaJm6RwE8CeGy5JJ3Ef7JbOn4u9/sg39x05i/9HjmFjn2GMNdYIBAItPnTJuB2bL5zq+uzvf1FDnE++xdo1fsIMEPE6WThhRGntttHSYh0+yTNQsnUVwIvxL4KjJfwK4VVVfM1i2qsb15qdNrsdjm95E88Q6DJwYQeNEx35pbpiAvqERDOdsnDcODWF6Y3Gvd2h4JD8dfWFKx4hqsSydciP8uFF8kul8ccQzruDa7uETB57feET18L8P54Wr0wGcAeBhAPebKlS1s3HnIfzuXf+Bddu78cSWfQCA4yOOaEsu+m6oc+ra/7K4BWe1NOMz71kSuD+vV+/14P0ZN8U8df+LM0Ev0sTx48MyRqJkk0T1ueP41nG9bts9fHZm5sDzEI+oHr6o6r96Pn9PRD5tokDVSmd3P259sB1dPf2YKBNw7KQTuTdPqsPw4EnMn9mEzoODmDujCTsODGDWlIk40H8cB44eR2f3AJ7Z0V2wP7/Iu5F7ob1TaOEUi9LLjfBNesZR7Ql6+Ob3W23wPMQjquCvE5HPA3gAjrrcAOAnIjITAFS1N2zjrNLZ3Y/PPrwJ3UePY+qkOmzb57yEPEFGM1YnTshZOJOcU5336RsKfXqvXRNV5P0WTjEx9wt50I1SakUAhItjkhUFPXzih+c3HlEF/4bcdFVu6ibk/xkcBVqUZKFsxvXm/+D8OfjsI5vzkfzECaPvKMyZPhm7Dx0DAMya0oAD/WPtgcUtU3FKYwNapkzCxl1OX/WlirxfpKNE+EGUWhEA5efhm3x6yKqHzywdUg6hgi8ivw1gt6ouzH2+EcD1ALoAfLmWIns3mt+ypw/DbwG/7jiI4ZHRbJi6CYoTjvbjhGd5fV1hM0l9LjtnZ+8gNrzei4sXzgDgRPWlirxfcKNE+KUKRphwl9swa9LSiSu4tvelQyuDlMN4Ef634XR6BhF5N4DVcHrOXAGnS+MPGS1dhXFFflfPIA76GvHE96bqlEkNOHbSWWdm00TsO3K86D69kf2G13sxf2Yzmhrqc1H9G7m1ool8nAg/Sa++3Dz8qMQRuax6+LQySDmMJ/h1nij+BgBrVPUHAH4gIu0h21U1rtBv2tUX2H9E3QQBPJH8qVMb8pWCP6p3lhWP7N3Py+fuLVnk40T4aTXaJmnpxBE5evjJwPTHbDGu4ItIvaqeBHAlRj38KNtWHT9ufwN/88hmHM/58mGcPr0Rnd2D+c/FRN673I3sz5zRiA2v92LJadPQ1FCf/wxogaVz3YozxhX5JCP8oIrAZBQfVVzjiE5WPfy0YZtBthhPtO8H8IyIHIQz6Ml/AICILAZwOGzDaqGzux833deGju6BkrYbOB7cd5wr8nOnN2LZGdOwcVdfPpL/00vmY+WSFkCdN2bdz35Lp1TxB8qL8JPOhIkiFFHFlR5+5WCbQbYIFXxV/QcR+QWcF65+pqquhzEBjpdflfQODOPv1m7FE1veLGh4LYUgn37u9EYsbpmCjbv6sKdvCIBg5ZKWfCS/ff/RAkuns7sfv+7swSWL9vuydEoT/6gRfqk3sElLJ6q40sOvHFmxpojDuLaMqj5XZNkOM8UxS2d3P268ZwP29B0re19js2+cz3v6hrCzd/RpYcvew9i4qy8fyfstnRsvXYCG+gljBDxI/EuN8MvNhImbhx8FG17qSmo7PxRKYiOZ8+GLcf+GnfjCo1uQ5AjpXsH3RvUAMH9mM/YfOY6unlGP3y/8k+snYN32bpwYUazvOBgavftfsColwvdTqrDHHeIwipibTMuMCz18kmUyK/gbdx7Cx//5eRw+djLxffsF3h/Vd3T3o6tnEPNnNuU9fBdX+M+c0ZSP+Nd3AFGtGwAlRfh+sUyy0TaMJC2NNC0d2z18ViSkHDIl+L0Dw1h17wto8wisCfwCDxSP6p2RqkY9/I27+vLdIrteflCjbZh1U0qEb7LRNi1LJ820TNs9/Kw0BpPKkAnB/3H7G/irB9oTtWzGY/7MZuztO4bdh4YABEf1fmG/8dIFaGroGtOI68/DB4oLO1BahB/H9vESJjDl+vs2pmXa7uFnpTGYVIZMCP7ND6T/DlhHd39e7AHgZK5fezeqv3jhTKgqlsyeUiDsg8MjBRWANw/fK86DwyNF7R3ATIQfp9E2rr