{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "7787fcd7", "metadata": {}, "source": [ "# Thomas-Fermi Solver" ] }, { "attachments": {}, "cell_type": "markdown", "id": "bf23ccb6", "metadata": {}, "source": [ "Now we will take a look at the Thomas-Fermi solver. This solver attempts to solve the following integral equation for the charge\n", "density n(x):\n", "\n", "$n(x) = \\frac{g_0}{\\beta}\\;\\text{sp}[\\beta(\\mu-qV(x)-{\\bf K}\\cdot n(x))]$\n", "\n", "Here $g_0$ is the density of states, $\\mu$ is the Fermi level, and $\\beta$ is the\n", "inverse temperature. These parameters can all be changed in the `PhysicsParameters`\n", "dataclass. $\\text{sp}(z) = \\ln(1+e^z)$ is the softplus function." ] }, { "cell_type": "code", "execution_count": 1, "id": "eb703550", "metadata": {}, "outputs": [], "source": [ "from qdflow.physics import simulation\n", "from qdflow import generate\n", "import tutorial_helper\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "20fccca8", "metadata": {}, "outputs": [], "source": [ "# Define a set of default physical and numerical parameters\n", "phys = generate.default_physics(n_dots=2)\n", "phys.gates[3].peak = 7.5\n", "x = phys.x\n", "q = phys.q\n", "numerics = simulation.NumericsParameters()\n", "\n", "# Calculate V(x) and K(x, x')\n", "V = simulation.calc_V(phys.gates, x, 0, 0)\n", "K_mat = simulation.calc_K_mat(x, phys.K_0, phys.sigma)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "c2aaaa8f", "metadata": {}, "source": [ "Additionally, the Thomas-Fermi solver requires the following matrix in order to\n", "help with convergence issues which we shall discuss later:\n", "\n", "$[g_0 \\delta_x {\\bf K} + {\\bf 1}]^{-1}$,\n", "\n", "where $\\delta_x$ is the resolution with which the x-axis has been discretized,\n", "and ${\\bf 1}$ is the identity matrix." ] }, { "cell_type": "code", "execution_count": 3, "id": "b51f349a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculate the inverse of [g_0 delta_x K_mat + 1]\n", "delta_x = x[1] - x[0]\n", "g0_dx_K_plus_1_inv = np.linalg.inv(phys.g_0 * delta_x * K_mat + np.identity(len(x)))\n", "\n", "# Run the Thomas-Fermi solver\n", "# This may take a few seconds initially due to numba compilation time\n", "n, phi, converged = simulation.ThomasFermi.calc_n(phys, numerics, V, K_mat, g0_dx_K_plus_1_inv)\n", "\n", "# Plot the results\n", "fig, ax = plt.subplots(1, 2, figsize=(6,2.8))\n", "tutorial_helper.plot_potential(fig, ax[0], x, q*V, mu=phys.mu)\n", "tutorial_helper.plot_n(fig, ax[1], x, n)\n", "ax[0].set_title(\"Potential energy\")\n", "ax[1].set_title(\"Charge density\")\n", "fig.tight_layout()\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7883402d", "metadata": {}, "source": [ "The Thomas-Fermi solver uses a successive iteration method to find n(x).\n", "This involves starting with some \"guess\" $n_0(x)$ (by default zero is used),\n", "and evaluating the integral equation above to find an updated function $n_1(x)$.\n", "\n", "This process is then repeated until one of the following occurs:\n", "* A maximum number of iterations is reached\n", "* The difference $\\Delta_n = n_i(x) - n_{i-1}(x)$ lies below some absolute tolerance,\n", "satisfying $|\\Delta_n| \\delta_x < \\text{abs}\\_\\text{tol}$\n", "* $\\Delta_n$ lies below some relative tolerance, satisfying\n", "$|\\Delta_n| < \\text{rel}\\_\\text{tol} \\sqrt{|n_{i-1}|*|n_i|}$\n", "\n", "For the sake of illustration, we'll show the successive iteration method without\n", "any additional improvements, which can be done by setting\n", "`NumericsParameters.calc_n_use_combination_method` to False." ] }, { "cell_type": "code", "execution_count": 4, "id": "56464061", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\dlb8\\OneDrive - NIST\\Documents\\qdflow_paper\\QDFlow-sim\\src\\qdflow\\physics\\simulation.py:1632: ConvergenceWarning: ThomasFermi.calc_n() failed to converge.\n", " warnings.warn(\"ThomasFermi.calc_n() failed to converge.\",\n" ] }, { "data": { "image/png": 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hq4hoCmFLzZ54IhDj8y/wmGP09Y8/AmVl/GNHj8EqAmJ6tiPwPerfX69p8iKiGV5ik3TEF65zBxKmT9euXYtXXnnFvc0wDBWZ7dixA2PGjFHbDj300BaPXbRokRJYRqsUJIfD0eHZpRs3blQRsCWY5IgjjlDn37x5s1s0x40bpwTTglEno1t/oDAzVfzuu+8iNzcXXUVEUwg5336rr084oeXP+KWUbjmbNnExHzjrLPQYOFTasxq2I3Bd0xLNww8P+FMTOgCXAzuTIo1EKHZz585V65i+DLTWBUDLR+8X/P3336sIlWLE9CpTr4wyH3744aA8z1hOYveA66IU1gPB58R07+LFi3FCax84nUBEUwgpLGSgCxCZNq31fY49VosmU7Q9RTT5uq2Wkc6KJpEKWqGzxMXFwclFcQ+mTJmCDRs2YHgH0x9LlizBoEGDcMcdd7i3sdDoQOfzhZEs1y65tmkJ83fffYeoqCiMsobJdpKFCxfiiiuuUMLJdG6giIjq2aefflrlxJk/nzFjBn744Yd29+e3Bua1uf+ECRNUWbEFK6pY1cXt/CVwkZpVXwUFBV7HKCsrU9+UmE7IyMjAlVde6VWxJQQH/l2Vl/ObIzB+fOv7WCnar77qOb8FesfW1+sopSPtJhYimkJX4WcsWzHy8/NRUlKitvGzkgLIwps1a9Zg69atKo3J++0xYsQI7N69WwkS07NM07799tstzscUL4/L8zU2NrY4Dj+D+Tl+6aWXqsIhFvpcf/31mDNnjjs12xmYkuXnPiNfakpRUZG6VLJBvLuLJvPiN954o6rKWrVqlcpvM9xnFVVr8Bd84YUXKpFjzw1LkXnhG07q6urUcVj+zGtWjTE3fuaZZ7b4Za1fvx6ffvop/vOf/6h/TFYptRA8rCiTA5jj4lrfhyYH1kQQCk1PSs1ybbKt190eVqZs9+7APi/h4OGee+7Bzp07MWzYMNX0TyZOnIivv/4aW7ZsUW0nkydPVlWyDDba48wzz1TtKxRXVrHyc5mfuZ6cffbZqjKXPZI8HyM/X9iuQtMBBjFsDznnnHNw/PHHq6KfrvD888+rNVa2pnD907rccMMN6DJGmJk+fbpx3XXXue87nU6jb9++xoIFC1rd/7zzzjNmz57ttW3GjBnG3Llz2zzHDz/8wO4mY9euXer+hg0b1P3ly5e79/nwww8Nm81m5Ofn+/W8Kysr1TF4LfjP7bczUWkYV13V9j4ul2H06qX3W7asZ7y7Cxfq13P00Z17/Mcf68ePGxfoZ9YzCeTfZ319vfrM4LXQc/H39xzWSJPOEnRr8FygZS6b97nQ3Brc7rugy8i0rf0JQ3IuHDMNax2Dtz0rwnhMnnvZsmWtHoOphaqqKq+L0PlIc+rUtvdhCnPKFO/9e0qkOXhwGzusZRc3ALoivd92elYiTUEIL2EVTea5uVDsm7vmfeafW4PbO7I/e4CYt2dK1yqH5r6+pcfsJ2IvU1vHYT8TK8SsC50zhI7BWGnlSn3bEsW2mDxZXwfA9SoiaLcIqI65LAD/BPAPWiMB2O69i5Utq67WF0EQwkPY1zSDCYuC2MzKviM26naF2267TUWs1mUP7VmEDlFcrKea0EKOa5oHk2i2G2lyjug2ADQtmMFvegBYh+FhmUYLUctGtLAwNM9ZEIQIE82cnBzVsFrMT1MPeL8tFwlu92d/SzBZBs1iH8+mW+7rW2jERWMuRrd1XhoM8xieF6FjbN7cLByJif6JJvuX6YTTYyNN/lN+0rz9v2a0yUIhGkB83Xq02ZNHpwlCpBNW0WQfz9SpU5UdkgUbVnmfXoStwe2e+xOKouf+lmCyfJq+hzT49T1GRUWFWk+1+OKLL9S5WZ4sBNd71Z/2K87YZGTV0KB7Nrsz7MG2WthaRJpvcQc2rQI4hW8OgIvNn73Zumj6dE8JgnAwpWfZbvL3v/8d//znP5Wl0m9+8xvV6Hr55Zern7PXhqlRC5YM0wSY/TebNm1SM9tWrFjh7iuiYLJsmdtoDcU1U6tHxxppw4ZalkLTt5A9oWym5eMvuOCCA5ZaC12PNP0xLGcKd9IkfXsti2S6MVwm5z89uoC1sMBbZF57WmJahg7veqdorceKaApC+Ai7IxDd6umsz94gCht7fiiKVrEPG2hZ1Wpx+OGHq8ZVmgXffvvtqsmWY2bGm53ybNx9j8MagRYDUNk4yxE5hIJKoWRPEI/PniI26AqREWkS2l7Scq+7R5p79+prfh/z8trl2uQ35u1zPbazOJweo1w2X8NcdfPjiYimIBzEokmsUTSt8VUrtjDnnnuuurQGXShY+HMgWClL8RVCH2n6K5r0oCUbN6JHiCaNDbzgdzv+Uz0MaNz6GaovuEtNqU447zyknHQL8I4ZbYpoCkLEEPb0rHBwwHmx27d3bJ6kOWChx0SaLUTTHLTtOroU5ddfgKZhS9E0YSWq//Un2EeZP9SjCBVSCCQI4UdEUwhZywWrYJOS/B9tZUWaTOt25wpaqzupRWvvd/qqcvUNMOaWAucD+BWAeUD555fBQCPAlhvztcuaptARuBRlzcmMJGw2m1pS666IaAohLwKi448/0AWHM3BZRGO1bPSYSJNtIzsBp20PGlJfAYbRIgtAOfubANeZ21Ef/6Y2PtjYck3TjxUI4SCHvtv33nuv19LVY489FrLzz58/v0VdCSksLMSpp54a1HN/++23ai4nOyc4EJsDPh599NGAHFtEUwhpEZC/qVnC+i9r/bM7r2u2KppmlFk35P+AX5vbNiQjZs8EgNOUDgHqZvxNb1+ur/Ly9DWHRXBSjCAcqG4j1XLECCB2swuhs7AXnn3vwYQTrlgnw0Ec7Mpg4SgvNHLvKiKaQkiwIkX2X3aEnrCu2a5oTvi7NjOoAhK3X4PE9dcCO/WfZdP073SK1hRNfs5YLcdicBBGGOXXhulidC49y9s0euFkEqZHefGMyjjhhBEZ7UE5kJptf54RKiNWtv+lpaW5p0HRnnTkyJFqUsnQoUPVlBO2/BHOyOSA6h9//NF9Pm5rLT27bt06HHfccer8jAx5fM8xjZdddpmaZPXQQw+pSSXch9NLrHO1Bqe10Dp13Lhx6vlffPHFyqP8v/81awW6gIimEFLRtIzH/aW7V9DS2MASOK81zSUMKHfDdajpr7c9CVEvpcFYuB9Ry8xvFoc40WD7zC2aRNpOIgCmzFPCdOG5O5mq7d+/vxoPxvQoL4SzMNmzzpa7tWvXqlGNFFHfbgYKFsc2rl692j0CjFEshZBDrB9//HHVb2+lQNlKeNNNNynRss7Hbb5QnClmmZmZWL58uZqVTEMa3/OzXZDPldfs6ed5LRH2Bz5vji+bNWsWekTLiXDwiGabUz7awErPWund7gbdGvmFmKlmt0MjC3vWAfWJi4BxelPMN2MQ1SsZUeNyEfvfaWg8dyuQBtSPfB6Ja2eDASfXOimatBYU/1mho6laWpZS6DytQjmIgrOFrYiUfe/sV6e40K+bA6IJI0GKoCdMd1owmrv55pvVUOpbbrlFRY0pKSlqEEZb1qSEbX8cqvHyyy+rlCrhLM0zzjgDDzzwgLtfn6LK7XwNXJ+cPXu2coajQU178IsCfQBok8o11quu4hihriGiKQQdFq20aSN3AKx07s8/o1unZrke6TY2oDl7I1B/3Ov6L7AKiPlhOuKfPxXRRw2CY9xeNO61AUMM2I/7CmARFS8TOdFHH8LHflkIJTSeaM4ehv7cAYTpU0aYNHuxYJ87LUV37Nih3NOI5xhFC0alFFhGgEynUpg66snN9UZGsJZgEhbw8PybN292iyYjVgqmBdO0TOseCKZj+dyWLl2KW2+9FcOHD1dp264goikEHRatWOOsBg7s2GOHD2+2ouMyi8ffVrdqN/FazzRtAR3TzT/67XGI6z8eMeeNU+s9cVccirq1fWEMyYcxoQouVCNqU6qIZqTA5cBu9u+wLSgoc+fOVeuYvgz0+GP1FDVrJjEjVK5bMr3KcYmMMmlvGgxiY2O97vPvhMJ6IIaYExImTJigBnsw2hTRFCIeK8rkl8YDTTfxJTNTXyi8NEc40EixSI00vdYz1+r1TAxnzhWI3jgIMeeOdRdnxPxqDGJ/NwH2X+QDeYA9ZikSNp2ofiaRptCVARn04vZkypQpak2SEVhHWLJkCQYNGoQ77rjDvY2FRgc6ny+MZLk2ybVNS5jpBU5r01H+Wof5CUW2kaXnXUQKgYSILQLqCSnaVitn1wENyZ8AvfTdmNXjlGhaRM8cgJjyyXodMxpoGPI2YFYPi2gKnYXrjmzBoD93SUmJuwKWAsjCmzVr1qjJUO+++26btqYWXPukLzijS6ZnmaZ9++234Xs+pnh5XJ6vNcFitMp100svvRQ//fSTKvS5/vrrMWfOHHdqtjM8/fTT+Pe//61eDy//+Mc/VDETq2i7ioimEBlFQO2U0/c40VwLNIx9Q6f5qoHYuMMQPS7X/WNblA1xJx0G7NeRp33S5yKaQpdh5ezOnTsxbNgw9Oqlv7FNnDgRX3/9NbZs2aLaTtiqweEZB5r2dOaZZ6r2FYorDQwovFZVrQUrclmZe+yxx6rzLVy4sMVx2K7y8ccfq1nG06ZNUxOqOESDRT9djSo5HYvPjeuxFFEWFvE96DKG0CkqKyv5Ea+uhfa54QaWAhnGLbe08sO/GYbRj6UH3LH1x99+u378tdd2v3f6qKP0c3/tNXMD/7nAMArmZhoF78Eo+GuMUf/HT1o8zv7ORqPgtlS9z11xhpFkGIbTMH78UR8vJyfkL+Wg/fusr683NmzYoK6Fnou/v2eJNIXwpWd/AvBb01KOPM6u6J4ZabrXNNczoHYAo7Wlj+3nHEQf4WtKC0TP6I/oLeb2wXY46/YBe5vTs6Wl3duPVxC6KyKaQnjSs4wD2BrGOoEz2fRlbqeIlno/3qpR6G6i6Wls4E7Pbgaa+D/TtD56/Qi1hulLVJ8UxOabM8FygKbElSpFm5Ojez4Zb+7fH6pXIgiChYimELK2C692E9rIfa4b9kETkT8DmASgHsDC1iNNFue145wVcVDUaNPJoljLN5Z6ac/5EmDPuAuIrZmOqNzW+xfi+h2jHWBsQOOQj5RoslWNwkmkV1MQQo+IphBU6uuBsjJ922skmFVox1niQ81/iVeY2/7pfQwKDo1JWL2+e3f3S83SEMXdZrYFaBz1kb5dBcRNmNHm42OmjwEqzGKg4d8DW5uPR0Q0BSH0iGgKQYVjrAj7MzMyPFKz75q3f+Gx84Wm3cYKc73T+kca1bwe6tMK1v16NDkbdOSP+vb+GMQcyW8MrRM9vR+wT0+DcA7eoUaJEWk7EYTwIaIpBBVrTY9RpnuwAnsOuT4ZBxhH16P+rbdQ88gjcDbsAWab+yz2Po61HtodRdO9nkkDk62Aa4j2wLPtTdPC2AbRU/NgK0hXt41+FSKaghABiI2eEDLRdGNGmcYxDpTMPgqO7StVo3/tP55Dr2tXIurdVOAr7+NYkWZ3GkbdwkJvD+BqrAT66oXZqF39EDXGdDhoBVtqPKLLh8KBYiDXAdf2WkQZyRJpCkIYkUhTCL1ofqGvalOfguPwlbrN5K+A69ytqPhEz+rDUrMoyCfS7E6i2SI9uwVoilkNmDMxY2oOgS2u2YSaGD52mrG2qfpGJuBo/ElVFkt6VhDCh4imEBLRdBuMcD1zBTOVJajefxtwgrmNYjEVaEx8DU291gF2Uzh7UnqWRUADvlDWeHx9cdlHuPf9+RPgyRHAvbHAq7MBl2nZGZs3kz0q6i+1sd/nKkUroikI4UNEUwhtpMm1zHKgLulV4PIGvW1TFLDKXCn4NVA75Bl9+6ueEWm6XzvbTUaYk+PLgZgJ2m+2vgx462KgbJuONLd+AHz/iN4tdtxooFLftg//GtgB5JqOe9KnKbTHMccc456TGUnYbDa888476K6IaAqhFc0f9FXdrL/rNGUdkNh0LZKNeQCb9aOB+lH/0q45X7Zc06QQdQcnHJoPWJXD7te+DXAOMvtGSuIQM0n3jnx+B1C3H+g1FjhZD77Hl3cCpVuBaK55luh+FcfQzSrSNG1DRTSFdnnrrbdw7733ehmoP/bYYyF71+bPn6+8X30pLCzEqaeeGrLnwakpHIbd2nPpDCKaQmhFczkzsVVwzliv72+LR9TdWbDd64RtoxlCHVWLBnyiW08czb2JcXG6V9M6ZiRTVaV7VInb2GAH4Oqvp0vYilMQNSEXtfuAVc/rH5/2DDDjBmDIcYDTDqz9PyBqTA5sxXrysCuvRImmZW7ASJPiLAitkZWVhdTU1IC/OXY6dnSBPn36ID5et1IFm4qKClxyySXKBD5QiGgKQbWRaxFt/QA0xPwbGKc/7aO/GwtbegpsvZIQ+8Gh2lavD1A/8kVdCLS5Za9md0jRFhbq6/R0c4YobdZ3OIFcPR4pqrgPbP3TsOkdnZLNmwoMnqXbciZdph+7YTFgy0xEVJmpkjn1SnitSJOfXdZwbyF0KMv9Wnt4Lh34luSZnuVtzrvkZBKmR63ZreTbb79VE04SExMxYMAANZCa8y09I1RGrBSftLQ0XHPNNe6xYiNHjlSTSoYOHaqmnDSZll2ckckB1T/++KP7fNzWWnp23bp1OO6449T5s7Oz1fE5HNvisssuw1lnnaVGe+Xl5al9rrvuOve52uPaa6/Fr3/9a8ycOROBQlpOhKDBkX3Wv2sVbTFqXA3UTfpfbZ9XD8QunYaEJ05VAuI6uQL2PR8Cgw3Yj/9UFc5wf4zTx6Bobt3aPYqBLNF0R5lFrH7d7a6cjXaOVx8eG9/U98ec3fzYUWcAUbFAyUZg/wbuOwxOLgZnuWBsb0RSUjySkoC6Oh1tpqWF+MUd7NQ1oSZlQVhOnVJzG5Ac16lU7aRJk5QgXX311e7tnIXJ8V333XcfXnjhBezfv1+N++LlxRdfdO9HweLIsHnz5rm3MYqlEHKMGIWPx+W2W265Beeff76aj/nRRx/hs88+U/un8xukDxTnk08+WYna8uXLsW/fPlx11VXq/JbIEs7ZpGDyetu2ber4TLd6vhZf+Py3b9+O//u//1OvL1BIpCkEDSuNysIVplZVEVA90HSMubC5Mwaxw6ci5qIJiDlmMGJOGg/bT3qdzxhXCSf2adH0KQbasaP7iKZleYftQFPaD9pz1gDikqejvhzYYbbfjPUQzYQMYNhJ+vb6xUBMqtl2kgo49vysHm9Fm+YsYUE4YKo2OjpaiRrTo7yQBQsWqEHQjEg5WPrwww9XA6VffvllNDSYhXqAigRvuukmNYuTF3LnnXeq/RmJnnHGGbj55pvx+uuvq58xakxJSVFridb5uM2XV199VZ2H5xs/frw6D2dp/utf/0Kxh09kZmam2j569GicfvrpmD17Nj7/nObVrcPB07feeqsSTD6HQCKRphA0WqRmN3E9swwYRRdyIGrtQMT9eqI7VRR7yUTE3j8B9tML1RSQxvhPkLSqedK6ZfhuVaV2q0hzB2AfbFY21QKxww/BlvcBlwPIHQ9kj/R+/JhfAVvfB37+GJhx+jTUMW0dDdhTfkBs5Vi1rsmIWypow0BSrI74wnTuQML06dq1a/HKK6+4tzEFzCHOO3bswJgxY9Q2DnL2ZdGiRUpgGa0ynepwOFT6tiNs3LhRRcDJyc1DC4444gh1/s2bN6O32V81btw4JfoWjDoZ3baG0+lUKVmmh5k+DjQimkLQKCryibY2Avb4bwGz3id29QTE3De6+R/jGaMQff0hQO0nQDJQP24hktZcrPs4bc39jpbTTncTzaahK8zqBBuiR/fFLtO3fXgrhYQDjzSPswqwXT9SCS3SAPvA/yJ572VSQRtG1Je8TqRIIxGK3dy5c9U6pi8DPcYSeYoa+f7771WESmFiepWp19deew0PP/wwgkGse+JB8++Awtoa1dXVWLFiBVavXq3SvIT78ssAo85PPvlERbSdRURTCBpWdsVTNOtHvqkXBeqA2MQjEDXYcnEHbAkxSJh9OOoLYoARDtinfwusYhoXwJBmZ53uGmk6B5qLsSXxiDoqG3vu1ncHNHscuMkaASRkAg3lQHlTJlATBaS54BiwTg3tlrYToaPExcWpKMyTKVOmYMOGDRhuDa31kyVLlmDQoEG444473NtYaHSg8/nCSJZrl1zbtISZLSJRUVEYNWoUOgOjXd8o9JlnnsEXX3yBN954A0OGDEFXkDVNIXSR5ibAPulrfXtfFOLOmNbiMdEnDoNtsxmKjquCQXVdo+92p0jTeu1u0dwOGHnapcBWlAZ7dib2m103A1op7GMw0/8wfTu/MBMo09+0nXl7gb0imkLH4drjN998g/z8fJSYi+GsgKUAMiJbs2aNWgt899133RFaW4wYMQK7d+9W0SXTs0zTvv322y3OxxQvj8vzNTbqynFPGK0mJCTg0ksvVYVDLPS5/vrrMWfOHHdqtqNQcLk+6nnJzc1V5+Ft36i5w8fv0qMFwV/RZMvFBgOuUbo6yLYzHdHHmJU9HkTPGoSYNdoph+ua9qhVKkL1FE32QPLSnSJNY7sLyNGlxNEVfZG/Votg5jAg2fyO4IslmrvXJsBWlqKP07vcK9KUQiDBX+655x7s3LlTFfL0Mv8BTZw4EV9//TW2bNmi2k4mT56sqmRZEdseZ555pmpfobiyipXCy5YTT84++2xVmXvssceq8y1cuLDlEm1SEj7++GOUlZVh2rRpOOecc1RPJYt+IhYjzDz11FPGoEGDjPj4eGP69OnGsmXL2t3/9ddfN0aNGqX2Hz9+vPH+++97/fzNN980TjzxRCMrK4srYcbq1atbHGPWrFnqZ56XuXPnduh5V1ZWqsfxWmido45iU5lhLFpkGMZew3CgwCh4GUbBezD2nT7ZcFU3tv7eTrzLKHhT71cx6DbDuLj5ZxkZ+pjr10f2u249zw0bDMOwG4bDlm8UvK5fU+mvLzK+uNsw5sMw3prT9jG2fqT3eXyYYRRfNU49tuBpm2FcbRh//7s+/uzZoXxV3YdA/n3W19cbGzZsUNdCz8Xf33OHI02G2ywPZrPrbbfdhkceeUSF1J7lyf7C6qsbb7xR9f6sWrVKVVFxUZm9Oq3BbzMXXnghrrzySrXIy4ZXXhjWWzA3fuSRR+KBBx5o99zs76Gdk3V58MEHO/z8Bf/WNFWWhanZlKWAuYQZWzUTtpTWiyliZxwKFtkS+7hP3ZEm6Q7rmnQCqqjwiDT3Ak1JP+p2E671ZByKvUv07QGHt32cftP1dfnPQJTDrALMNGDsbpQ1TUEIE34XArEk+fHHH1dVScw1M3xn3w3Daua0mS9mfpo5ci4Q+wMFl+J1+eWXq/vPPfcc3n//fdVkyx4bX3h+hvt//OMf1X0K96effqpCeT6WMBdOmIZoD6YFrF4lf2A+3jMnXxXp+cFIS89+BjQO+1BvqAXih89q83Exxw4BtiYCvevhHLUZ4DKoRwUt1/gjeV3Tet0JCdoRCGsBe79v9cYGIGboISh8zVsYWyMxE8gYDFTsBBzOyQDeBpLYq7kbvXqNUPtIy4kghBa/Ik3mubnQSzsjVkgxMlu5cqWyX2LlFQWEi8cs62U/z+LFi/3yL+QxTjjhhOYnExWl7rOcuTW43XN/wsi0rf0P9CUgJydHLQwzYq6jvUo7sAmYZdXWhXZTQtvw7bS+VyjR3AY0DTdNDcqiED1DN0i3RvQRAxG1U1vHGYOrYdQ2qWiNWG97JIum53qmakHdAzQNWq43VgFN2XlqsoktWpu0t4f185qGKXp8WhTgqFslkaYgRLJo3n///Vi2bBl++9vftioWNN+ltyGjvU2bNikfwgPBaiqWI/tWSPF+kfVV3Qdu78j+bcHGVzpFMK1MwaT7xMUXNzfRtwb3q6ysdF/2RPKndgSlZhltqX5ntlwMMkvSixMQPcNzKrU3tgFpiNpt9m/25TjJDS2KgSI5Pdui3WQv4Oz3s5lrjUFJY6a6mT0CiDFTtm2RY4pmaf1Q1aZD7GnLkKPrgkCLzk6sjAiCEMz0LKM5f6GZLi+RjGU4TCZMmKDcJVixxTSzZRHV2heDUDnz97QeTRVt7QCMo3XoGVWYiahxbZSMmo3L8bFHweH8VHnU2nt/hriNk4CTul+kqdgDOPvsN78tJqLIrhd2cycc+Fi9tCELCkuyMbDGBqQYcORtQFYtQHcwjkljBa170LUgCEGl0+YGLNbhxdeVgSXM/sDUKG2RPP0FCe+3tdbI7R3Z319mzJihrmkE3JZoCh3DCv5VYsAAXNsrgFz9byWmahRsMTrJUbQG2PxvPelj0hwg00xSxI47FGAxTTbQOOZTpGy8qdtFmu5/lhT4Y0zrwPIsFBfG+S+aZqS5Z1caZlRFA30ccPbeBVsBv6DqLycimoIQOjpcPct1SK4DMjqjQLJHh2ue1rW/0C1i6tSpXqa7FGDeb2uMC7f7mvSyEKirY1/YfEv4moQgFAGVcdrJKsAcchAbrxsQa/cD/zoR+Opu4Ov5wKunA03mDMqYKf2B/ebw5WHr3SPCumOkaeyyA1naGSW6YTCK1+rtvf34fpljRpplhfFApc50uHL2q5SvldApMyuNBUGIwEjziiuuUCa4//jHP9R6oudcto7CdhM6QbB4aPr06WqqOFtGrGpazm/r16+fKsIhN9xwA2bNmqX8DelyTzcKVvM+/7w5xVd9gJQpp4oC0y2cpr/EctpnCpbO+qeddppKI9OsmE26Rx99tN9RstBB0dwONA76WG9oAGIH6S85H/4OqCsBsoYD9ho9CuuzPwGnPgFETe4D28oUGKPL4Rq4H5xJ7Rlpco4kC40icSyWr2iy2pW+sSQ6ZiL2m+uzvf2INBPSgdS+QHWBDbbKNBiohZFdAxRzcoXep7Q0KC9DEIRAiCbnk7355psd9ipsDc5E4/w2OlCwmIfRKuevWcU+FD9W1FpwDA0FjyNpbr/9dmXlxGGmjHwt3nvvPbfokgsuuEBdsxd0/vz5KsLlfDdLoFnYROcKHlMIku8sJ3yM+E5vqLAhZvwQ7F0KrH9dV5Ces0hHna+cAvzwFDDzJiB9ZDai8vPgRDnQpxHGnibYGmJBB6zMTKC8XEeb48xZmxErmhyFZqzWf2kuwBk9Bc5GIDZZt5P4A1O01QWAUc114EIgww7skkhTELqFaLJghuNkAiGaxBp42hpfffVVi23nnnuuurQF22J4aQuKJG2jhBCuae4AHIPMIZj74xA1sxd++oe+O/4CIG+Kvj34WGDnl8C6V4GjbotCdNNEOFk5m8351T8jdsdoYIyONimaXNeMeNGksUE/syWqHqiNHusu8LH5uTjCFO32zwB75VDE4UcgzYBR4ERWlh6VJJGm0BrsaGAgwgAhkrDZbMqnlsY0B4Vo/u///q/bXJcRnu/IFnoSCoLVdM8B1PycN/rphTdbcQpsw7Kw8Q3983HnNb9XEy4yRfMV4Mhbgbi0w2F3vQbEAfacbxC7TYsm1zUj1eCA1azWa1eiuR5w9DMnLlTbUO7Q/afZHRjgQH9aUls2EXE0OEgBnLsLkT1d56plTVNojbfeesvr85kG6hw2zUsomD9/vsoEWjUjFuzz51DpYMKAi563vvDcXS0c7bBo0kiAo1s+/NB0d/H5BnGgUTDCwYElHByWzEgTk7SbUlR1HxT8GIOqvUBcCjDspObHjD0b+OC3UNM/WCyTOWYiUA1VQNQ4/FMk/3xNxFvp0QGSrrCcl6s8sdlukme6U1XGoLjS7NHswGxcq6J4f8EUuuipYdRNVT8iO1uLpkSaQmtkWYveAcZut6tlrs7SVdHqCKxp8RyMzWknIa+e5dgWGgFQsVnt6nkRwRQsrOkbFA7Xz9VABj/tgRjbaGx4U/9s5Bnezf0JGcDI0/XtjW8B0WPzgFKdgnQM+1G5CkX6iDArNcu0tFqO3wO4cs03oywBhflpHRdNc/xfYf4IVUhFmqJ/cBcCSaQZWjjM2FVbG5YLz92R9KwVVfI23dxY9MjgxrOAk85unHBCW1QuX3EgNes9PCNUWpayMDMtLc3d507LVBaF0pKUhjacctLUpCf5cEYmB1RzKc86H7cR3mYEasHZlxwKzfOzOJPH53BsCy63MZX70EMPqQ4H7nPddde5z9UeFEmrCJQXzxqZkEWapaWl6o3v7KwzoefDFKX1Qd4rB3AUb1QpRRKbOQO7zCVlSyA9GXayFkzuM2tODrAkERhaA+fAQmA1Ij7SbM3YwBimPwCiKtNRsi26w6KZYYpmWS2HUdOUFnCkr0OOaX4vkWZoMerqUJxi/oMOMb1ramDrxDxIpmo5EIOCRL9vC3YT0M/7vvvuU57fLMy06kxefPFF934ULBZszps3z70tNTVVCSF9yCl8PC633XLLLarIk0t4LOxk4SWh/agvFGea57BtcPny5ar3/6qrrlLnt0SW0L2Ngslr9tPz+Fyv9XwtrcF96BnOpUSmi484opWJ7x2kw7L7q1/9Sj1xQWgLSzD5ZZbBkD37v3pDExCVNxVFq9ue8DHI9HFnda2zbwaiCvQaIPJqu1Wk6e7R3G0AmQ51O6q+L2rNAT5Z2m/dL+KS9czNavatVGvRdfbaid5msCCRpuBPqpZmMhQ1K+oibOfjoA1GpOxGYIcCfcY5ycpzchUjwZtuukmZv1gGMOw44P6MRM844wzcfPPNeP3119XPGDWmpKQgJibGfT5u84XdEDwPz0dh43k4gIPWpp5GNlwD5fbRo0fj9NNPVy2Hvj37nlBgaevKTg9eGEEz2uY0rZBHmgzH6cPKkJ4WdL6FQAzthYMbaz2T6cPoQsA+2Gw3YW9l1EC4HEBybyC9lWE4jMD4s9pioHBVFJJrR8COnUC2AdeOSkQ5aJbffSJNY2e529TBaNR+uil5QHxqx47LaDN/XyJQzb83J1zZ+yyDJYk0Q4wtKUlFfOE6dyBh+pS96hxg4ZV+drnUGMgxY7S7BnvpWxvt+MQTT6holelUh8PhtX7oDxs3blQRcLJH9MxokOfneqSV0Rw3bpwSfU9RZHTbFqNGjVIXC4o7n+ejjz6qBDnk1bP8BsG2Dd/WDeaqRTQFryKgvaweNe18yqNRsE8XwgyYaXrS+sBtg44GNiwGdn4NTEqcCjs+VeldR9QGxO2Z6WVwUFlpjt+KVGODfZtVOpXY6w9xG7V3FBYD5S+zAVU8WANcmVXIbGyONLnU1QWfEaEDqDW6TqRIIxGK3dy5c1v93B44cKD7tqeoWQWhjFC5bsn0KlOvNJuh8Uww8A3O+DvwtXA9EDTQYbDXVTosmvz2IQj+FgFRNF15ppKUJmDHFq1w/bSTXqtYorn7G+DQadNVWhexQGPf/yJu10wkDdFRLMWCKdpIFE2V/aoG7MnL9AY7UFWvLYCyOrCe6buu6arKQBQNH9IbkFbXvIbMLxCR6I4kRA6sePUt1pwyZYoa79jRvvslS5aoucl33HGHexsLjQ50Pl8YyXLtkmubljCzO4MFO56RYiBg60sgrFK7XkokCAeINI1csxCmIgN7ftDf0/q3I5oDj2pe14weM0zNoCRNg75VTjiRvK7pFWnuAewDzBmitUBpTd8uRZrEUWEW4KU5EFemR68RKQYSDgTXHr/55hvk5+er0YxWBSwFkIU3FJWtW7eq2chtGc5YcP2Tjm2MLpn2ZJqWhgW+52OQxePyfCzI8YXRakJCgrv3n/Uy7NCYM2dOl4pNaejA18GiIR6Xa7ZffPGFqroNuWjymwN9ZzmTkgOhuXDreREEz0hTFcJk69JwW80A1Z9JJ5y+LZdIvGzjouOBxiqgLilbpXWJY9DmFqKZnx/Zounsu1VvqIpCSUW6l1lBR7DaTupLTO+9FANGoUtM2wW/ueeee7Bz505VyNNLpYH0VCous23ZskW1nXDoBqtkWRHbHmeeeabqoqC4skKVwsuWE09oT8rKXJoM8HwLFy5scRy2q3z88cfKM3zatGk455xzlOsci3662kvKwiXW3dCvnGu3rOLlsUOenqVpOsNpVi+x2qkrhu1Cz480jSVV7kIYl328O2piRWhbRMcCueOBwpVAcVUW0ksSgeE1cOYVuUWzX7/IE02uK1r2gUo0fwKcuaaKVsSisDDNSwA7k54t3TtOv51JgGt3KbKyeqn3QCJN4UA2pIcddpgSD18oVp98Yk5EaAUKbWs8+OCD6uKJp9sQ5w+/8YZp/eWBb68phY1RYFt4tp5YHMgakG0vvASDDosmw3GWFXNKiCAcKNJsKtykBkmT+oZpersffrF9DtGiWbAtEZn7s+Big2LvGmBl5Iomhcvqt1ZrmuzRzKpU920VidhfmuIlgB2Bk05ISdEkqExtDNC0fzOys3XEIG0nghAaOpye5eJuoMzahZ4dadLYwI6l+k4TUFIx0Wuwcnv0MUezFq8BouvNBb0cF4wd9RErmlZqlnMulcsY11szzF63KjoR2JTrUWInbDdj4nUrTkU156jpbQ7XKhkPJgiRLprMEz/++OMdsnMSDk7R7EPnmhwzNKwBikr7dijSJIWcqhVrKmg60JS/TY3YimTR9HQDQro2NkBdXqejTIu0/kCNKwswq2abEtbKmqYghJgOp2fZ58IKJxq2s+HUt3+Gdk3CwY2Vns1zAo68LfpOdRT27M7wO9LszaDUBlRTFFOnsZ9fGZXbM5Yhbt+EbiGarl21gGli4Kgb0en1TIv0AcCulSlArU15+TrTfkaOuV4sa5qCEKGimZGRgV/+8pfBeTZCt4cJCHchUAPg6mWqWmUsSspTlBDmaGOcdqFjTtZwoGwrUBs7ClH0j04DmgZ8D+y6Cv2GNws0K9njzXXTcOJVBMRK86LdbmODuqpxXY40U/tzJGcSUM0/2ya4cgrQ32w5kTVNQYgw0ayrq1PlwZ4mvoLgC93F7OaaW0YdUJZTru9UJsFAlKqcjW1pQdkqrKClaJY1ZSOnKgpIc8HZf4OqoM2aroWSgllQAAzpghgFJdKsAZri1qovCUwnV5RP6LJoMtJUB6ziN4QmuDJL0cd0FpNIUxAibE0zJydHGeU+//zzXka6guCJFWXSmzmeepllFsJUZvmdmnX/mzMj0qKKLKBCf79z9t6rRJOdTpGWovUSzUKmplfoDfVAcengLqdnuaZJXJW6CtfIqBXTdkGIVNHctGmT8hhkuwntk2bMmIH/9//+X7umucJBXDnLTgiKSLq20XJUaJf17A44Y+Vor2gU7EqBrVQ3drpyyyK2V9PLQq8QaOq9UW+otaFof0ZACoGIo9wsv01vQpZZZySRpiBEmGjSvJf2RnRVYKTJJlYKJl0kOIDUsimSQdQHN17Dp3dXqnVIUluq1/SyhnU80izZbENUjTkiLLsh4kVTRZoFNDbYrTdUR6GsTlfsZJiGPp0hzZzu0lhiNm2mOJFh9oXKmqYghIZOec/S0f7CCy9URgccWvq3v/1NieXll1+u7JI8x8wIB68bUFPxZrexQeneqV4eqv6QY0alNUWAzW6qTaYLxs6mbiGaHN+lqIxDAxLVTEx/13PbMzioKTHD1SQgpVZH8uXlQAeHPgg9HM6P9HToiRRsNhveeecddFe6bNjOlpMTTzwRTz75pHK552BQztwUDk683IAczcYGBbuaLfT8JT4NSDWF0dWkjRHYwuHYtSfiRJNTRmprvdc0jWztNG+r4hqkDenNk5Y6hWVwUG5G7azMjS/VbzgFk2PSBMGz/e/ee+/1MlA/kP1cIJk/f77ypfWlsLAQp556atDPT4N4TmHhciIt/fj6X3jhhdC3nLRXXbtixQocffTRgTqk0J0jzWygKcmckl4LlNfnKaP2jgoHU7Ts1ayvn4J4l2kfF70asRVDYXlKR4JoWlFmSoq+MNLENF1GbFTrIqiuiqa1rlmxabz7K6+rfAuSk3srwea6ZmYn3IaEnkkW5+cFAbvdrpzhOksftegffM477zy1lMgBI3Sxo1h3dAZnUEeDcaQM3eyFgxsr0uyfBjhztuk71VGoRpoSjegO/q1Z65rlDaNUFSppGqBHhEVSpOlrbGAUGO4iqKZqvRiZFgjR7AeU1w1tttJrXCOuQCGGbmiuhtqwXDrixOaZnuVtZgI5mUQN0fYYtEHDGtamJCYmYsCAAWogNedbWjBCY8R6ySWXIC0tDddcc417rBizimxFZF0Lp5w0mebLNFnngGoaxFvns4zXfdOzrI3hhCyePzs7Wx2fw7EtLrvsMpx11ll46KGH1DxM7sMRX9a5WuOjjz5S01s++OADNY2Lr2HmzJk44ogjEDGRpiB4Rpr9YyiaBaZoRqMWKRjcgdSsbwXtvooc9Km2AckGmvqtBXYD/cyAi32a/CwJ58CdFqK5txrQnSGoqxodsEgzJQ8oNtL1F4g4wBG9UYnm7t1SQRsqjMY6FF9h/nJDTO8XamBLaGdEUDup2kmTJilBuvrqq93bOQuT47vuu+8+lbpkjQrHffHi2ZNPweLIsHnz5rm3paamKiHkGDEKH4/LbZwucv7556s5lhQvFo9atTC+UJzZlUFBW758Ofbt24errrpKnd9zugld6CiYvOaMTB6fqV/P1+LJe++9h0MPPVRNYfnXv/6lBlxznBnFn+IcEtE8UKgvVbOCp2j2tQFGpmlsUJWgjA0yOiGadAUihfsyMJG9mn2a4MzbqSLNvifpn9HggKlJNfQ6QkTTuX8HYLr1lBdPDpxo9qFeJgN1NiDdgDNhu9u0XSpohfY+v6Ojo5WoeaZHFyxYoAZBWxEph0tzoDRnUD777LNqQDRhJEjfcU/uvPNO921GcjfffLMqDqVoUphSUlIQExPTbjr21VdfRUNDA15++WUlbISzNM844ww88MAD7kHUmZmZajtfw+jRo9VoStbPtCWa27dvVxE0nz+HY3MI9m9/+1uUlpZ22aAnpiOLqr/5zW/U7LPWYOjPcFw4uHEXAjnYfK/zqa5Kc45kF0SzYHcqUMY/4CYYvUuUaNIRiELJczJFGzGiSVekxNV6gwMo3DshoJFmI0uSa2gF5IArvQB9rArl0q4fXzgwtvgkFfGF69yBhOnTtWvXenU8qPSzy4UdO3ZgzBid6mHU5suiRYuUwDJaZTrV4XCo9G1H2Lhxo4qALcEkTKHy/Js3b3aLJn3OKZgWjDrb8wjg45kG5uuyItxHHnlEDbl+5plnuhRt+i2aDIWZ77700kvbfPNFNAUr0sxsBFy99cKbo7xXh3s0LSg0tmigqTEKtsoMGKiGkV0H/KB/znVNiiZTtJMmRY4bUFOeOd2lHigsHhAw0UxVkawNqOGgBAdcGaUYaFbNSqQZGtQaXSdSpJEIxW7u3LlqHbO13nwLT1Ej33//vYpQ+ZnP9CqFiVHmww8/jGDgOxiEv4P2inooqv369fNKCfMLAL8Q7N27V0XUQRdNhsMVFRXthv9cKBYOXrgub7U9pNYYqEzVRQv1+wZ22g0nOhbIGASUbwdsNQNgcN5WpgPGTgM22JRochh9uIuBfEXT2XuT3lBjQw3SEM12Ef3docuRJnFVJyIK9XClV6OfWSAlkabQHqx49V1GmzJlCjZs2NDhGclLlixRrRxs6fDMNh7ofL5QyLh2ybVNS5i/++47REVFYdSoDtiH+cBodfHixepLAdPEZMuWLeq4/fub1lrBrp69/fbbvRaBfWEUKmbuBzdWajYqCojfVwUuvZHygnFdirSsFK2j1uxPTAdcO7RxQKRU0HpNOKEbUK897iIoGhuoiDkqUJEm4KwwZ46lNaK3+dVXIk2hPbju+M033yA/P1+t8VkVsBRAFt6sWbNGdUG8++676n57jBgxArt371bRJdOzTNNy7dD3fEzx8rg8H5f4fGG0ynVHZjBZOMRCHzrPzZkzx52a7Qy//vWvVZUtDXf4pYCv+49//COuuOKKLhcCBazlRBAs0WQ1p2PfVsDMqJQVTVatJp2NtDLNtG5tpXYV4pKeve4n1XYRKaLp5TtLN6Ac881QE0m6bmxgQVch0lRuLuCmOtDL/CuWSFNoj3vuuQc7d+7EsGHDlHMbmThxomrNYBTGtpPJkyerKllWxLbHmWeeqdpXKK5cuqPwsuXEk7PPPltV5rIVkedbuHBhi+OwXeXjjz9GWVkZpk2bptYcjz/+eFX00xUYXX766acqO8r1WIozi4so7l3Fr/Ts0qVLcdhhh/ltcsBvF1y4FQ5iCz27OeGjCSirGIO0wZ2