9fKmmmZdre2Gp7+YjdZELwK4Er8FMn1+HosZGCRlzXpweAc0+bViDs7ri1/kZcf1QfZO+EVQTlRPhJN9pGIaqQV6OHT4iNUPDL5OixkTE2jlsZAMXTMot5+f7hC4PsnaCKoNwIP+lG2yQtnThU2sNnxUFshIKfAK6Nc+aMxgKbBxgVf7/w+718QDE07Kw7NDwSOI5tUEUAmInwwwgTx0pbOpX28Nm4SmzEmOCLyJkA7gNwGoC34HS8dpep41Wa9t2Hxoi9F7/w+718b5ZOY8OEgnFsXcIqgluvPsdIhH/vs1246xevYnB4BLdefU7Bb4pTSXgxaelU2sNn4yqxkahj2sbhJIDPqOpvwRn8/C9FZKnB46XKsZOFfensOxzt7V1X+IeGnfcD2ncfwrrt3Xjwhd24/JxTcVZLMy4/59TA7b0Vgb9S8I9xW2xZ0Ji2Qcv9wyh6CRsH995nu7D6iVdw77Ndgb8l+JjlE3fM06TGtHUrDto5xCaMCb6qvqmqG3PzRwG8DGCOqeOlzR5fND+io4LorQzc+aCpW1Fs2t2HO5/agc7uAdz5VLyeK4KeCrzTYpVC2HLvoOl+wgU7uKJwiTpwehzxjjKIelLHIqRaSMXDF5EFAM4HsKHId6uQ63Z53rx5aRQnEUQKP3u7VN53+PiY+aCpm91z3txTAADrOw5i6elTC8a3dRlvPmyb0WVBQlx8eViWTth3N162EE0N9aGCG9X2iGOPVNrDN0XajcG2Nj7bWq44pPlbjAu+iEwB8AMAf62qR/zfq+oaOKNnobW1Nda7U0tamrDd0zd9KTQ1AIPDhfPTJk/ApLp6TGuqx74jxzDnlMb84OOAMxD5X1yxGN96phNDwycLPqvqmPl7/7MLN166oOj05t85Gy909eYF5m1TJuXnvYIZZb6YyPqXBQlx0PIwAQz7LorgRhXlOOJdaQ8/K2Pa2tr4bGu54hDWTpY4qmrsD8BEAP8O4LYo61944YVKSBLc/XSHzv/c43r30x2ZOn5P/3G9++kO7ek/nuh+g+g4cFQ/9t0N2nHgaCrHi4qt5YrDnT97Red/7nG982evxNoeQJtG1GSTWToC4B4AL6vqnaaOQ0gx4lozSUXmtltDUSl3oHpT2FquOESxP5PCpKXzTgAfBfCSZ/zbL6jqTw0ek2SQNPvSScoqMNUFQtpWhq0VV7kpwbWKMcFX1fUAZNwVCRmHNEUuKYEz5eHbKsBpk6UIP83rm2/akophcojDSjfamrqJ0+48zdbG0SxVfGn+Fgo+qRgm+8OvdOdppm7itNMRbRVW9hoaDwo+MUIUYcpy52lZ8fBtFdYs5eHT0iFVT5SL2KSYVPrFq6x4+LYKq61WUxxo6ZCqIEwMkryI44gOPfxksFVYbbWabMdk52kkA4R1JhbW70ySnYfF6d+m0p2nxe3LZzySKl9UTP0OMkqa/TcxwicAgiPitPq8DyPOcejhJ4OtHr6tTx5xoKVDjFGqsJfbX06loIefDLZ6+FmydNK8j2jpZBy/BRD0+Bj06G6yX/eo9kScR9641kdSv9fUY3ra/ezb2l10lsYbSNOmY4SfIYpFY/7IPSgyqkS0nuVBzJmHbxZbnzziwLRMEgn/RV/swvHfsDbZMCb7Q6GHnww2XS9e6OHHg4JfBXiFHUB+Pkr0XqkbNkoEFrU/FPalMwo9fAdbnzzikOY9SsG3FO+N5hU8APl5m6P3KCId9aZN09JhHn4htkbSNl3r5ZKpEa9IOFGi92KC514ctl70Sdo1cX5nVvvDp4efPejhZxD3Rr1q6Wz8fNv+/HRw+CTu+kVHfr1iIu8XPFtEPkx8otg1US909oc/Cj18B1utpjjQw69yegeGce+zXQAU162YUyDsz73Wg3Xbu/PTW648e0w6pO3Ru0u5L2VFvdDjiFxcQaCHX4itwmqr1RQHevhVhDdyX9u+F4AzDrsbtW/ec7hA2K9aOhuXLNqfn/pvpGq6eNMadYge/ij08B2yZDXRw7cUf+S+tn0v2rp68evOnnzEDgC3XHk2brny7Px6fmF3LY5qGKknrm0TRShMigk9/GSwVVir4Qk4KvTwLaGzux93PLYVi2Y1Y/LEOmzdexi/7uwBMBq5A8DKJS340rVLsXyuE+HfeNmCgpuxGoQ9iHuf7cJdv3gVg8MjuPXqcwq+C4vwK23p0MNPBluF1VarKQ708FPGjdwPDQ5j+76jWDJ7KiZPrMPPtu1DV88g1ncczK/7rsWzcOH86bhuxRyPwC/EzOaGMYKYDdQ3HaXccUWjikmcG4IefjLYKqy2Wk1xoIdvkN6BYdz9TCfaunoBAItPnYL/7OzB7kND+XU2vN6bn1/wtia8++wWTJ5Yh8aGCXlxB5ApgQ+6sa9bMQeb9xzGdSvmjNkmTHyi3JBRxSTNIQ7p4Rdiq7DaajXFgR5+gmzceQg3378Rx0+MQCAAgG5PJ0Ubd/Xl5y+YNx0T6ybkI3y/wGeZIOsmbhQf5YY0mZZJDz8ZbBVWW62mONDDj0HvwDD+bu1WPLHlTQgUIoAAGDpZfP1pk+ux+NQpWHzqFOzsGcR5c0/Bp65YnHlxDxKMoeGRgqlLuVF8GPTwS4cevoOtVlMc6OGXyI/b38AtD7bjrbE2MwCgboJgRmM9BIKWqQ2YMnkiVl+/HGe1VG9jalyCIvnGhgkF0yiENdomKUz08Eehh+9gq9UUh0x4+CLyXQDXAjigqstMHQcA/vYHmwvEflId8hH+tMZJ+NZHLsQF82eYLIK1+G/YoEg+yKsPu7HC7J4kLZ040MNPBluF1VarKQ5Z8fD/BcA3ANxn8BgAgP91/XLc9vAm6IjiHz+8Ar9XpIGxFih24fgj+qBIPki8y029DMOkpUMPPxlsFVZbraY4ZMLDV9VficgCU/v38nsr5tSsyHspZtf4I/qgSD7oxo7baFtpSycu9PALsVVYbbWa4lBTHr6IrAKwCgDmzZtX4dJUF1HsGn9EX6qAx220TdLSSTMtkx5+IbYKq61WUxwy4eFHRVXXAFgDAK2trQHNrsTFewNGsWv8EX0ClTtVAAAR8ElEQVSQRZOmbVLq9mmmZSYFPXyzVPr/myRZ8fCJAbwiH8Wu8Uf0pXr1cW/4JIWiGtMy6eGbxVarKQ6Z8PBJcnR29+Orj2/Dl65dGphlAxS3a/xCHiTscRpt07J0qjEt0xT08B1stZrikAkPX0TuB3AFgFkisgfAHap6j6njZQ2vyN/x2Fas7ziIEyNbsfT0afl1/BZOMXGOGuHHabRNy9KJQ1bTMunhO9hqNcUhEx6+qv6xqX1nFe/NVSjyU7G+4yCWnj61QOT9Fk6UCL9UwYgrMJW2dLKalpk2tgprVs4vQA+/pvD+s+9+phNrfvUaegaGC0T+hovm4dUD/bjhIieLyRV5v8BHifCDiHNjh20TZXAUk5ZOXJiWWUiWhNVW6OHXAK5l0zJ1Eh5q24OegWFsfeMwAGDrG4fxlQ8uy4v82va9WLe9G8vn7kVTQ11ewP2iGiXCD7q44jTaholBlIrGRkuHaZmF2Orh2/rkEYdMePikOK7QHx46gY27+jBtsvMv2LS7D59737nY98gmfOY9SwpE3tsnvVeY40T4pTbaxr0Yk7yIK5EyWi5ZScu01cOv9P83STLh4ZNC/EJ/2rTJAIC50ydj275+nDf3FDyzoxud3QN4Zkc3vCLv9eq9whwnwk9S2MsVtSxbOllJy7Q1krb1ySMO9PAzgPtP/O0FM/H/fvnqGKGf2VSPfUeAZXOmY/Ypjbjhonl48PndAJyUyxsuOjMv8t5o/7oVZxiJ8IOI69NHEYosWzqmoIfvYOuTRxzo4Vc5nd39+Nh3n8fuQ0M4bdok7DtyHKdOnQRgVOgnN9QBAHb2DmLD671YPndvQQZOkKVjKsIv1dsP2xdASycraZm2YuuTRxzo4Vchnd39+OzDm9B99DhmNE3MD5l49NgJZwV1RLu+zhH1xS1TcUpjA86c0ZgbUrHQulnb/kZuzzom/bKcCD/o4irV2/fuI+6FSkvHfmwV1qyc37Sh4JeBOz7u1jcOY+jESH64xL7BE/l15s9swrZ9/TjtlMk40D+M+jpnmEU3sv/TS+Zj5ZKWMf58kG8PoKQIP+qNkXSjLS0dM9DSyR60dCzG683f8sBv8pG8a9kAwOmnTMLRA87Yiq5H3zJlEja/cWRMZL99/9G8pRPkz/uFvZQI308c66bUfQG0dGjpmMXWJ4840NKxENey2b7/CAaOv5X35vPoaEefkyfW5ec7uvuxcVcfLl7ojLjlj+y9lk6UxtnB4ZGi6wDFo3T/jVGqdVPuy1Vh0NKxH1uFNSvnF2BapjW4ls1znQfxyptHMPzW6HdHjp0oWHfWlAYc6B8O3Nf8mc1oaqgfE9l7LR2vbx8U4QetExThl5uWGbfRNopQlFthhEFLJxlsPx9ZgGmZFcYV+h+8uBs9AyeKrtM0sR6Dw6MC7zbGeufnTm/EsjOmYeOuvsDIvrO7H7/u7Bnj2wPFrZugdYDiAlxuWmbcRtsoxzHZ7UOlhYqWjllsffKIAz38CtA7MIy/W7sVT2x5ExOgODa29+ECTp3agIMDYyP6udMbsbhlCjbu6sOeviEAUiDw/sj+xksXoKF+QmTrJqgBt9wIP0lvP+w4XqKKl8knAT+0dAqxVVizcn4Bevip0tndj5u//xu8/OYRlDLcljei937e0zeEnb0D+eV+gfdH9idGFOs7Do4R9ij2DpBchB8nLdOkvx+1DEHEFao0K5c40NIh5VCTgu+N5odHyh9V0RvVA45fDwhUFUtmTwmN7M+c0Yj1HcDYRtvx7R0guQg/zgAocf19F5ONtiafTKJAS8cstj55xIGWjiE27jyET9z7Ag4NFvflS8Eb4fujejczBwDOPW1aUUtncHgkcqNtWGZOJSP8sO+iCK7JaDqucCclqLY/KUTFVmHNUsWX5rUyYfxVqp/7N+zEwtt/gj/41rOJiL0b0XuZP7MZC97WNGbdLXsPY932brhe/pLZ7nbOk8X2/Uexbns31rY7Ub0r/lctnY2VS1pyF8HYrhV+vm1//olgbfteAPBtg6LLvNt7CVpebJ9RvgvaX6nrAKOi83Db7tD1opYtDaL+tlKJcy7KodLnsRYwda0UI7MR/o/b38CtD23CybfKt2z8+CN6wInqu3oGMX9mUz4zx8uWvYexcVdfgaXT1NAVmIcPYFx7x/tEABSPar37vPXqc6oywo8TAcWN8JOKaE1FbWk/OSRlcSWNrU8ecWCjbUx6B4ax6t4X0OYTWxPMn9mM/UeOo6tnEABwcsRJ0t/ZOwhAcPHCmVBVnHva1ALxd4V/PEtnlOgVQXEx0IJp0A3srxhcTHr4UcUkjujEFcakBNWUUKYtwLZaJ1mxzNImE5bO/Rt2YsHnf4IL/v6pVMQeGI3o3QFMvGzZexgbXu/F812H4Fo5y86YVrDO0PDJ/LrFLB3vfKFoj877LR3/ZwC+/YQ9oqtv6hD2uFnseC5RrICodkEcWyHuY3JSj9emrBBaLA5p2iCmSdOmy4Tg3/7oltSP6Ub0R445wu1txHW/A8Z6+K7wNzaMdr8AOH3gewXUOx+tIig2HSvKQSLtrxhcwgWmeCUBJOvhh1UsQcQVxqQE1ZQgpS10abcZRCVLFV+avyUTgl9pijXiurji7xf+P798sa8CmIChYedtr6HhkYL5KBUBECTa41cKQLCoholtUCUBJBvhh1UsQcQVxjiVSzGyEuHbKqxZivDT/C0U/ATY0zeEV/YdDV3HL/zfeqazoAIoJpouUSoCIJqlEyzSxUXVezw/YeIYRTijimtYxRJEfKEqvXIpRlYi/KQqwKSxtSKKAyP8KuDYyUIBPHD0WKTtXOF3Pfz23Yewbns3Hnyh9EdmvxgXE+dyLR3vKFzjHT/qd6WsE1bmpLcB4lUuxchKhJ9UBZg0WYrw06xUjQq+iLxPRLaLSIeIfN7ksdJmb1+hwM9smlh0PTct1K0g/NN9h539bNptprE5SqUABF90l59zKs5qacbl55xqpHxRiFoxlLsNkNzNZ+omTjviTqoCTJosRfhpVqrGBF9E6gB8E8A1AJYC+GMRWWrqeGkza8qkgs8nPf3he6P/g0edPvPdCuKN3IApe3LTkdx289/WVFAZlDpfbBr2nf8J5dDgcMHU5c6ndqCzewB3PrUj7HRkhrgVhan9pLXfIGy1dB58YXfsJ2PbSDOoMpmHfxGADlV9DQBE5AEAHwCwzeAxU+PNvqGCzzsPDhadHzzh3JhN9XXoPz56k46cdKyd/ly/+q+8eST/XfuuQ7Hm/dOw77zrhC1/W/PEgqmXvlzl0Dc4ttfQsO9KWaeU9crdppztTO0nrf0G4V7n/uu90rR19RZMq5mvPfkKOrsH8LUnX8GDN11q9FgmBX8OAG/1uwfAxf6VRGQVgFUAMG/ePIPFSZbjvk7XvJ+9867IH8h1pTyYG0XlRC5zM1cfFHT5EHfePw37zt/FRNDyTXsOF0y9PJ+72Z4vctOFfVfKOqWsV+425Wxnaj9p7deW40WlfoIUTKsZzT3lq1axpQOg2H9izC9S1TWq2qqqrS0tLbEONLWMQWKkyHw9gMn1wEQp/Oz+NU8S3HbVYkydXD/mc7H5mc0T89Mvvv9cnNXSjH/4/WUF07s+fD7u+vD5secBjPlcbFmxdcKW3/lHK3BWSzPu/KMVY85d3O9KWaeU9crdppztTO0nrf3acryorL5+OVYuacHq65dXuihlk+ZvEVO1iohcCuDLqvre3OfbAUBVVwdt09raqm1tbUbKQwghWUREXlTV1ijrmozwXwBwtogsFJEGAB8GsNbg8QghhIRgzMNX1ZMi8mkA/w6gDsB3VXWrqeMRQggJx2hvmar6UwA/NXkMQggh0eCbtoQQUiNQ8AkhpEag4BNCSI1AwSeEkBrBWB5+HESkG8DOSpcjgFkADla6ECGwfOXB8pUHy1ce5ZRvvqpGemvVKsG3GRFpi/pyQyVg+cqD5SsPlq880iofLR1CCKkRKPiEEFIjUPCjs6bSBRgHlq88WL7yYPnKI5Xy0cMnhJAagRE+IYTUCBR8QgipEWpe8McbaF1EbhORbSKyWUR+ISLzPd+NiEh77s9I188RyvcxEen2lOOTnu9uFJFXc383Vqh8/+gp2w4R6fN8l8b5+66IHBCRLQHfi4j831z5N4vIBZ7v0jh/45XvT3Ll2iwiz4rIeZ7vukTkpdz5MzKQRITyXSEihz3/x//h+S702kipfJ/1lG1L7pqbmfsujfN3poisE5GXRWSriNxSZJ30rkFVrdk/ON02dwJYBKABwCYAS33rrATQlJv/cwAPer7rt6B8HwPwjSLbzgTwWm46Izc/I+3y+da/GU432amcv9wx3g3gAgBbAr5/P4An4Ax4dgmADWmdv4jlu8w9LoBr3PLlPncBmFXh83cFgMfLvTZMlc+37u8B+GXK5+90ABfk5qcC2FHkHk7tGqz1CD8/0LqqDgNwB1rPo6rrVNUdlfw5AHNtKl8I7wXwlKr2quohAE8BeF+Fy/fHAO5PuAyhqOqvAIQNyPoBAPepw3MApovI6Ujn/I1bPlV9Nnd8IP3rL8r5C6KcazcyJZavEtffm6q6MTd/FMDLcMb79pLaNVjrgl9soHX/P8PLJ+DUxC6TRaRNRJ4TkQ9WsHzX5x4FHxGRM0vcNo3yIWeFLQTwS89i0+cvCkG/IY3zVyr+608B/ExEXhSRVRUqEwBcKiKbROQJEXl7bplV509EmuCI5Q88i1M9fyKyAMD5ADb4vkrtGjQ6AEoVEGmgdQAQkY8AaAVwuWfxPFXdKyKLAPxSRF5S1c6Uy/djAPer6nER+RSAewH8TsRt0yify4cBPKKqI55lps9fFIJ+QxrnLzIishKO4L/Ls/idufN3KoCnROSVXMSbJhvh9OXSLyLvB/AjAGfDsvMHx875tap6nwZSO38iMgVOZfPXqnrE/3WRTYxcg7Ue4e8BcKbn81wAe/0richVAL4I4DpVPe4uV9W9uelrAJ6GU3unWj5V7fGU6Z8AXBh12zTK5+HD8D1Op3D+ohD0G9I4f5EQkeUAvgPgA6ra4y73nL8DAB6FY6OkiqoeUdX+3PxPAUwUkVmw6PzlCLv+jJ4/EZkIR+z/TVV/WGSV9K5Bkw0Wtv/BecJ5DY7V4DYsvd23zvlwGp/O9i2fAWBSbn4WgFeRcKNUxPKd7pn/fQDP6WiDz+u5cs7Izc9Mu3y59ZbAaSCTNM+f51gLENzo+LsobDB7Pq3zF7F88wB0ALjMt7wZwFTP/LMA3leB8p3m/l/hCOau3LmMdG2YLl/u+1Pg+PzNaZ+/3Lm4D8DXQ9ZJ7RpM/ORX2x+cFvIdcET9i7llX4ETzQPAzwHsB9Ce+1ubW34ZgJdyF/JLAD5RofKtBrA1V451AM71bPtnObHoAPDxSpQv9/nLAP6nb7u0zt/9AN4EcAJOxPQJAJ8C8Knc9wLgm7nyvwSgNeXzN175vgPgkOf6a8stX5Q7d5ty//8vVqh8n/Zcf8/BUzEVuzbSLl9unY8BeMC3XVrn711wbJjNnv/h+yt1DbJrBUIIqRFq3cMnhJCagYJPCCE1AgWfEEJqBAo+IYTUCBR8QgipESj4hBBSI1DwCYmAiHxbRN5Z6XIQUg7MwyckAiLSDuBCLewLiJCqghE+qRlE5GER+YaIrBeRnSLyLhG5Lzcwyz0h2/0WgB2qOhJ3H4TYAAWf1BLvAPCaqr4LTq+i9wD4HIBlAP5ARCYFbHcNgCfL3AchFYeCT2oCEZkMYDqAr+cWDQG4R50BKoYBDAKYKyL3iMgjvs3fC+DJiPsYFpEPisg/ichjIvIe07+NkKhQ8Emt8HYAG1X1rdzn85AbiEJE5gLYq6qdqvoJ70a5gTOmq9OVbpR9qKr+SFX/G5xOu24w/LsIiQwFn9QK74DTM6LLcjg9GAKOcG8es4XDSji9kMbZx5fg9IJIiBVQ8Emt8A44XdO69k6jjo4V6xVuP37/ftx9iMPXADyhufFMCbEBpmUSkkNE3gbgHwBcDeA7qrpaRDYCuFhVT5Swn78CcCOAFwC0q+rdRgpMSIlQ8AkhpEagpUMIITUCBZ8QQmoECj4hhNQIFHxCCKkRKPiEEFIjUPAJIaRGoOATQkiNQMEnhJAagYJPCCE1wv8HqD2BQX+0JrUAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy.linalg as alg\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "def set_k(k, N):\n", " return np.array([k]*(N-1))\n", "\n", "def set_m(m1, m2, N):\n", " m = np.zeros(N)\n", " for i in range(N): \n", " if i%2==0:\n", " m[i] = m1\n", " else:\n", " m[i] = m2\n", " return m\n", " \n", "def define_matrix(k, m, boundary='free'):\n", " A_diag = np.zeros(len(m))\n", " for i in range(0, len(m)-2):\n", " A_diag[i+1] = (k[i]+k[i+1])/m[i+1]\n", " A_diag_p = [-k[i]/m[i] for i in range(len(k))]\n", " A_diag_m = [-k[i]/m[i+1] for i in range(len(k))]\n", " if boundary is 'free':\n", " for i in [0, -1]:\n", " A_diag[i] = k[i]/m[i]\n", " if boundary is 'wall':\n", " for i in [0, -1]:\n", " A_diag[i] = 0.\n", " A_diag_p[0] = 0\n", " A_diag_m[-1] = 0\n", " if boundary is 'wall-2':\n", " for i in [0, -1]:\n", " A_diag[i] = 2*k[i]/m[i]\n", " A = np.diag(A_diag) + np.diag(A_diag_m, -1) + np.diag(A_diag_p, 1)\n", " return A\n", "\n", "def diag_matrix(A):\n", " u, v = alg.eig(A)\n", " # Sort eigenvalues/vectors\n", " idx = np.argsort(u)\n", " u_sorted = [u[i] for i in idx]\n", " v_sorted = np.zeros(v.shape)\n", " for i in range(N):\n", " for j in range(N):\n", " v_sorted[i,j]=v[i,idx[j]]\n", " return u_sorted, v_sorted\n", " \n", "def plot_spectra_with_m(N, k1, m1, m2, boundary='free', fignum=None):\n", " plt.figure(fignum)\n", " plt.clf()\n", " for i in range(len(m1)):\n", " k = set_k(k1, N)\n", " m = set_m(m1[i], m2[i], N)\n", " A = define_matrix(k, m, boundary=boundary) \n", " u, v = diag_matrix(A)\n", " plt.plot([m1[i]/m2[i]]*N, u, 'o', color='C0', ms=1)\n", " plt.xlabel('$m_1/m_2$')\n", " plt.ylabel('Spectra')\n", " plt.title('$k$ = {}'.format(k1))\n", " plt.show()\n", "\n", "if __name__=='__main__':\n", " N = 50\n", " k1 = 1.