PtCzRLKsaj1R+WY0Hmvp+h8SC4yNCNPkF2ory3G5AmWafW1Wqx1ivrsMvH0k5QENZXyRhJZDsQpbZuieRpuDJV1995XWfn+GsPfGFYvXJJ5+0+eZRaFvjwQcfVBdPPG376MLzxhtvtHicb68pi0vpW94Wnq0nFv44G7HKlsIZaPz6GGOozMVe5og9m149YQjMFC6/xaxcaRZB+MHTTz+twniG6Jyc8sMPZoVHG/A58M3g/nyz2bzq24900kknqdCci8VMDfjCEmc2x3IffiPhNyIZdxbYCSeOOPN9rwOqXTldirSs9Oy+ij5Atb7d1H8lkB8ZkaaVmqVJimr/YHtqhi6Cclbpb/SWHWAg4LpmdalZyJAEpDfqc0mkKQjBxy/RpCCyEIh9ORkZGSqKpN8sw90jjzxSzdrkgjIjTH5j8bcgiCXLN954o1orXbVqlSo9pjizwbU1mAKgUfyVV16J1atXK5cIXpgLt6Co8zmxx6ctmFb497//rQSYqYmCggL86le/8us5C360mzA9m2q6AdXalLGBNaGjM1hVtwWF6UClLjt39t0G7I0M0fRMzdJgwcg3gFRd2WevGOhlth4IuK5Zsd90dkgAkqr1E5BIUxCCT4y/5b4sSeaF/rJsGmWlVH19vRI6ihDz1h31OmTfDJtTuVhLnnvuObz//vvKmeLWW29tsf/jjz+ucuRc0CV0d2D4zfw3H2tFxe2lFCorK5UXIZtq2bBLWMDEKq6OpKGFtiPNgamAK6q5EKYOyV0STau/s7QmHSjnGmEdXH2KtWie0CzYTJOydzPsbkD55W43oKqScQEXTUaaZV+NBajLUUBs4wYAg8DidhYrerSzCYIQYDpso8dF1dYaXTtj+ss07m233ebexnJg+gSyB6g1uJ2RqSeMTDsyZobnpGchz2PBdC97knj8tkSTlV+e1V9VVXqChdCMFekMjAdcKaXehTBdEM3YJD3do7Y4FrayNBiog5FTrUST39MolPzVsFdzSBeGPAdKNB2l25pHouUfEnjR7AMU2fvR5UBNOrFhLQA9NYItP0Hy6RYEIZzVsyxBZg+Pb1kx7xdZi0Q+cHtH9m/rGOwfYpq5I8eh3RQbZa0LW2wEb9zFMNEshKlTt10VOuTqSqRJ2KupqDKVKcuuRJPp0HCnaH3dgJpSmougCveMDUqkWcdQtkHfd9q2Isk0immnlVoQhAAgLSd+woiYqV3rsmePmX4UWoim+lqTbroBlWUHpHo03RRNR/XI5l7N3drKLKJEk25AfZqLoCrsecrAh9FhINc0lf9svXaod8XudY8E4zBqQRB6oGiyeIhegr5Vq7zflsEvt3dk/7aOwdSwr7vRgY7D8mn6KnpehNZFM8vBcEg7gTSU6Miwq32KlmjWV2rzc2qGM39HRIgm08JEtbYVAI7eW/SGGhZBpSKlNxAVwHlCTFU72ARbpxcvXUmFIpqC0NNFkynSqVOnKqd6C3oJ8j7HxLQGt3vuT1gI1Nb+rcFzsrDJ8zg0Bqa7RUeOI7QtmhkNTtUKQWpKhyEuBYhvORWoU+nZ8vJJgOnMZXetUrfDLZotLPR67dUbqmPQgISApmY9DQ6MWq3ErpRy9DLfX4k0BSG4hHWeJot6aJ/EwqLp06erhlW2jFjVtGxdoeku1xPJDTfcoEbW0BSYLTC0cGI17/PPP+8+Jp0lKIBsI7EEkTCK5IXrkWxZ4blZ7cuIkbZNFEypnA2MaCZV7EeT6VRVvn+8Ws/s6qxLK1LdXzkYA7hcmso06HKg+NLIEs1NgJFtvhFVnMpiC55o1sTDhgYYaTXoL2uaghC5oskojRf2U/o6zbNdxF84SJRDT2nbxCIc2jFxaKlV7EPxY0WtxeGHH65aRdgvSiMF+h+ycnb8+PFew0ct0SUXXHCBumYv6Pz589XtRx99VB2XpgasiGUFLsfFCJ2H/wysKCeufgOazF9b2f6JSDu86++slZ4tLssAOIw61YAjb2PYezUdDsBqK1bpWU83IHMkWkqARTMxU6d7XdXJiEIljNR69Ldmd8qapmByzDHHqM9Uf9xzQonNZlM+teyxPyhEk6Ng6GHI6JDjV/gGdAVrSrg/NlDk3HPPVZe2uOyyy9SlPegmRCciXoTAwA4c9/cnwyyEaQQq6gchNwCiYaVn91ekA1UxQN8mOHvvDrsrEJfY6QrG3khl58kEx+Am9TNHlQ4JAx1p0o4wia5LVemI4QmTHciL0z8T0RQ83dE8R2rReY02d55Wd8Fk/vz5KqjxdWUrLOQavFm5FiSoAf/85z9bbB87dizWr18fWtGkiQC9AC0TAUHwSs0mAa6YjfpOPVBnpLnHWXWFhAwgPg1oYMqzgk2QTTBySnWkadYGMSNPAetqKrgzqVkmR5gUMfJdQJr21rRXDA6KaFopWntFDg2BgGQnck1DA2k5ESw6ajbjL3a7XdWkdJaOFG52Fhrh3H///e77HJBNI572Aq6gFQLxDWOaVBBarZzNAhyJ2/WdOpvqJwyUaOgUrQ22Kl31YmTVKNG0BjLQ4CDU/qtelbPsmdy73z0SrdK0uguGaLIit77SDLETDWSbXxQk0gw+NBx3OWrDcvE1Oz9QetaKKnmbLm50b1NDtD2+WdLhjRNOODKL/ed0fvP0GGeESvc11pikpaXhmmuucY8VGzlypJpUMnToUDXlhMYxhIEVs5I0iLfOZxmv87anIc26deuUOxvPTz9wHp9zMD2jRqZyH3roIZXd5D70DrfO1RqsXbHqWHhh7Ut5ebnX0l3IIs2rrrpKrSv6joERDm4s0eyXCbjSTSWpiUYTYgMSaVop2n3rAKOKa975QIYDWKeN0pkapY0fU7ScshI2N6CKTe6RaPv3TApqpFmzeqjuiU0EsprYFxsnohkCDGcdij80fRJDTO9Ta2CLMb+VdTBVy0iLgkTrUgvOwqQ16X333afqUVhjYi2Zec5HpmCx9mSex0zl1NRUJYQcI0bh43G57ZZbblH1KvQEZ43KZ5995hYyXyjOrClhIeby5ctVnQw1huf3nG7COZsUTF5v27ZNHZ/rtZ6vpT1onUoXOA7ODrlockIIq1X5RnAWm2fO3PKTFQ5e0RySArgydDWKUR0X0OrRNLOCtql6GGKxSqVBjT2NsCFerWtaojlJa1V43IBSzQk/dqCoYHTQRDMpF6go025DtOxLr2c1Un9JzwptpmrZF09R80yPsjOBsyatiJTFlZw5yS6FZ599VtV/EEaCN910k9cxWZDpGY3efPPNqqOBosmokROkYmJi2k3HMgCjprz88stITtZfBuglzmEgHLphFYVyDZTb+Rpoe8ruCRaj+iOa7KT48MMP1bkCQYdFc+3atUrhied0EdLVoiChB/jOJgJGhk6tuCqT3A42gcAqBqotm4QMLFZpUMfuPYjFcCWarDcIdTGQV3q2EHDkmfMKa4FqZy9V5drZ4dsHSs/+XDYKYLbOBiQ5NynRlPRs8LFFJ6mIL1znDiRMn/Iz/ZVXXvFOP7tcamoVB1mQ1vzGFy1apASW0SrTqVw37Kjpy8aNG1UEbAkmOeKII9T52S5oiSYna1EwLRh1Mrr1BxYE0TY1UNW6HRZNhseC0JZo9mVwmaaN7Z2sdDW9UgOB1XZSVjwRGeaED0fDasQaWjRJqEXTK9IsAJy55ki0mijU0A2ILnpRQUrPNvZVES0jzdgofoE9QUQzBKg1uk6kSCMRit3cuXPVOqYvHGJh4SlqhMMtGKFy3ZLpVaZeGWWyhz4Y+GY0+TvwbXdsDX4BYNqZhatdKV6KGHMDoeeJZp/oZgu9pvJcVfUaaxodBCrSLCoZiqH12kqvqdcPSCw9NzJEU7kBmaFndQwakYCcIKRmLdGst0zb4ynMW93Vs6GuIBa6BxQNDsnwhHOQOS95+HBz0rufLFmyRK0P3nHHHe5tLDQ60Pl8YSTLtUuubVrC/N1336k++lGjRqGrcF4y10BpaBMoxLBdCKho9mK+MFlX+NWVDgzoep4Vae4vzVS+rqSp7/qwGhz4+s4aWaa7QGViUNyAPP1nG1gBZJq2I36X22zBo/BRELzWHb/55hvk5+erKVNWBSwFkIU37KfcunUr3n333TZ75y249knzGUaXTM8yTUvDAt/zMcXL4/J8nqMVLRitct2UznBc7mMmkw5tjAx9J1p1BhYAzZgxw8sAp6uIaAoBFc1se43bd7Zy/5iApWatdbzoOKDaSAOq9PqGM3dX2AwO+CXamh9gRZrWSDSjSq/tBE00cy3Tdv0n7EoshJXBknVNoTVoSrNz504MGzYMvZQTB1QxJ6OxLVu2qLaTyZMnqypZVsS2x5lnnqnaVyiurHGh8Pp2VNBxjZW5xx57rDrfwoULWxyH7Soff/yxsj+dNm0azjnnHBx//PGq6KercBrVm2++GdAok0h6VggIVn9kun2Hu+WibP8kpE4P3BvMtUH62Jb/nGwaHDjg6rVPR5qHh140Wa3LZRWmQnNp/sOocxhHvACOyt7BFU2zuMioi4ENTriSy5CVDhSX6BStjHsVfB3V6K3Nwh9fKFaffPJJm28YhbY1HnzwQXXxxNNtiJOh3njjjRaP8+01nTBhAr744os2z+/ZemLhjzUg11nr6vSX2EAikaYQ0EgzwWZaZjmA8sqRAY00m9c1bUCl7pMzsqq90rMU7wZzOHOoUrPMIsXEAMZeh/LEJY3lQ4MqmjEJenKMUc0vD4CRVo1BMulEEIKOiKYQUNGMiTUt9BqBGmdOwEXDWtdEhRlqZdqVaNLKMj7eW8xCbWzg3FvU7Aa0L3huQBZJOYCrRldZ0bR9oHluSc8KQvAQ0RS6DLMtlmgiwWy5qGOrYgpS+gRHNO2VOpJTBge7HSpFGup1TV/RbKrdAEQH3w3IUzSd5topUuzob1Ypi/+sIAQPEU2hy9AmklWbxEjco2/UR6nqThbvBBJrrmZNiVkNlwo4d2v1CrVoelXO8j1IW643NADF+0bqp2c+p2CQlM0vD6ZnYLJTJp0IQggQ0RS6jBVlJsYBrtT9+k4Na8xsqjUikFi9miV7tSsVI7umau0MEtZIs5BDsU2Hkjqg2pWt1h3ZpxrMSLOhwgxzkwz0Nsv6JD0bHPxpphd6/u9XqmeFgInm0AzASK/y8J3VrRGBxD2MumgkRtLgIBFoyvgBidWnhVc0lRvQz3pDdRRqkapSs8E0GUjMAWrWDIFa3U1kjywbyaMlPRtg2KTPZnt6mLJ1gvfFMrTnwGpeTu+iWT1/zwdyDhLRFAInmqms4tQl3q7qJOW7mhjgWbNppjBWNGYpf1eKhfJ7DUOvpq/vrCunSG+ojkUj4tE7iOuZVqRZUaa9QREH5DSxYb23RJoBhh+kQ4YMUcOTKZxCz4Q9o7QO5O+7PUQ0hYCJ5iBWb6bYzT7FNBVlBtp3lSnPxGygutQ0OMhxwtFne1hE0yvS/BZwZVeGxA3IUzT3lI92L7Rk2GilJ6IZDBh98AOVpuQHsoYTuh80g+dEFn8yCCKaQsBEs398s++svSI34OuZFmn9aaWXAlQyjVIPV69iLZrD9M9DEQxw+aOoyHtNE7n1phuQXshMCbZoZgNVdQO0aXsckBSzHsCRkp4NEvxApXG4r3m4cHAhhUBC4Mza+RUsSTf315f3DXjlrGeK1oVo2Cp0Y6KRXeUVaVI0OzDgvlPQutOqGFbjAinU6ZYbkO6zCUWkWU9LQdPSMy52i7qWQiBBCB4imkLARLM3P73NXsGa0hFBizRT++tro8Jst8hsVKJp2WXSF9qy9Qt2apYWngw8jL2Nqv2FNJQOD51o0ujXNG23JexQ1yKaghA8RDSFwE04cRSoMVWkvHR88NKzZkTZVDlA30h3wdhrgEVvpg910Nc1fY0NHDyhaVRfURR8YwNLNJto9GuKppGkX7SYGwhC8BDRFAImmumxG/QNF7eNCV561ow068rG6hspgLFLh5ahKgayjm9Ft466dfqviWudeybo5xlEYwOSmMX/24BaXZpgJOtxT/Sotut6LEEQAoyIphAw0UxKMJv77UC1PS946VlTjMoLTYODOMBeujGkorl3r75W00Rq2Cu6Qm9oAErLh6ibgTar94UtPTRPMGri3Kbtpv2spGgFIUiIaAoBE83oBF2Ignr+lxz0SLO4cKyuHGWkF7NcTVYJtWj253MpBBy9WbkK1TtaY2QiLhWIN9c4g4m3aXsdBplWtLKuKQjBQURTCJho2hJ36Rt1NlWgEuw1zdKqXGVZR5r6rAGKwiSayg1IF+GgJho1phtQKNCm7aY6p9gxQE9Mk3VNQQgSIppCwETTSDGrY+qiVUtIsCJNzpGMTQaqkaYs64izz7aQGhz4RprOnGK9oTIWdsSHTDRp9GCvzHKbtvc3i5Ek0hSE4CCiKXSJ+no99Jn1m0Zahdpm1MQqJyB+oAcDmnYwRUt/V1TqIhhnr/zwiSb7QrO05y6qkkLiBuQZaTZWmN9Oklzoa7b8iGgKQnAQ0RQCEmVmRXFNrdY0a09QghllzpYMVorWwXYLZVkHGDnlIRNNjkKz2jos0URGg7rvqtRmu6EUzZrywfpOIpAbo10dpO1EEIKDiKYQENEcRue4FG1N46xOVh/mwcQqBkKFtqwzMuu9RJPmBoyAg4ElyKmpQBoLb5iVTtf2gc7KviEXzeqyUfpOApAXpSNeiTQFITiIaAoBEc3BrEVJtmzkMpBsmgwEC6vtxFlp9nXQwi4fyMwEEhKC60HrlZqlYO+pc7sB1ZWaw6dDuKZZXm5OOokCesXsVjdFNAUhOIhoCgERzX7MkibpIa6NVb1CFmk2lmvLOoqWsaterXcGO0XrK5qOgt1u+8DywokhjzQrqwdDjdJkmjxuk7qW9Kwg9GDRfPrppzF48GAkJCRgxowZ+OGHH9rdf/HixRg9erTaf8KECfjggw9aDBW9++67kZeXh8TERJxwwgnYupVjk5rh+Ti1wPNy//33B+X19WSsiKYv7fMSLbP2/mpAcigizap9psFBEuDYu1PdDLloNq7VlVAuoHj3eK/nFwrRrHVluftVk+P1v3OJNAWhh4rmokWLcOONN2LevHlYtWoVJk2ahJNPPhn79u1rdf8lS5bgwgsvxJVXXonVq1fjrLPOUpeffvrJvc+DDz6IJ554As899xyWLVuG5ORkdcwGn0Wue+65Rw2WtS7XX3990F9vT8P6cO4dZVdraqSmYmjQ07NWpLkvf4KOsmxAk30VYDSL2Z49IRBNugFlLtcb6oGymkHqZmqQ3YA8RbOB3xjMf9oJ8dvVtYimIPRQ0XzkkUdw9dVX4/LLL8fYsWOV0HGC9gsvvNDq/o8//jhOOeUU/PGPf8SYMWNw7733YsqUKXjqqafcUeZjjz2GO++8E7/4xS8wceJEvPzyy2ri+jvvvON1rNTUVPTp08d9obgKHcP6cM6zFSo7O1JWNi746VkzkiveN1iJFWnKWQ5UAoO0bmGX6bUQ7B7Npt46JYpaG2qQrjxhOSw7FHCmZiNd8hu0aXtUvA6vRTQFoQeKpt1ux8qVK1X61P2EoqLU/e+//77Vx3C75/6EUaS1/44dO1BUVOS1T3p6ukr7+h6T6djs7GxMnjwZf/3rX9VU9rZobGxEVVWV10Vo/nDOMdfSGOlVVIxAUpAjzeRc7b1ajXSgRguGo89GVQwUUtFUbkDmiaqjVO9oqNYzvUzb6/Wfsi1JmyxUVobuOQjCwYTuDA8TJSUlcDqd6N3b2zqG9zdtMj+EfaAgtrY/t1s/t7a1tQ/5n//5HxWhZmVlqZTvbbfdplK0jHxbY8GCBfjzn//cyVfac7EKTlITNjSbtTf2DXqkSfMEilPN7lSgKhro44Azd3foRXMD4Mo2lxIq42BHXEhFU5m2ZwJGfTRscMJI0r8QKQQShB4omuGE66gWTOHGxcVh7ty5Shzj482hkB5QVD0fw0hzgBpxcXBjRZoJCdv0jQa9xhZs0bTWNffsTgQq+ftywNVrvxbNw4InmlwWLynxEM3PPN2AkkPqBmTB99qojYMNdhjJNe5I0+Vi5ia0z0UQejph/ZPKyclBdHQ0iotN304T3ucaY2twe3v7W9cdOSZh+pbp2Z07dQWmLxTStLQ0r4vQLJrRibo/kAORG5AY9EKg5gpVG1ChXcqNrBpgLzBwoP45M+iBTlNaFbmJibonVLsB6dJVl+kBmxJq0cymaOpFVCOlXrWMUjCrq0P7PAThYCCsosnoburUqfj888/d21wul7o/c+bMVh/D7Z77k08//dS9/5AhQ5Q4eu7DqJBVtG0dk6xZs0atp+bm5gbglR18ohmVZJq110cps/ZQRZrEVWkqNMUrH2A9V3Z2cKJNz9Qse0KVG1CabpJ0lOsnFI5I01ljFrEl2ZFnFmRJilYQemB6linPSy+9FIceeiimT5+uKl9ra2tVNS255JJL0K9fP5U2JTfccANmzZqFhx9+GLNnz8Zrr72GFStW4Pnnn1c/Z7/l73//e9x3330YMWKEEtG77roLffv2Va0phAVBFNFjjz1WVdDy/h/+8AdcfPHFyFThg+Av1gezkaxdDoy6aMQkArHmtI1QiGZTxWDE4ycgzYCx1wkbotW6Jq30KJoTtd9AUHo0XburAXMcV13pqLCJZlNVBuKwS7kycTzYljL9u7HWdwVB6CGief7552P//v3KjICFOocccgg++ugjdyHP7t27VQRocfjhh+PVV19VLSW33367Eka2kowfr5vKyS233KKE95prrkFFRQWOPPJIdUyaIVipVort/PnzVVUshZWi6blmKRwYw9CRJv8RGSl6Xc+oiQ9JatbTQKCmZDzi8R8lXs5dxYhBXyUWq1YFN9IkzuIdbjegsoKJXu0woYJGEvYNOVCxZqKB/rxhiqYgCD1MNMnvfvc7dWmNr776qsW2c889V13agtEmjQt4aQ1WzS5durQLz1iwxoLZ7QA10kg1p3zUJIYkNesZaZbuPQQqGxvDqHODWzRJsEXTbl+tbzg93IDCsKbZUGG6KSQYyDN7REU0BSHwSG2d0OX1zF78V5Ssi2GcValB79G0sCK6osJRbkccR+Iy1fYSEtGsApqyVuoNdUB5Yz9Vl5QcpOHb7U46qRzSPOkkVq+ximgKQuAR0RQ6jfWhPIhresn6g7qpKitkkaYV0VU2ZXMitT5/3o+qOMcSzd1mUW9QRDMfcPbe7OEGlKZMF6JjEVL4fleVj9B34oA+UaXqpoimIAQeEU2hy5HmgOTmCScNFX1CJprRcdoZiGKFGv1P2Zm7PagGBy1Es5epylXRIXcDsuD7XV4xWt+xAblxumdWrPQEIfCIaAoBmHBiuM3a6yoGhCw9a61r1rICqEKHd67cIq9eTZpABWoYNddvrfZfSzRdOfv1hqo4NIXYDchzpmZ1fT+gSd/PTtTRr0SaghB4RDSFLotmv+hqt2hWlo8MWaRpVdCyL9RWqXtcXFkVSszYp5mUFNhpJ4WFumI4Lo7GHFo0jUwzL1ypp1CHK9JsMFLo3K5IMd2ZRDQFIfCIaAqdxvpQ7he3C4jWt8vLxoas5cSzgtaoMPtrsxqUmNF4INApWus4dE9UXVD5nm5A2k0hLJFmJuugEt2iGZeoXa1ENAUh8IhoCl2ONHOTzVmmTqCyamjII03iqDDVk+48ptVdoIuBLIfFwYP1tbHHANL0Wq69YkDYRJOm7dGpMe5JJ9GJ9PYT0RSEYCCiKXRZNNOTzQrSRqDOFbrqWc9Is67MLIRJBVy7tNFCoCPNFqK5uxTaUYAGC2PCJpokMdtjPFiidpSXSFMQAo+IptD1CSdJ2/WNBs6DTgx5IRCpLDK98hIBR+H2kIhmU8kWcP4zKdtziFfkG2o4V9OoN71KkrVLvYimIAQeEU2h01gfytFJZqVNPYdTxas1tlDhNjjYM4HTwRRNzpVqGHZQRbMJaIpZbp4QKMofG95Ik6JZo53ajeRa9YctLSeCEHhENIWuTzhJMYcw10UjMcum1thChRXZlVb3U648pKn3cmB/c9tJoAuBlGgWAU19TQu9WqDS0Qe2aIS0CMq37cRVq8uFjZQGpJuj0Zzac0IQhAAhoil0Gnckk6LTgUZtbEhTsyQ+FYhPswwOOKsLcNClZ09zpElDgq6KBx9vFRSp4yo3oC16Q02UNjbIA2xR4Ys0HdXmuJXkJljBPoVTEITAIaIpdEk0uaRnpNS6J5yEsgjIM9pUolmlQ1xn7l4lmn37AjE0cWf6tKhr5ygoABwOfTwelwYKzlyzTLcyRhkshCs12yyaGeYdJ/LMtVZZ1xSEwCKiKXQafiBnmelA4qxODkt6kuuaXEtFhVYKI6cE2A1ER+ueSrJjR2DWM5ny5XGVsUG2GWpXJsKJmLCLZmOl6RSf5NLWhiKaghBwRDSFTsHorbYWeiRXiq7AcVSnqdmOocZdsVrJlTzAyKpTkSYZNkxf//xzYCtntRtQvb5driO8lDCLZn2V+QQSgL7mjE+JNAUhsIhoCl1az2SkiSRzwkllTljSs1bbibMiV9/IaFKRZrBFE+n6y4Kzso+6DnekWVVhvth4oG+sjv6lglYQAouIptC1CSeMaBINdbu+om9Y0rNWpGkvH2puMGDs0vZ2w4frTdu0HWun2b7d19igHlxGJQ1lwyNCNCvLTYOHWKBfrF7ElUhTEAKLiKbQKawP4wEJTrdZe3V5aC30fHs1q/dP0DdSAMfu/ICKpvX4EebYSsfenYBpCF9lGitYzyNcollRMVz1p5I+ybqyV0RTEAKLiKbQpUhzYHyJ2xWnomxsyFtOPCPN/bsP4cgT9a/aYV+tzA4ClZ61RFOJsAE08fjscHEC+/dOCH+kmQ3UNOWyIkqRZVobimgKQmAR0RS6JJqDUjZr8VCiOTqskWbRvuHKyo805S0DCoChZsa2rExfOkNNTXPLihLhcqApx3QDqgf2lw0Kv2iqSSdJzePBEnU+WURTEAKLiKbQKawP49z09fqGHahs6B8W0UzO1ZM+aoxMoForeFPfdaqCNjnZ7KvsQrRpPY4zOjPpGpAPOPI26I21NtQgA9HxQEII7QN9iY6jfV4C0KBff1yiti8S0RSEwCKiKXRtwkmqmbdsZKSTjBSzVTCU0IUnJY8GB6lAlR7s6ey9I2AVtF6pWZhuQLnmwaui1XkZZXKGZziJz452i2ZMkhQCCUIwENEUuiSaicmmEtXb4ExOQqxZHBOOFC1deSyDA1ev/e5eza4WA7Ummq5eevwWKuJQh+SwpmY9i4FQr7802JJ0LlpaTgQhsIhoCp3C+jCOTjcjrrooJPbWH9jhQBcD2YBy3QdiZFe7I01L7LaYVrGBEE0js0bfrkiBgaiIEU36/xIjuRI0FZT0rCAEFhFNoVNYH8a2rGJ9ozJWrS2GC8vgwFXpYXBgRpqjRunrTZsCJ5rINCtuKnS5cCSIJt9/V61ZypxSDz4zEU1BCCwimkKXIk0jS4/RcJUlIzkM65kWaabHrL3MLJdNbzY4GDOmWTQNs4+xK6Jp7HUCafpATRXhr5y1SBsIuGrM8WDJjcgT0RSEgCOiKXRaNJUneKZp1l6SFdZIM8N06qkuOsTD4GC3W+xosl5dDeSbg0k60m7C0WKexgbOrcXq+Orn5WaPZhiNDSzSB9A0P1XfSXagj/n8OZ1FEITAIKIpdFo0lVl7mv5Erts3ICJEc9/uSc0GB1Gr1WDquLjmKHHjxo4d10rp5ubqlhMeu6l0A9SCIYdfF0yOmEgzfSDQWG3+EpK0aJJKPe5UEIQAIKIpdAqulWVTQczApqJoYljTs5ZoFpUMV4YDxN73ezX30jNF21HR3GC2Y44bZ24oBBzZy/TtBkauY8JuoecpmjXFpv9sBjAsVqulrGsKQuAQ0RQ6jMulo5cR8bvcvrMFBUeHNdJk5WhcClDtZXCw0l1B21nRXG96N4wda274mW5DP+rbtUBpYy5iEoBMcyk1nHBdd//WY7T/bBIwPvM7tV3aTgQhcIhoCh2GgsmCmkPzvtIbHEB+yWFhFU0aCzDarOHokXLdduEYssldQdvVSNNTNJ29zd7U6ihUIwO9xmlHonDDLw7V1eP4JiiGjnxXXUukKQiBQ0RT6DAlZl//hL5L9Y1aoNLoFRY3IE8omjQasO3QfnbG6BIYu4zApme3Ac5ehfp2VRwakYDeeshJ2OEXB0deDrBf98umDdW/HxFNQQgcIppCh/n8c309sL+Zu6yOghMxYY00Sbpa17TB2DRVbxjggnPLHrdoxsQA+/Y1C+GBqKsDduxoGWka2brfxqhQ9cMRI5rEOaIPUKCfV+xAPTlbRFMQephoPv300xg8eDASEhIwY8YM/PDDD+3uv3jxYowePVrtP2HCBHzwwQdePzcMA3fffTfy8vKQmJiIE044AVu3bvXap6ysDBdddBHS0tKQkZGBK6+8EjWszxcOyJtv6uu0XF1lY1TEwhZt2riFkQzdMgn7tpP0iKxYoL76JbWNxu2nnqp//sor/h3P6uvMyQF6mSPPmn5aD/TRbTb2Uu2o0HsSIoa0gVGw7zTfiL7637OIpiD0INFctGgRbrzxRsybNw+rVq3CpEmTcPLJJ2MfQ4JWWLJkCS688EIlcqtXr8ZZZ52lLj/99JN7nwcffBBPPPEEnnvuOSxbtgzJycnqmA0N5twoQAnm+vXr8emnn+I///kPvvnmG1xzzTUhec3dmdJS4Msv9e3oTG0LZJQnI7mXNk4PJ1YFbQEmAYX6ydRnvQF8o7dffHGzaLKYqT0oln//u09qlkF11h8BGim4gKqfpqhtvc3Z15EAK2gLtxyj7/RyIQVOEU1BCCA2g2FZGGFkOW3aNDz11FPqvsvlwoABA3D99dfj1ltvbbH/+eefj9raWiV0FocddhgOOeQQJZJ8OX379sVNN92Em2++Wf28srISvXv3xksvvYQLLrgAGzduxNixY7F8+XIceuihap+PPvoIp512Gvbu3ase70tjY6O6WFRVVannyWMzWm2LgrvSYBtWjR4JG/zjgaa3h+ODlVtxrVlUGi4KVgB/nwbExTThst/mASeU6vmatYF/zVgbjdX3vodN2afhxg4aJgST1S8A3123GWe/Nlp/JaZve1j/wgOPsTcRfe+sa3cf/n2mp6cf8O9TEDpKWGv+7HY7Vq5cidtuu829LSoqSqVTv//++1Yfw+2MTD1hFPnOO++o2zt27EBRUZE6hgX/eCjOfCxFk9dMyVqCSbg/z83I9Je//GWL8y5YsAB//vOfO/wabVn1pgtAz2XfxmMjYl0vexQQnw40VsZi638vwogTntAtMWZbTMCoARKeuAx7Gydg0CxEFH0PBUobRgHFNiDPAMKcMg8GtvrmL6+CcFCJZklJCZxOp4oCPeH9TW24a1MQW9uf262fW9va2yeXFi8exMTEICsry72PLxR2T7G2Is0DUbP1FthWH3gmlRGoWYx+HMfo4vGiooCkJF2t6UwZh5z778YhMxB24lOB320CSrcwvfo4HN/2RlTZj4jyjDQNoK7R04PW+wUaHtti44D4uJbncWRfiMoHj8RJg7LQLwJetyf88vLbDUDt1ysQ//6DcDgNNNkPnI7uThhJA8P9FISDmAjoLusexMfHq0tHGfHM/wvK8xFaJ6WPvihm3X5Qvk29xvDC9dbXwv1UBKHHEdbSjZycHERHR6O42BwvZcL7ffpYn3zecHt7+1vXB9rHt9DI4XCoitq2zisIgiAIYRXNuLg4TJ06FZ9bjX9mIRDvz5w5s9XHcLvn/oQVsNb+Q4YMUcLnuQ9TqVyrtPbhdUVFhVpPtfjiiy/Uubn2KQiCIAitYoSZ1157zYiPjzdeeuklY8OGDcY111xjZGRkGEVFRernc+bMMW699Vb3/t99950RExNjPPTQQ8bGjRuNefPmGbGxsca6devc+9x///3qGO+++66xdu1a4xe/+IUxZMgQo76+3r3PKaecYkyePNlYtmyZ8e233xojRowwLrzwQr+fd2VlJZe/1LUgCJGF/H0KwSLsokmefPJJY+DAgUZcXJwxffp0Y+nSpe6fzZo1y7j00ku99n/99deNkSNHqv3HjRtnvP/++14/d7lcxl133WX07t1bCfLxxx9vbN682Wuf0tJSJZIpKSlGWlqacfnllxvV1dV+P2f5oxSEyEX+PoVgEfY+ze6K9IEJQuQif59Cj3UEEgRBEITugoimIAiCIPiJ9Gl2EiurzTSQIAiRhfV3KatPQqAR0ewk1dXaT9YfVyBBEML3d0obTUEIFFII1EnY01lQUIDU1FTY6CfXTbDs//bs2SNG1vK+9Nh/L4wwKZgcvkBPaUEIFBJpdhL+Ifbvr+cpdkf4AdidPgRDhbwvPed9kQhTCAbyFUwQBEEQ/EREUxAEQRD8RETzIIOTWubNm9epiS09GXlf5H0RBH+QQiBBEARB8BOJNAVBEATBT0Q0BUEQBMFPRDQFQRAEwU9ENAVBEATBT0Q0eyA7d+7ElVdeiSFDhiAxMRHDhg1TFbN2u91rv7Vr1+Koo45CQkKCcn158MEHWxxr8eLFGD16tNpnwoQJ+OCDD9ATefrppzF48GD1OmfMmIEffvgBPZUFCxZg2rRpys0qNzcXZ511FjZv3uy1T0NDA6677jpkZ2cjJSUFZ599NoqLi7322b17N2bPno2kpCR1nD/+8Y9wOBwhfjWCEGKCNqlTCBsffvihcdlllxkff/yx8fPPPxvvvvuukZuba9x0001eQ3o5pPuiiy4yfvrpJ2PhwoVGYmKi8be//c29z3fffWdER0cbDz74oLFhwwbjzjvvNGJjY41169YZPYnXXntNDTR/4YUXjPXr1xtXX321kZGRYRQXFxs9kZNPPtl48cUX1e99zZo1xmmnnaaGwNfU1Lj3ufbaa40BAwYYn3/+ubFixQrjsMMOMw4//HD3zx0OhzF+/HjjhBNOMFavXm188MEHRk5OjnHbbbeF6VUJQmgQ0TxIoPANGTLEff+ZZ54xMjMzjcbGRve2P/3pT8aoUaPc98877zxj9uzZXseZMWOGMXfuXKMnMX36dOO6665z33c6nUbfvn2NBQsWGAcD+/bt48ge4+uvv1b3Kyoq1JejxYsXu/fZuHGj2uf7779X9ymSUVFRRlFRkXufZ5991khLS/P6NyUIPQ1Jzx4kVFZWIisry33/+++/x9FHH424uDj3tpNPPlml6crLy937nHDCCV7H4T7c3lNgynrlypVer5O+wrzfk17ngf5tEOvfB9+PpqYmr/eEKfqBAwe63xNeM13fu3dvr38bNHhfv359yF+DIIQKEc2DgG3btuHJJ5/E3Llz3duKioq8PvCIdZ8/a28f6+c9gZKSEjidzh7/Otub1vP73/8eRxxxBMaPH6+28XXzy1RGRkab74k//34EoSciotmNuPXWW9UYsvYumzZt8npMfn4+TjnlFJx77rm4+uqrw/bchciExT4//fQTXnvttXA/FUHoFshosG7ETTfdhMsuu6zdfYYOHeq+zXmfxx57LA4//HA8//zzXvv16dOnRTWkdZ8/a28f6+c9gZycHERHR/f419kav/vd7/Cf//wH33zzjdeYO75upq0rKiq8ok3P94TXvhXGvv9+BKEnIpFmN6JXr15qbam9i7VGyQjzmGOOwdSpU/Hiiy+2GMQ7c+ZM9WHJtSuLTz/9FKNGjUJmZqZ7n88//9zrcdyH23sKfL/4Hnm+TqYseb8nvU5PWABIwXz77bfxxRdfqNYkT/h+xMbGer0nXOtmi4n1nvB63bp12Ldvn9e/Dc7cHDt2bAhfjSCEmHBXIgmBZ+/evcbw4cON448/Xt0uLCx0XyxYIcmWkzlz5qjWA7ZdJCUltWg5iYmJMR566CFVPTlv3rwe23ISHx9vvPTSS6q15pprrlEtJ56VoT2J3/zmN0Z6errx1Vdfef3bqKur82o5YRvKF198oVpOZs6cqS6+LScnnXSSalv56KOPjF69eknLidDjEdHsgbAHj9+HWrt48uOPPxpHHnmkEox+/foZ999/f4tjvf7668bIkSNVH+O4ceOM999/3+iJPPnkk0ok+DrZgrJ06VKjp9LWvw3+u7Gor683fvvb36q2JH6Z+uUvf+n1pYvs3LnTOPXUU1V/L3s02Qfc1NQUhlckCKFDRoMJgiAIgp/ImqYgCIIg+ImIpiAIgiD4iYimIAiCIPiJiKYgCIIg+ImIpiAIgiD4iYimIAiCIPiJiKYgCIIg+ImIpiAIgiD4iYimcNDwj3/8AyeddFLQz/PRRx/hkEMOUR62giD0LEQ0hYOChoYG3HXXXZg3b17Qz8VRbDQ8f+WVV4J+LkEQQouIpnBQ8MYbb6gJHBy2HAo4wu2JJ54IybkEQQgdIppCt2L//v1qXuNf/vIX97YlS5aoEV++Y8w84ZDlM844o4WwnXXWWXjooYeQl5eH7OxsNZTZc1za4MGDcd999+GSSy5BSkoKBg0ahPfee089j1/84hdq28SJE7FixQqvY/Nc3Pbzzz8H9PULghBeRDSFbjdT9IUXXsD8+fOVKFVXV2POnDlqPuTxxx/f5uO+/fZbHHrooS22f/nll0rYeP3Pf/4TL730krp48uijj6oIdfXq1Zg9e7Y6H0X04osvxqpVqzBs2DB1Xw8Q0QwcOBC9e/fGf//73wC/A4IghBMRTaHbcdppp+Hqq6/GRRddhGuvvRbJyclYsGBBm/tXVFSgsrISffv2bfEzDtx+6qmn1ADv008/XYmib8TK882dOxcjRozA3XffjaqqKkybNg3nnnsuRo4ciT/96U/YuHEjiouLvR7H8+3atSuAr1wQhHAjoil0S5hSdTgcWLx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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Use