\n", " # m1 = [1., 1., 1., 1., 2., 5., 10.]\n", " # m2 = [10., 5., 2., 1., 1., 1., 1.]\n", " n_ratio = 100\n", " m1 = [1.]*n_ratio\n", " # m2 = list(np.linspace(0.5, 1, n_ratio/2))+list(np.linspace(1, 5, n_ratio/2))\n", " m2 = np.linspace(0.5, 10, n_ratio)\n", " plot_spectra_with_m(N, k1, m1, m2, boundary='free', fignum=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On retrouve donc un spectre gappé, avec un état se situant à l'intérieur du gap, traduisant un effet de bord sur la chaine masse-ressort.\n", "\n", "### Cas N impair\n", "\n", "On prend ensuite le cas suivant, avec $N = 51$ et on étudie les états propres de la matrice en fonction du rapport $\\frac{m_1}{m_2}$, on trouve donc :" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\Romain\\Miniconda3\\lib\\site-packages\\ipykernel_launcher.py:47: ComplexWarning: Casting complex values to real discards the imaginary part\n", "C:\\Users\\Romain\\Miniconda3\\lib\\site-packages\\numpy\\core\\numeric.py:492: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy.linalg as alg\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "def set_k(k, N):\n", " return np.array([k]*(N-1))\n", "\n", "def set_m(m1, m2, N):\n", " m = np.zeros(N)\n", " for i in range(N): \n", " if i%2==0:\n", " m[i] = m1\n", " else:\n", " m[i] = m2\n", " return m\n", " \n", "def define_matrix(k, m, boundary='free'):\n", " A_diag = np.zeros(len(m))\n", " for i in range(0, len(m)-2):\n", " A_diag[i+1] = (k[i]+k[i+1])/m[i+1]\n", " A_diag_p = [-k[i]/m[i] for i in range(len(k))]\n", " A_diag_m = [-k[i]/m[i+1] for i in range(len(k))]\n", " if boundary is 'free':\n", " for i in [0, -1]:\n", " A_diag[i] = k[i]/m[i]\n", " if boundary is 'wall':\n", " for i in [0, -1]:\n", " A_diag[i] = 0.