physics parameters with a somewhat larger K_0\n", "phys_high_K = generate.default_physics(n_dots=2)\n", "phys_high_K.K_0 = 30\n", "phys_high_K.gates[3].peak = 7.5\n", "x = phys_high_K.x\n", "q = phys_high_K.q\n", "\n", "# Set numerics parameters to use basic method only\n", "# and to run for the full number of iterations\n", "numerics_basic = simulation.NumericsParameters()\n", "numerics_basic.calc_n_use_combination_method = False\n", "numerics_basic.calc_n_abs_tol = 0\n", "numerics_basic.calc_n_rel_tol = 0\n", "\n", "V = simulation.calc_V(phys_high_K.gates, x, 0, 0)\n", "K_mat = simulation.calc_K_mat(x, phys_high_K.K_0, phys_high_K.sigma)\n", "\n", "# Find n(x) using a different number of iterations each time\n", "num_iterations = 7\n", "n_result = np.zeros((num_iterations, len(x)))\n", "for i in range(num_iterations):\n", " numerics_basic.calc_n_max_iterations_no_guess = i + 1\n", " n, phi, converged = simulation.ThomasFermi.calc_n(phys_high_K, numerics_basic, V, K_mat, None)\n", " n_result[i,:] = n\n", "\n", "# Plot the results\n", "fig, ax = plt.subplots(figsize=(3, 3))\n", "tutorial_helper.plot_n(fig, ax, x, n_result)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "ccb50536", "metadata": {}, "source": [ "Here we see the function n(x) oscillating around for a bit before converging to\n", "the center.\n", "\n", "Note that we get a `ConvergenceWarning`. This is because we have intentially set\n", "the maximum number of iterations to be small so that we can track the convergence\n", "of the method.\n", "\n", "Now let's try again with a larger value of K_0." ] }, { "cell_type": "code", "execution_count": 5, "id": "4bf673a9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Use physics parameters with a much larger K_0\n", "phys_high_K = generate.default_physics(n_dots=2)\n", "phys_high_K.K_0 = 80\n", "phys_high_K.gates[3].peak = 7.5\n", "x = phys_high_K.x\n", "q = phys_high_K.q\n", "\n", "# Set numerics parameters to use basic method only\n", "# and to run for the full number of iterations\n", "numerics_basic = simulation.NumericsParameters()\n", "numerics_basic.calc_n_use_combination_method = False\n", "numerics_basic.calc_n_abs_tol = 0\n", "numerics_basic.calc_n_rel_tol = 0\n", "\n", "V = simulation.calc_V(phys_high_K.gates, x, 0, 0)\n", "K_mat = simulation.calc_K_mat(x, phys_high_K.K_0, phys_high_K.sigma)\n", "\n", "# Find n(x) using a different number of iterations each time\n", "num_iterations = 10\n", "n_result_basic = np.zeros((num_iterations, len(x)))\n", "for i in range(num_iterations):\n", " numerics_basic.calc_n_max_iterations_no_guess = i + 1\n", " n, phi, converged = simulation.ThomasFermi.calc_n(phys_high_K, numerics_basic, V, K_mat, None)\n", " n_result_basic[i,:] = n\n", "\n", "# Plot the results\n", "fig, ax = plt.subplots(figsize=(3, 3))\n", "tutorial_helper.plot_n(fig, ax, x, n_result_basic)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "24b38fcd", "metadata": {}, "source": [ "Here n(x) appears to be oscillating between 2 values and converging very slowly,\n", "if at all. In general, as K_0 gets larger, convergence becomes more problematic.\n", "\n", "We can help out a bit by using the improved method discussed in\n", "[arXiv:2509.13298](https://arxiv.org/abs/2509.13298).\n", "The old method simply updates n(x) each iteration to be\n", "the result of evaluating the integral equation\n", "$n_1(x) = \\frac{g_0}{\\beta}\\;\\text{sp}[\\beta(\\mu-qV(x)-{\\bf K}\\cdot n_0(x))]$.\n", "The improved method instead sets $n(x)$ to a combination of $n_1(x)$ and $n_0(x)$\n", "each iteration as follows:\n", "\n", "$n(x) = [g_0 \\delta_x {\\bf K} + {\\bf 1}]^{-1} [g_0 \\delta_x {\\bf K} n_0(x) + n_1(x)]$." ] }, { "cell_type": "code", "execution_count": 6, "id": "e87c0536", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Use the same example as above\n", "phys_high_K = generate.default_physics(n_dots=2)\n", "phys_high_K.K_0 = 80\n", "phys_high_K.gates[3].peak = 7.5\n", "x = phys_high_K.x\n", "q = phys_high_K.q\n", "\n", "# Use the default, improved method now\n", "numerics_improved = simulation.NumericsParameters()\n", "numerics_improved.calc_n_abs_tol = 0\n", "numerics_improved.calc_n_rel_tol = 0\n", "\n", "V = simulation.calc_V(phys_high_K.gates, x, 0, 0)\n", "K_mat = simulation.calc_K_mat(x, phys_high_K.K_0, phys_high_K.sigma)\n", "\n", "# Find n(x) using a different number of iterations each time\n", "num_iterations = 10\n", "n_result_improved = np.zeros((num_iterations, len(x)))\n", "for i in range(num_iterations):\n", " numerics_improved.calc_n_max_iterations_no_guess = i + 1\n", " n, phi, converged = simulation.ThomasFermi.calc_n(phys_high_K, numerics_improved, V, K_mat, None)\n", " n_result_improved[i,:] = n\n", "\n", "# Plot the results\n", "fig, ax = plt.subplots(figsize=(3, 3))\n", "tutorial_helper.plot_n(fig, ax, x, n_result_improved)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "6b42a9ed", "metadata": {}, "source": [ "The improved method converges quite quickly. However, even this method has its\n", "limits and will break down for very large $g_0 \\delta_x {\\bf K}$." ] } ], "metadata": { "kernelspec": { "display_name": "qdflow_venv", "language": "python", "name": "qdflow_venv" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.2" } }, "nbformat": 4, "nbformat_minor": 5 }