\n", " A_diag_p[0] = 0\n", " A_diag_m[-1] = 0\n", " if boundary is 'wall-2':\n", " for i in [0, -1]:\n", " A_diag[i] = 2*k[i]/m[i]\n", " A = np.diag(A_diag) + np.diag(A_diag_m, -1) + np.diag(A_diag_p, 1)\n", " return A\n", "\n", "def diag_matrix(A):\n", " u, v = alg.eig(A)\n", " # Sort eigenvalues/vectors\n", " idx = np.argsort(u)\n", " u_sorted = [u[i] for i in idx]\n", " v_sorted = np.zeros(v.shape)\n", " for i in range(N):\n", " for j in range(N):\n", " v_sorted[i,j]=v[i,idx[j]]\n", " return u_sorted, v_sorted\n", " \n", "def plot_spectra_with_m(N, k1, m1, m2, boundary='free', fignum=None):\n", " plt.figure(fignum)\n", " plt.clf()\n", " for i in range(len(m1)):\n", " k = set_k(k1, N)\n", " m = set_m(m1[i], m2[i], N)\n", " A = define_matrix(k, m, boundary=boundary) \n", " u, v = diag_matrix(A)\n", " plt.plot([m1[i]/m2[i]]*N, u, 'o', color='C0', ms=1)\n", " plt.xlabel('$m_1/m_2$')\n", " plt.ylabel('Spectra')\n", " plt.title('$k$ = {}'.format(k1))\n", " plt.show()\n", "\n", "if __name__=='__main__':\n", " N = 51\n", " k1 = 1.\n", " # m1 = [1., 1., 1., 1., 2., 5., 10.]\n", " # m2 = [10., 5., 2., 1., 1., 1., 1.]\n", " n_ratio = 100\n", " m1 = [1.]*n_ratio\n", " # m2 = list(np.linspace(0.5, 1, n_ratio/2))+list(np.linspace(1, 5, n_ratio/2))\n", " m2 = np.linspace(0.5, 10, n_ratio)\n", " plot_spectra_with_m(N, k1, m1, m2, boundary='free', fignum=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On retrouve également un spectre gappé, cependant les états à l'intérieur du gap ne se présentent que d'un coté du spectre.\n", "Comme le système a un nombre de masses impair, il commence et se termine avec la même masse ce qui justifie la présence des deux états à l'intérieur du gap pour $m_1 < m_2$, comme $m_1$ est plus légère il y aura des modes précis ou elle oscillera sans transmettre d'énergie aux masses voisines." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "The raw code for this IPython notebook is by default hidden for easier reading.\n", "To toggle on/off the raw code, click here." ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import HTML\n", "HTML('''\n", "The raw code for this IPython notebook is by default hidden for easier reading.\n", "To toggle on/off the raw code, click here.''')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }