diff --git a/CHANGELOG.md b/CHANGELOG.md index fea4211a6..ab92152c9 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -10,6 +10,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0 - Added `estimator` module to documentation. [#86](https://github.com/feos-org/feos/pull/86) - Added benchmarks for the evaluation of the Helmholtz energy and some properties of the `State` object for PC-SAFT. [#89](https://github.com/feos-org/feos/pull/89) - The Python class `StateVec` is exposed in both the `feos.eos` and `feos.dft` module. [#113](https://github.com/feos-org/feos/pull/113) +- Added uv-B3-theory and additional optional argument `virial_order` to uvtheory constructor to enable uv-B3. [#98](https://github.com/feos-org/feos/pull/98) ### Changed - Export `EosVariant` and `FunctionalVariant` directly in the crate root instead of their own modules. [#62](https://github.com/feos-org/feos/pull/62) diff --git a/examples/data/lennard_jones_nist.csv b/examples/data/lennard_jones_nist.csv new file mode 100644 index 000000000..63c07e69d --- /dev/null +++ b/examples/data/lennard_jones_nist.csv @@ -0,0 +1,614 @@ +t rhov rhol p +7.00000E-01 2.01239E-03 8.43237E-01 1.38071E-03 +7.01000E-01 2.03841E-03 8.42829E-01 1.40027E-03 +7.02000E-01 2.06469E-03 8.42420E-01 1.42004E-03 +7.03000E-01 2.09123E-03 8.42010E-01 1.44004E-03 +7.04000E-01 2.11803E-03 8.41598E-01 1.46025E-03 +7.05000E-01 2.14510E-03 8.41186E-01 1.48069E-03 +7.06000E-01 2.17243E-03 8.40772E-01 1.50136E-03 +7.07000E-01 2.20003E-03 8.40357E-01 1.52225E-03 +7.08000E-01 2.22790E-03 8.39941E-01 1.54337E-03 +7.09000E-01 2.25604E-03 8.39524E-01 1.56473E-03 +7.10000E-01 2.28445E-03 8.39106E-01 1.58631E-03 +7.11000E-01 2.31314E-03 8.38686E-01 1.60813E-03 +7.12000E-01 2.34210E-03 8.38266E-01 1.63018E-03 +7.13000E-01 2.37134E-03 8.37845E-01 1.65247E-03 +7.14000E-01 2.40085E-03 8.37422E-01 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+1.30200E+00 2.26136E-01 4.02586E-01 1.23961E-01 +1.30300E+00 2.29596E-01 3.98474E-01 1.24495E-01 +1.30400E+00 2.33282E-01 3.94117E-01 1.25031E-01 +1.30500E+00 2.37231E-01 3.89473E-01 1.25568E-01 +1.30600E+00 2.41495E-01 3.84489E-01 1.26107E-01 +1.30700E+00 2.46147E-01 3.79091E-01 1.26648E-01 +1.30800E+00 2.51287E-01 3.73174E-01 1.27192E-01 +1.30900E+00 2.57074E-01 3.66577E-01 1.27736E-01 +1.31000E+00 2.63768E-01 3.59036E-01 1.28283E-01 +1.31100E+00 2.71882E-01 3.50035E-01 1.28832E-01 +1.31200E+00 2.82726E-01 3.38258E-01 1.29383E-01 \ No newline at end of file diff --git a/examples/lj_models.ipynb b/examples/lj_models.ipynb index 6e201df03..59a9eb7e7 100644 --- a/examples/lj_models.ipynb +++ b/examples/lj_models.ipynb @@ -4,37 +4,40 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Comparison of equations of state for the Lennard-Jones fluid\n", + "# Comparison of equations of state for model fluids\n", "\n", - "In this notebook, we take a look at three model fluid equations of state and compare them.\n", + "In this notebook, we take a look at various model fluid equations of state and compare them.\n", "These EoS are:\n", "\n", "- The PeTS equation of state (from `feos.pets`),\n", - "- the uv-theory equation of state (from `feos.uvtheory`), and\n", - "- the Thol equation of state (implemented in as Python class).\n", + "- the uv-theory equation of state (from `feos.uvtheory`), \n", + "- the uv-B3-theory equation of state (from `feos.uvtheory` using `VirialOrder.Third`), and\n", + "- the Thol equation of state (implemented in this notebook as Python class).\n", "\n", - "The PeTS equation of state is for a Lennard-Jones fluid with cut off distance of $r_c = 2.5 \\sigma$ and a potential shift while the uv-theory and Thol equation of state model the full Lennard-Jones potential. Thus, we don't expect similar results when comparing uv-theory and Thol to PeTS." + "The PeTS equation of state is for a Lennard-Jones fluid with cut off distance of $r_c = 2.5 \\sigma$ and a potential shift while the uv-theory and Thol equation of state model the full Lennard-Jones potential. Note that the uv-theory was developed to model Mie potentials and not primarily adjusted to the Lennard-Jones fluid. Thus, we don't expect similar results when comparing uv-theory and Thol to PeTS." ] }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from feos.si import *\n", - "from feos.uvtheory import UVParameters, Perturbation\n", + "from feos.uvtheory import UVParameters, Perturbation, VirialOrder\n", "from feos.pets import PetsParameters\n", "from feos.eos import State, PhaseEquilibrium, PhaseDiagram, EquationOfState, Contributions\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", + "import pandas as pd\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "sns.set_context('talk')\n", - "sns.set_palette('Dark2')\n", + "#sns.set_palette('asd')\n", + "sns.set_palette(\"hls\", 8)\n", "sns.set_style('ticks')\n", "colors = sns.palettes.color_palette('Dark2', 8)" ] @@ -48,7 +51,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -102,15 +105,12 @@ " \"\"\"\n", " tau = self.tc / state.temperature\n", " delta = np.sum(state.partial_density) / self.rhoc\n", - " a = 0.0 #zero(state)\n", + " a = 0.0\n", " \n", " for i in range(6):\n", " a = a + N[i] * delta**D[i] * tau**T[i]\n", - " \n", - " # print(\"2\")\n", " for i in range(6, 12):\n", " a = a + N[i] * delta**D[i] * tau**T[i] * np.exp(-1.0 * delta**L[i])\n", - " # print(\"3\")\n", " for i in range(12, 23):\n", " a = a + N[i] * delta**D[i] * tau**T[i] * np.exp(- 1.0 * ETA[i] * (delta - EPSILON[i])**2.0 - 1.0 * BETA[i] * (tau - 1.0 * GAMMA[i])**2.0)\n", " return a * np.sum(state.moles)" @@ -125,7 +125,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -134,15 +134,15 @@ "eps_k = 150.03\n", "eps_k_k = eps_k * KELVIN\n", "\n", - "parameters = UVParameters.from_lists([12.0], [6.0], [sigma], [eps_k])\n", + "parameters = UVParameters.new_simple(12.0, 6.0, sigma, eps_k)\n", "uvtheory_wca = EquationOfState.uvtheory(parameters)\n", "uvtheory_bh = EquationOfState.uvtheory(parameters, perturbation=Perturbation.BarkerHenderson)\n", + "uvtheory_b3 = EquationOfState.uvtheory(parameters, virial_order=VirialOrder.Third)\n", "\n", "parameters = PetsParameters.from_values(sigma, eps_k)\n", "pets = EquationOfState.pets(parameters)\n", "\n", - "thol = EquationOfState.python(Thol())\n", - "s3 = State(thol, temperature=300*KELVIN, pressure=1*BAR)" + "thol = EquationOfState.python(Thol())" ] }, { @@ -154,18 +154,19 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "s1 = State(uvtheory_wca, temperature=300*KELVIN, pressure=1*BAR)\n", - "s2 = State(pets, temperature=300*KELVIN, pressure=1*BAR)\n", - "s3 = State(thol, temperature=300*KELVIN, pressure=1*BAR)" + "s2 = State(uvtheory_b3, temperature=300*KELVIN, pressure=1*BAR)\n", + "s3 = State(thol, temperature=300*KELVIN, pressure=1*BAR)\n", + "s4 = State(pets, temperature=300*KELVIN, pressure=1*BAR)" ] }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -174,7 +175,7 @@ "-0.0016213224956115704" ] }, - "execution_count": 51, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -185,16 +186,16 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "-0.000940704010881386" + "-0.0016138652202999679" ] }, - "execution_count": 52, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -205,7 +206,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -214,7 +215,7 @@ "-0.0016144150962601586" ] }, - "execution_count": 53, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -223,55 +224,124 @@ "s3.molar_helmholtz_energy(Contributions.ResidualNvt) / (RGAS * 300 * KELVIN)" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Compare critical temperatures" - ] - }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(1.320000346982154, 1.3097658041494296, 1.3208296613277397)" + "-0.000940704010881386" ] }, - "execution_count": 54, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(\n", - " State.critical_point(thol).temperature / eps_k_k, \n", - " State.critical_point(uvtheory_wca).temperature / eps_k_k, \n", - " State.critical_point(uvtheory_bh).temperature / eps_k_k\n", - ")" + "s4.molar_helmholtz_energy(Contributions.ResidualNvt) / (RGAS * 300 * KELVIN)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compare critical points\n", + "- Reference data for the Lennard-Jones from Potoff and Panagiotopoulos (MC): $T_c^*=1.3120$, $\\rho_c^*=0.316$, $p_c^*=0.1279$" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "uvtheory_b3:\n", + "Tc*=1.31329, Error: 0.099%\n", + "pc*=0.1286, Error: 0.548%\n", + "rhoc*=0.31425, Error: 0.553%\n", + "\n", + "uvtheory_wca:\n", + "Tc*=1.30977, Error: 0.17%\n", + "pc*=0.12448, Error: 2.674%\n", + "rhoc*=0.30233, Error: 4.327%\n", + "\n", + "uvtheory_bh:\n", + "Tc*=1.32083, Error: 0.673%\n", + "pc*=0.13486, Error: 5.442%\n", + "rhoc*=0.31865, Error: 0.838%\n", + "\n", + "thol:\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "thread '' panicked at 'called `Result::unwrap()` on an `Err` value: PyErr { type: , value: AttributeError(\"'builtins.StateHDDV2' object has no attribute 'temperature'\"), traceback: Some() }', feos-core/src/python/user_defined.rs:210:1\n" + ] + }, + { + "ename": "PanicException", + "evalue": "called `Result::unwrap()` on an `Err` value: PyErr { type: , value: AttributeError(\"'builtins.StateHDDV2' object has no attribute 'temperature'\"), traceback: Some() }", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mPanicException\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[84], line 21\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 19\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m\n\u001b[0;32m---> 21\u001b[0m \u001b[43mevaluate_critical_points\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n", + "Cell \u001b[0;32mIn[84], line 11\u001b[0m, in \u001b[0;36mevaluate_critical_points\u001b[0;34m()\u001b[0m\n\u001b[1;32m 9\u001b[0m eps_k \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m150.03\u001b[39m \u001b[38;5;66;03m# eps / kB in K\u001b[39;00m\n\u001b[1;32m 10\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m:\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m.\u001b[39mformat(names[i]))\n\u001b[0;32m---> 11\u001b[0m Tc \u001b[38;5;241m=\u001b[39m \u001b[43mState\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcritical_point\u001b[49m\u001b[43m(\u001b[49m\u001b[43meos\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39mtemperature \u001b[38;5;241m/\u001b[39m eps_k_k\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mTc*=\u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m, Error: \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m%\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m.\u001b[39mformat(np\u001b[38;5;241m.\u001b[39mround(Tc, \u001b[38;5;241m5\u001b[39m), np\u001b[38;5;241m.\u001b[39mround(np\u001b[38;5;241m.\u001b[39mabs(Tc \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1.3120\u001b[39m ) \u001b[38;5;241m/\u001b[39m \u001b[38;5;241m1.3120\u001b[39m \u001b[38;5;241m*\u001b[39m \u001b[38;5;241m100\u001b[39m ,\u001b[38;5;241m3\u001b[39m)))\n\u001b[1;32m 13\u001b[0m pc \u001b[38;5;241m=\u001b[39m State\u001b[38;5;241m.\u001b[39mcritical_point(eos)\u001b[38;5;241m.\u001b[39mpressure() \u001b[38;5;241m*\u001b[39m (sigma \u001b[38;5;241m*\u001b[39m ANGSTROM)\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m3\u001b[39m \u001b[38;5;241m/\u001b[39m KB \u001b[38;5;241m/\u001b[39m eps_k_k\n", + "\u001b[0;31mPanicException\u001b[0m: called `Result::unwrap()` on an `Err` value: PyErr { type: , value: AttributeError(\"'builtins.StateHDDV2' object has no attribute 'temperature'\"), traceback: Some() }" + ] + } + ], + "source": [ + "def evaluate_critical_points():\n", + " names = ['uvtheory_b3', 'uvtheory_wca', 'uvtheory_bh', 'thol']\n", + " print('')\n", + " i = 0\n", + " for eos in [uvtheory_b3, uvtheory_wca, uvtheory_bh, thol]:\n", + " rep = 12\n", + " att = 6.0\n", + " sigma = 3.7039 # in Angstrom\n", + " eps_k = 150.03 # eps / kB in K\n", + " print('{}:'.format(names[i]))\n", + " Tc = State.critical_point(eos).temperature / eps_k_k\n", + " print('Tc*={}, Error: {}%'.format(np.round(Tc, 5), np.round(np.abs(Tc - 1.3120 ) / 1.3120 * 100 ,3)))\n", + " pc = State.critical_point(eos).pressure() * (sigma * ANGSTROM)**3 / KB / eps_k_k\n", + " print('pc*={}, Error: {}%'.format(np.round(pc, 5), np.round(np.abs(pc - 0.1279 ) / 0.1279 * 100 ,3)))\n", + " rhoc = State.critical_point(eos).density * (sigma * ANGSTROM)**3 * NAV\n", + " print('rhoc*={}, Error: {}%'.format(np.round(rhoc, 5), np.round(np.abs(rhoc - 0.316) / 0.316 * 100 ,3)))\n", + " i += 1\n", + " print('')\n", + " return\n", + "\n", + "evaluate_critical_points()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Phase diagrams" + "## Compare Phase diagrams" ] }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 74, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 51.7 ms, sys: 0 ns, total: 51.7 ms\n", - "Wall time: 50.6 ms\n" + "CPU times: user 40.1 ms, sys: 0 ns, total: 40.1 ms\n", + "Wall time: 38.6 ms\n" ] } ], @@ -282,15 +352,15 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 75, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 41.8 ms, sys: 3.92 ms, total: 45.7 ms\n", - "Wall time: 45.1 ms\n" + "CPU times: user 39.8 ms, sys: 0 ns, total: 39.8 ms\n", + "Wall time: 38.2 ms\n" ] } ], @@ -301,15 +371,44 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 76, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 1.64 s, sys: 3.88 ms, total: 1.65 s\n", - "Wall time: 1.64 s\n" + "CPU times: user 49.9 ms, sys: 0 ns, total: 49.9 ms\n", + "Wall time: 47.6 ms\n" + ] + } + ], + "source": [ + "%%time\n", + "vle_uv_b3 = PhaseDiagram.pure(uvtheory_b3, 150*KELVIN, 500)" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "thread '' panicked at 'called `Result::unwrap()` on an `Err` value: PyErr { type: , value: AttributeError(\"'builtins.StateHDDV2' object has no attribute 'temperature'\"), traceback: Some() }', feos-core/src/python/user_defined.rs:210:1\n" + ] + }, + { + "ename": "PanicException", + "evalue": "called `Result::unwrap()` on an `Err` value: PyErr { type: , value: AttributeError(\"'builtins.StateHDDV2' object has no attribute 'temperature'\"), traceback: Some() }", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mPanicException\u001b[0m Traceback (most recent call last)", + "File \u001b[0;32m:1\u001b[0m\n", + "\u001b[0;31mPanicException\u001b[0m: called `Result::unwrap()` on an `Err` value: PyErr { type: , value: AttributeError(\"'builtins.StateHDDV2' object has no attribute 'temperature'\"), traceback: Some() }" ] } ], @@ -320,15 +419,15 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 78, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 13.4 ms, sys: 2.94 ms, total: 16.4 ms\n", - "Wall time: 16 ms\n" + "CPU times: user 26.5 ms, sys: 0 ns, total: 26.5 ms\n", + "Wall time: 24.4 ms\n" ] } ], @@ -337,23 +436,116 @@ "vle_pets = PhaseDiagram.pure(pets, 150*KELVIN, 500)" ] }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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trhovrholp
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\n", + "
" + ], + "text/plain": [ + " t rhov rhol p\n", + "0 0.70 0.002012 0.843237 0.001381\n", + "10 0.71 0.002284 0.839106 0.001586\n", + "20 0.72 0.002584 0.834868 0.001815\n", + "30 0.73 0.002912 0.830543 0.002069\n", + "40 0.74 0.003271 0.826147 0.002350" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# import reference data from the NIST database\n", + "nist_data = pd.read_csv(\"data/lennard_jones_nist.csv\", delim_whitespace=True)\n", + "nist_data = nist_data[::10]\n", + "nist_data.head()" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Compare phase diagrams" + "Plot the Phase-Diagrams" ] }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 20, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -361,21 +553,21 @@ } ], "source": [ - "s3 = NAV * sigma_a**3\n", - "colors = sns.color_palette(\"Dark2\", n_colors = 4)\n", + "s3 = NAV * sigma_a**3 # factor to calculate dimensionless density \n", + "colors = sns.color_palette(\"Dark2\", n_colors = 6)\n", "plt.figure(figsize=(12, 6))\n", "\n", + "plt.plot(nist_data.rhov, nist_data.t, linestyle=\"\", color=\"k\", marker=\".\", label='MC', alpha=0.5)\n", + "plt.plot(nist_data.rhol, nist_data.t, linestyle=\"\", color=\"k\", marker=\".\", alpha=0.5)\n", + "\n", "plt.plot(vle_uv.vapor.density * s3 , vle_uv.vapor.temperature / eps_k_k, color=colors[0], label='uv (WCA)')\n", "plt.plot(vle_uv.liquid.density * s3, vle_uv.vapor.temperature / eps_k_k, color=colors[0])\n", "\n", "plt.plot(vle_uv_bh.vapor.density * s3 , vle_uv_bh.vapor.temperature / eps_k_k, color=colors[1], label='uv (BH)')\n", - "plt.plot(vle_uv_bh.liquid.density * s3, vle_uv_bh.vapor.temperature / eps_k_k, color=colors[1], )\n", - "\n", - "plt.plot(vle_thol.vapor.density * s3, vle_thol.vapor.temperature / eps_k_k, color=colors[2], label='Thol')\n", - "plt.plot(vle_thol.liquid.density * s3, vle_thol.vapor.temperature / eps_k_k, color=colors[2])\n", + "plt.plot(vle_uv_bh.liquid.density * s3, vle_uv_bh.vapor.temperature / eps_k_k, color=colors[1])\n", "\n", - "plt.plot(vle_pets.vapor.density * s3, vle_pets.vapor.temperature / eps_k_k, color=colors[3], label='PeTS')\n", - "plt.plot(vle_pets.liquid.density * s3, vle_pets.vapor.temperature / eps_k_k, color=colors[3])\n", + "plt.plot(vle_uv_b3.vapor.density * s3 , vle_uv_b3.vapor.temperature / eps_k_k, color=colors[2], label='uv (B3)')\n", + "plt.plot(vle_uv_b3.liquid.density * s3, vle_uv_b3.vapor.temperature / eps_k_k, color=colors[2])\n", "\n", "plt.ylabel(r\"$T*$\")\n", "plt.xlabel(r\"$\\rho*$\")\n", @@ -384,13 +576,222 @@ "plt.legend(frameon=False)\n", "sns.despine(offset=10);" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Calculate Errors compared to NIST data (MC)**\n", + "- dimensionless vapor density $\\rho^{v*}$\n", + "- dimensionless liquid density $\\rho^{l*}$\n", + "- dimensionless vapor pressure $p^{v*}$" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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3/fr1iImJMeqY6enpFaqjJagDAV8zvkUJDQ3VOZWfJakDqytXruDMmTMQBEErPTc3VzNz2PDhw+FVDd9oqxsGHdZjy6DDmi0OgHUDh+pI1zmbE/xJPa8MjZ2JPBQpOTuZtYWEMFDR4uurGmCflKTdLUwuBwIDq13ritrQoUOxd+9e/Prrr5ogIC8vD3v27AGgGpyvtnfvXnz33XflyggMDMRrr71m8FgODg545ZVXcOzYMezcuRORkZFYtGiRwXy1atXCsGHDUKdOHbz55pv49ttv8cILL8DR0dHIs7QPDFiMkJOTo+k72K9fPwQHB1cof0RERLltHTp0wMKFCzF79mysW7cOCxYswLBhw1CvXj295WRnZ2tutu3N/fv3kZGRAcC8gMXasrKycOvftvz69evj7bffxtdffw0vLy8UFxdj3759mDt3Li5evIg2bdpg1qxZtq1wDcKgw3qqatChZs0WB7IMUx4HQ61g+p6znZt11jmg/+HuYoD9zDBWI8TEqAbYJ5Z5nwsMBKKjbVenChBFUec6e/fu3dObp2/fvqhXrx5SU1ORlpYGLy8vbNu2DYWFhejYsaPWAo43btzQjKEtq+w+xujUqRN27tyJY8eOVShfnz59AAB3795FRkaGyV33bYUBiwF5eXl49dVXcfnyZfj5+WH+/PkWLf/NN9/Ehg0b8M8//yA5OVly1ioPDw+jB7Onp6dX6lzbqampmpnT7HnAvboVyMPDA9OmTcN7772H4OBgNGjQAPn5+SgsLASgOoelS5eifv36tqxutcKgwzw1Oeig6snQ80rfc/alJ17CwVj9M5Cl5aahSb0m1WrByirB3R1ISKhy67A4Ozvj3r17yMnJ0Tm29fz583rzOjk5oX///oiNjUVcXBzeeustTXewkIea4CzVg0R9r3VL36JAepSUafkqeXhyhCqAAYuEu3fv4pVXXoFSqUTbtm3xww8/WHy2qPr166Nt27ZQKpXIzMyU3HfkyJEYOXKkUeWqV8qtLKmpqQAAmUyGdu3aVdpxK0o985evry/++9//ol69eli5ciXS0tJQu3Zt+Pr6YujQoQgLC0Pt2nx5PMzQTamudEMrXTPoYNBBNVtFx87omlmvLC83L6MWrCQr8fWtEoGKWsuWLZGamopjx46hX79+WmkXL17Evn37JPMPHToUsbGx2Lx5M5577jkcPnwYderUwaBBg6xSX/V6KhVdh0U9a5mTkxP+85//WLxe1sY7Mj3u37+PCRMm4NixY2jVqhVWrlyJRo0aWeVY6qmUi4uLrVJ+ZRg1alSVmHlC3cKiDqoGDRpktTeVqsqUoEMqXerGgUGHCoMOIv0efl6qp1rW9zoDYNQMY0SAqqtUamoqvvnmG7Rr1w6enp4AgAsXLuCNN94wuHB0165d0bRpU1y+fBmzZ8+GKIro2bOn1ixfllBYWIhVq1Yh8d8ud8OHD9dKX7JkCVq3bo3AwEA4Oztr5YuPj9fMwBoWFoa6detatG6VgQGLDgUFBYiIiMDhw4fRvHlzrFq1yuAUuKYqLi7GuXPnAHBxwspgiYkB7J0prSCAdFBi6NtKfelDfhyic2VxBh0MOojMIfUaPHDxgGTetNw0vkZIY9y4cYiPj0d6ejoGDhyI1q1bo7S0FOnp6Wjbti1GjRqFVatW6c1fq1YtBAcHY8WKFToH25vi+++/x4YNGzT/q6c1Vo+nGTBgAMaMGaOV5++//8bChQshl8vx2GOPoWHDhigoKEBmZibu37+vyffOO++YVTdbYcDykKKiIkyZMgV//PEHmjZtiqioKDRr1sxqx4uOjkZeXh5q165t16vDVwfXrl3TTJlc1QMWS7eCSHXNMhR0xJ+O1/ttpq58lsKgg6jmknoNerlJz+yoTueAfAKABg0a4KeffsKCBQuQlJSEjIwMNG3aFC+//DImTZqEH374wWAZQ4cOxYoVKwCoFiGXGo9sjPPnz2uNnalTpw5cXV3RtWtXDBs2DAMHDiyXZ/z48WjdujWOHj2KrKwsZGVlQS6Xo0mTJvD398fQoUM1C6BXRTLRUFtXDVJSUoI33ngD27dvh4eHB9asWYPWrVsblVehUE3BOH36dK0n0v79+3HgwAGMGDECrVq10mwvLCxEdHQ0PvvsMxQVFeGFF17ABx98YLFzUY9h8fPzw8aNGy1WblWWmJiIiIgI1K9fH4cPH9Y5G4i9MKcVRNcNesKYBCiiFHrTIwdHwm+JaZMlzOo1C5/+/qlJeVMmpmDy1skmBR0JYxKQcy+nXGChaKXQG3So08oOujVldjIism9S73fqBS/tdUA+P7+JymMLSxm//fabZlCSg4OD5JS2H3zwgda39FlZWQDKT393//59LF++HMuXL4e7u7tmJdSMjAytpr0ZM2ZY9FyovLLjV+whWLHkAHVzWkHM7ZrVtXlXyfSA5gE4evkoWzqIqNJIva9wQD5R1cOApQz1lLYANM1p+uTl5RlVpp+fHyZOnIhjx44hMzMTGRkZKCoqgpubG3r27Inhw4drWmfIuiZPnozJkydX2vEsPVZEaoC6oa5XutYsqAipoCPEO0Sya1b0iGgGHURUqaRmGOOAfKKqhwFLGebMkX369Gmd25s1a4apU6eaUy2yY5XZSmLNVhBD40EMBR2GFoBj0EFEtvDwe0dabprk/hyQT2SfGLAQSbCnVhJDzGkFMdQ1y1DQYUxQwqCDiGzN2AH5RGRfGLBQjVdVWkms2QoCWCboYFBCRPbM0BouZd+/qtiC7UTVGgMWqvaqSytJZbSCAAw6yESG7u6k0pnXcnnJIENf3uTkAGFhwO4yb/NBQUBMDOBu+0nEiGokBixUbVXHVhK2glQh9npDa+m8hu7upNIB5rVUXjVbPXeqEEPvo2FhQJL2RwOSkoDwcCCBk4gR2YZI1dLw4cNFQRDE4cOH27oqlSLleooYdypOTLmeotkWtCpIlM+Wi/gYmh/5bLmoWKUQU66naG2vyE/kwUjJ9IBlAXqPK4qimH03W1SsUmilK1YpxOy72ZLnQxJSUkQxLk71uyJp1sibnS2KQUGiCDz4CQpSbTeUXhXzBgWJolyunSaXi6JC9XyXTGdey+W11eNfGa+zSpSSon2aD/9URhVr2uc3kTEYsFRT1e0NT98NfPbdbDFoVZDWzX/QqiBxX+Y+s4IOqZ+U6ymSwZAxAYnUOVVb1rih4Q28bfN27Sp9dxcXJ53OvJbJm5Jiu+eONV9nxr53WJChhyEuzupVqHaf30SWwC5hZDcsOfg9YkuEWXWx5lgSNbvtmlWVugxJ9d0QRel+HdbIO2QIcFDHOKaSEiAxEYiP1z6Xh9N1see8us61LEPpzGuZvImJ0o+vNZ87wcHA0aPaaZZ6nRkzmMTC3dS8DEwSZiidiKyDAQtVmsoc/H7y+knJutjDWBKrMbUfurX63hvqEG7qDU1kJG/g7T1vV+n1f5jXQnkNsebjf+hQ+W2WeJ0plcDkyfpf/9HRlhnT8zAPJdDqKpDZCxDrPNguKwJaJgEezQDY4RdNRNVcLVtXgKoXZbYS8afjocxWarbl3MuBIkoBvyV+GLp+KPyW+EERpUDOvRwAkBz8vvv8bq2AAjB+8Hv7Ju0hl8m1tsllcihaKTStJIEtA7XSH24lSZmYgriRcUiZmIKEMQlwd9aeIsbXwxch3iGVH5golaqbAeWD64ycHEChAPz8gKFDVb8VCtV2Y9KlAgepNKm8Q4aobihKtB/Dcjc0+tKl0vTd8BiDN/CWyxsQAMi1X2eQy1XPrZAQ1U2kvnSpNOY1Pq9CAUm2eu5YotVI3+s/OFj6PcnQ+x2g8300LTcNGBGmCk7KapkEjAg3uPAkEVmJrfukkXVYqw9sRceSqLfbYvD7vsx99j2WxNJjNszph25opKm1+t7PmmV63shI+xxrEBBQtcahWGIMg0Khnabern7O6ktnXsvlrW5jmMx5fRsa0yPxPqr1mTSxnYiRz6h+f/xgDKO1cQwLUXmwdQXIOiz9hicVkIii/hm5uv5fV5sNflezu4DEnEGo1rpxMOfmwJygw5oDjXkDXzl5DT3fjUlnXvPz2urxt9brzJwvUQy9nxn4UsGYzxVrYsBCVJ5MFEXR1q089ig5ORkrV67E8ePHce/ePTz66KMYOHAgxo8fD2dnZ5PK3L59O9auXYtTp06hqKgILVu2REhICEaPHo06deoYLqACQkNDkZKSAj8/P2zcuNHs8hRRCr3jPSIHR8JviZ9J5UYOisSU36boTZca/J4wJgE593LKjTVRtFJounVZnSmDzBUKVdeFsl0d5HIgMFD10akvLTJS1a3BFLNmAZ9+qj89MhKYov9xkBQXp+pyoU9AgGpQrq5zSkgw/XqoB+WGh2t3D1MoVP3bAf1p6nE31shr7GBge1pLxRJ5yT7YYh0ea73O9L03dO4s3d3MyPczJdohDV7wQhp8karamJKCnPpyhH/VDYmNbj2o1k1XRL+VDPfHvA2Way5Lf34TVQcMWHRYs2YN5s6dC1EU8cgjj8DNzQ1paWkoLCxEmzZtsG7dOri6ulaozM8++wwrVqwAALRo0QJ169ZFWloaSkpK0KVLF6xYsQIODg4WOwdLvuEps5WSAYmhoENKysQUTN46uUKD33UFJIZm5DKZKQPU1eM5LB10WDOoSEl5MMDVlMBBKuiIjrbeDY0ab+CJbMsarzOp9wYz3mdz0BhhiMFuPBj7E4RExCAM7nErgAULgKQkKN1KkOYGeOUCvrll3u8A1diXgwdVY3xCQipwoQxjwEKkg03bd+zQyZMnRR8fH9Hb21tcv369WFpaKoqiKF69elXTTDt58uQKlbljxw5REATx8ccfF3ft2qXZnpaWJioUClEQBHHevHkWPQ9LNinHnYqr3gspmrL4n6lds8zpemVmNwejFp6rql2GiKj60vcebcqYnq5dxSAkiHIUaSehUFRgl+Fuqps3i6Krq/Y2V1dRPHXKYqfLLmFE5TFgeUhERIQoCII4ffr0cmkZGRmij4+PKAiCmJqaanSZISEhoiAI4sKFC8ulHThwQBPM3Lhxw6y6l2XJNzxDA+PtfiFFSw9gt2bfaqkfYwaSmhtUSF0vQ2nGpBMRWVIFx/Sk7MuVfJvNjDQQsNSrp3u7q6vFTokBS81z+PBhURAEsV27dmJeXp7OfU6ePCkKgiAKgiB+8sknesuaMmWKKAiCOGPGDJ3pBQUFYnR0tPjaa6+JgYGBYvv27cUOHTqIffv2FadNmyb+9ttvYlFRkWR99+/fr6nLlClTjD9RM3AdljLu3r2L33//HQAQFhZWLr1Vq1bo1q0bDhw4gG3btsHHx8dgmefPn8epU6cAAOHq6RbL6N69O1q2bInMzEwkJCRgxIgRZp6F5fl6+EquWWIXCymaMpbE1MX/zJlOVz09qSldr3x9VXV/uIuEutuVu7uqu4K+7hWG0tV8ffV3b5JKMybdBqricJCqmJfIJvS95+h5v0uLly4uDV5oIbXD3bu6t9+6peomZuHuYVQz+Pv7w9HREQUFBTh69CgCAwPL7XP48GGdfz/syJEjAICAgIByaX/++SfefPNNXLlyBQDg6uqK//znPwCAy5cvY+vWrdi6dStat26N1atXo0mTJjqPUbar4u7du3Hr1q0KD5WosEoJi6oIdYT7+OOPi4WFhTr3iYyMFAVBEMeOHWtUmbGxsaIgCGLfvn317jNz5kxREATxvffeM6neulhjljC2khjZSmKoa5Y5Xa8MXQ87VtmTKhnq1WfOZG3Mq51ui8eXyBSG3vpTUkT9nx0tW0pnnjXLInVkC0vN9MILL4iCIIhffvmlznR1D6C+ffuKPj4+4u3bt8vtk5aWpmn5uHDhglbagQMHxMcff1wUBEEcNWqUePToUc2wB1EUxZKSEvHo0aPixIkTRUEQRKVSqbMeeXl5YocOHURBEMTOnTuLgiCIa9euNePMjcOApYyYmBhREASxf//+eveJi4sTBUEQAwMDjSrzm2++EQVBEF966SW9+yxZskQUBEF8/vnnJcv66aefxOHDhxv14+/vX6nrsFiNPY4lMbdrluZiVr0xG1UpcKiKS5pUxbzVOVCiqk/XY2zo+a73PXzNGunPhrg4i9SZAUvNtGjRIlEQBDE8PLxcWmlpqRgQECD26NFDs19CQkK5/davX6/zHvXWrVti9+7dNV24DHX5+u2338SMjAydaWXvlZcuXSoKgiA+++yzRp+nqRiwlLFs2TJREARxxIgRevfZs2ePKAiC2LFjR6PK/Pjjj0VBEMRp06bp3efHH38UBUEQhwwZIlmW+klakZ8q9YZX0U8We20lkTofO1DZQUd1W8+OeSv2UqmKgZIxrxU7fXnTvww9/sZ8p6TzQX54wL36h2NYNGy29pmJ1PdL+qjvvRYtWqTZtmDBAlEQBHHq1Kl685WWlopBQUF6g4uH/fHHH6IgCKKfn594//59rbRTp05pjqce+zx//vxyZbz55puiIAji22+/rbV98eLFoiAIYkBAgM6WmYp47rnnREEQxMWLF4tZWVmit7e3KAiCmJaWZla5hnAMSxkFBQUAILkminrqYfW+liwzPz9fsiwPDw/4GTklbnp6usHyKl1FpwieM0d7m1pljCXRNRWvejtg3HgQG43nMGUmZvXswoZmai4rKUl1iRISTB8OFB8v/RDrYkxeqSUaAMPpzGt83kOHym+z9uObmAgEB6uW9ynLmOdkeLjqDlPq+Sz1WgCkX0dq5owVIvMZes8yZjifzvfw5GSgWzfVmBU1V1fV9hou514OwjaEYff5By+OoFZBiBkRUznrolWikJAQLFmyBLt378adO3fg4uJSbp8jR44gKysLjRo1Qq9evQyW2bFjR9SpUwdFRUX466+/0L17d62yAKBLly7o0KEDateurXMcy9F/3xQfHr+yefNmTb0bNGhg/Ik+5MKFC5pjhISE4NFHH0WXLl1w6NAhbNy4Ee+8847JZRvCgKUMR0dHAEBRUZHefQoLC7X2tWSZTk5OkmWNHDkSI0eONOq46nncLc7UhcVMGfweEWFeXaUWLDR3ALualYKSyrzM1gw67DVw6NqVeSsjb1UMlJTKB0sSlcVgxz7puh5KpfTjr1Q+eOuu8DX09gZu3rTqOixVVdiGMCRlar84kjKTEL4hHAljEmxUK+to3bo12rdvj5MnT2L79u149tlny+0TH6+a4WHQoEFGLQ7u5OSE9u3b488//8SRI0e0AhZ1cPLkk0/C2dkZvr6+UCqVuHv3LurVqwcAuHjxomYwfZcuXTR5b968iXPnzgHQPRC/ItSD7Tt16oTHHnsMADBs2DAcOnQI8fHxePPNNyGXy806hj61rFJqFdWwYUMAwO3bt/Xuo05T72uIOpI1pkxzol6ry8lRtUr4+akWIPTzU/2fk2M4XepOWf3JUjaoAFT/nzwpXSd1K8nDLw65XJW2ZYsqAClLVytJSopqYcWUFNX/Ze8cfH1VH0ZWCkri41W/1Wxxmcve4OlKt2bQYc0b6YAA/U+NkBDpp45UGvM+SDf0GFTFQCkxUfq1IpWmVEq/DqXSAOnXt6H3BjVd7ysVSa8qpK5HWpp0XkPpRgkJAebOZbDyL2W2ErvP79aaSRQASsQSJJ5PhDK7ij/hdBj672LMv/76a7m0wsJCbN++XWs/Y6gDikMPfSNz5MgRNGzYEN7e3gCAzp07o7i4GH/++admH3VQ4+HhgVatWmm2X7t2TfO3OsgwhSiKiIuLA6B9TgMGDICTkxOuX7+O/fv3m1y+IQxYylA/wJcvX9bbInLhwgWtfQ1p3bo1ACAzM1PvPhUt0yYMfdJKfT0v9QlvqFtX+/b676TUrST6ghJjAhLAakGJvhsDU4MOwHqX2ZpBh60CB0PxqtRTRyqNeR+kb95c/QIlc9hrsGNMOmC7YMeU40pdDy8v6eMZSqeKS8uVjgINpVdFwcHBqF27Ng4ePKgVFADA3r17cfv2bbRs2RIdO3Y0ukx1y8iJEyc0vW8yMjKQnZ2NTp06QSaTAVC1tAAPuooBDwKWh1tR7paZitvZ2dnoujwsOTkZly9fRp06dTBo0CDNdhcXFzz99NMAgE2bNplcvkHGDHQ5fvy4GBsbq3cxm+oiLy9P9PPzEwVBEI8cOaJzn7Fjx4qCIIjffPONUWWeO3dOM6Dr6tWrOvfp16+fKAiCGBMTY2rVy7HooD1Dg9vNGdFraPD7vn12Pc2vKQPUbTFQ3NBltubAanPWs7TEWpi2mm63puS11eNrrckcbLUurDUnLjR0PWw1W5upx923z/zrYa64U3HirIRZYtwpy8wMVlZVHHRvzALT9sqUQfdqr776qigIgrh8+XKt7ZMnT9abR8qdO3dEX19frftQ9axcy5Yt0+yXm5srent7i88995xm29NPPy0KgiCuW7dOq8zU1FTNOVZk0fOHvfPOO6IgCOKkSZPKpaknpGrfvr34zz//mHwMKTBmpxkzZohPPvmkeO/ePa3txcXFYlRUlPj666+L7733nnjgwAGrVLIyTZgwweIr3Q8ZMsTgSvd+fn52u9K9wbvZWbOs+0krinY3JY8tln+x9mW2VtChxnU6qrfqFChVt2DH2l9IVPYMgu3bGz5fo2cCq6BT2adE1/muWjfjrvNdxVPZp8wruIyqGLCIoigGrQoS5bPlWtdGPlsuKlZZKEq0EnMCls2bN4uCIIhDhw7VbPvnn380652cP39es33Pnj3iyJEjy/0sXbpUq8wRI0aIgiBotr/99tuiIAjisWPHtPYbPHiw6OfnJ+bn54tXr17VnMfDs3Xl5uZq0nbu3Gn0dSnrzp07YseOHUVBEMTt27eXSy8uLhZ79OghCoIgrl+/3qRjGAJjdho4cKA4c+bMcts/+eQT0cfHR/T29ha9vb1FHx+fCkeT9ub48eOa81m/fr1mUZ1r165p3kQmTpxYLl9QUJAYFBQk/vbbb+XStm3bplmQsuzUdunp6aJCoRAFQRDnzp1r0fOwqxYWS0wRbCP6bqRssfyLtS+ztYMOImuwRqBU3YIdc77ssFawY80W5bKPp6Xfkx4OVsoGLZZSVQMWYxeYtjfqm/myiyiWNX/+fL0By/3798UnnnhCFARBPHv2rCiKD1pEwsLCtPb95ZdfdC4/MWPGDK39PvvsM1EQBHHcuHGiKIpinz59xA4dOpRb0PyDDz4QBUEQk5OTxV9//VUUBEHs3r27znMYOHCgKAiC+L///c+4i/KQDRs2GL2chq51ZCzBqFnCrl+/DkEQtLbdvn0bMTExaNSoET755BM4ODhg+fLlWLJkCZ566ilN/7qqxt/fHzNnzsT8+fPx4YcfYunSpWjUqBHS0tJQWFiI1q1bY86cOeXyZWVlAQDu3btXLm3AgAEYM2YMoqKiEBERgRYtWsDZ2Rlnz55FSUkJnnzySbz11ltWPzeT+fpKTwGs7mxuzSmCraiiM25dv276rFiGSE1sZu3LbImZmm00kzPVYOY8J/WlGXotSKVJTT4ISE9MKPX6FkX9aQqF/vMHrDuBgamztZk7mUf79qrHQN8kkGqWfE+KPx2PW/m3dKbdyr+F+NPxCPGuuYPw3Z3dkTAmAcpsJdJy0+Dl5gVfD/v/QHB2dsa9e/eQk5MDDw+Pcunnz5/Xm9fJyQn9+/dHbGws4uLi8NZbb2lmBwt5aEKG0NBQhIaGGqxPQEAAfvjhB/z111+4cOECLl++jO7du5ebaaxz586Ijo7G4cOHkZ2drdmmS3BwMCIjIxEfH4/XX38d9evXN1iPstRjU+rVq4e6devq3S8nJwd//fUXMjIyNGO4LcaYqMbf379cE8/mzZtFb29v8f/+7/802woKCsSgoCDxzTfftGxYZQMHDhwQX3nlFTEgIEB8/PHHxf79+4tff/21eOfOHZ37qyPLX375RW+ZW7duFV944QXxySefFP39/cUhQ4aI//d//1cuarYEi39DUxlfz1uJ1LeopnRVMPebP1t3vSIi67Onlh2pdGu2dFizZcfY4Y2WNCthluQ4jVkJsyxynKrawlJVDR06VBQEQdyxY0e5tAsXLmi6d+nrQaTu2t+nTx/NQormdPP/559/NMMPPvnkE1EQBDEyMrLcfllZWaIgCOLo0aPFQYMGiYIgiGvWrNFZ5s2bN8Vu3boZvdL9tm3bNCvdX7hwQbM4pL7x3WohISGiIAji119/bdzJVoBRAcvAgQPFTz/9VGvbrFmzRB8fH00TmNrXX38tBgYGWqyCZBqrveFVoT5Bthr8bokecFXoMhORhVk62DGUbqtgx5yxM8ZcK0uLOxUnGbBYagA+A5bK9c0334iCIIiDBg0SL168qNmemZkphoaGaiZj0hewlJSUiL169RIFQRDHjx8vCoIgTpgwwaw6qZ8D7du3FwVBEP/44w+d+/Xp00cTUAmCIJ46pX8s1f79+zXnMmrUKPHo0aNa3eBKS0vFY8eOiVOmTBEFQRCVSqUoiqK4cOFCURAEsV+/fgbrvXLlSlEQBDEwMFAsKSmp4FlLM2pa4169emHTpk24ceMGAKC4uBh79uxB48aN4fXQ/ICenp6a/agaMjQFsBXXLZFS0WkvpdYlMaZbl62Xf7HRZSaiSiD1+taXZuh9RSrdVtNamzP1uDHXytJCvEPg6uSqM83VybVGdwerysaNG4fmzZsjPT0dAwcOxDPPPIPg4GD0798fhYWFGDVqlGT+WrVqITg4GACwZ88eAOW7g1WUenrjgoIC1KlTR+/UyE8++aRm+mNXV9dywzfKeuqpp7Bq1So88sgjOHz4MJ577jl069YNw4cPx7Bhw9CtWzeEhYVh+/bt8PLyQuPGjSGKoqY7mDHryTzzzDOoXbs2rly5guTk5IqdtAFGBSwvv/wyRFHEf//7X3z22WeYOHEicnNz0a9fv3L7FhYWSvZvIzJFRdc02b/fvHVJpHh52fXyL0RUg5nyZYctgh1j3iuNfS+tTMkvJ5cLWlydXJH8smVvzqjyNGjQAD/99BNCQ0PRsGFDZGRkID8/Hy+//DKio6Ph4uJisIyyN/MuLi7o27evWXUqu1L9448/DicnJ537lR2z0rlzZ806Lfp07twZO3fuxCeffIKgoCA4OjoiLS0NGRkZaNCgAYKDg/Htt98iPj4eTZo0waFDh5CVlQWZTGZUwNK4cWP06tULALBx40ZjTtVoMlEURWN2PH78ON544w1cvnwZAODu7o4NGzagWbNmWvvNmjULx48fx5YtWyxaUaqY0NBQpKSkwM/Pz+JPmsokNfjd3V0VnOgaiOrrC5w8qb/cyEhgyhT96VKD3xMSHmyz0TwBRER2xdB7YXV7r4w/HY+DWQfRtXlXi7esVJfPbyJLMmqWMADo0KEDdu7ciWPHjuH+/fvo0KFDuVkG7t27h127dpkdWVLNpOsDTapbV2Sk/hlopIIV4MEq26bOuKXGWbGIiGreDIIh3iHsAkZUiYwOWABALpdLTlecmpoKb29v9O/f3+yKUc2hrxVlzhz9AYkx3boMTXspNf2ojWdaJiIiIqJ/VShgMeTJJ5/EmjVrLFkkVSP6bv71taJERJh3vKVLgQ8/NG/5l+r2rSARERFRVWNSwJKcnIxly5YhIyMDzs7O8Pb2Rr9+/dC/f3/UqmXUOH6qpiy5CKO53bp69DCulYRBCREREZH9qnB0sXfvXowbNw7Hjx9Hs2bN0KBBA+zbtw/Tpk3D0KFDcfHiRWvUk+ycvtm61MGKvnEoaWnS5bZvr39KTHW3Lnua9pKIiIiILKvCAcuiRYvg4+ODxMRE/Pjjj1i3bh2Sk5Px7bff4s6dO3jhhRdw69YtK1SV7IG+6YX1BSVDhkhPL2zI0qXmr2lCRERERFVXhQOWs2fP4tlnn0WDBg0022QyGfr27Yv169ejuLgY3377rUUrSbYn1YJizUUY1d26uKYJERERUc1U4YDFxcUFJQ/fmf6radOmCA8PR6I5q/KRXTKnW5cUQ4swqjEgISIiIqqZKjzovnPnzoiLi8MLL7ygc4B9s2bNcP36dYtUrjKdOnUKu3btwqFDh5CWlobbt2/D2dkZbdu2RXBwMMLCwlCnTp0KlxsZGYnFixdL7vPxxx/jueeeM7XqVqduQXmYulvX1KnS+aUWYVQHIJxCmIiIiIh0qXDA8tprryEsLAzTpk3Dxx9/DDc3N6305ORkeHh4WKyCleHChQsYOnSo5v9mzZrBx8cH165dw9GjR3H06FHExsbihx9+QMOGDU06RuPGjdGyZUudafZ+vYxpQeEijERERERkDRUOWHx9ffH5559jxowZ2Lt3L/r06YM2bdrAwcEBR48exb59+zB58mRr1NVqRFFE48aN8eKLLyIkJATNmzfXpO3duxfTp0/HyZMn8dFHH2HBggUmHaN3796YP3++hWpcuby8DKdzEUYiIiIisgaT1mEZPHgw2rZti++++w6JiYnYvn07AMDJyQmTJk1ChLkr/lWyRx55BAkJCahbt265tMDAQLz//vt4++23sWPHDty8eRONGjWyQS1tx9dXugXF2G5dbEEhIiIioooyeaX7tm3b4quvvkJJSQkuXrwImUwGT09PyB+e7qkKcHR0lEzv3bs3AKCkpAQXLlyocQELIN2CUhaDEiIiIiKyJKMClqeeegpffPEFevToUS5NLpejVatWlq6XXcnPz9f87eTkZFIZp06dwltvvYXs7GzUq1cP3t7eCA4ORtu2bS1VTatity4iIiIisgWjApbc3Fzk5uZq/r9z5w7mzp2LyZMna433qK62bNkCAHB1dYWXoQEdeqSmpiI1NVXzf2JiIr777juMHj0aM2bMMKplav369YiJiTHqeOnp6SbV0xC2oBARERFRZTKpS1hRURE2bdpUboA6APz2229YtmwZNm7caJEK2trly5exZMkSAMDLL79c4S5vTZo0weuvv45evXrB09MTLi4uyMjIwLp167B+/XpERUWhdu3amD59usGysrOzkZKSYtJ5EBERERFVRSaPYRFFUef2oqIirZaEquz+/fuYNGkS8vLy4O/vj5deeqnCZYSHh5fb5u3tjdmzZ8PT0xNffvkloqKi8Pzzz8PT01OyLA8PD/j5+Rl13PT0dK2ubERERERkvxQKBbKyssptd3JywiOPPIKuXbti7Nix+M9//lNun0uXLqFv374AgISEBMl7ypkzZyI2NhbDhw+vMjPYmhyw2Iu5c+di9erVFc4XEBCANWvW6E0vLCzE5MmToVQq0bx5cyxevNikhSOljBs3DqtXr8b169eRmJiI0aNHS+4/cuRIjBw50qiyQ0ND2RpDREREVMW0atVKs86hKIrIzc3FpUuXcP78ecTGxmLJkiXo1auXjWtZuap8wOLs7AxXV9cK53NxcdGbVlxcjDfeeAP79u1DkyZNEBUVhaZNm5pRS93kcjk6dOiAnTt3IjMz0+LlExEREVHVMmHCBISGhmptu3LlCt5++20cOXIEs2bNwp49e6rkzLymMjpg+fvvv9G+fXu7mxHsjTfewBtvvGGx8kpKSvD2229j165dcHNzw6pVq/DYY49ZrPyHqVttiouLrXYMIiIiIqq6mjVrho8++gjPPPMMrl+/jrS0NHh7e9u6WpWmlrE7RkVFYdCgQQgICMCkSZMgk8lw7NgxpKeno6TsaoJVWGlpKd5991389ttvaNiwIVauXIk2bdpY9Zhnz54FoFq8koiIiKgqUyqB+HjV76rA29tb8sY/MjIS3t7eiIyM1GxbuHAhvL29MW3aNL35RFGEQqGAt7c3EssuYmeGshNdFRUVWaTMqsKoFpYdO3ZAqVQiNTVV81sURSxcuBCLFi3SrMXSpk0bFBQUWLvOVvPRRx8hLi4OLi4uWL58OXx8fKx6vD179mgCFl1r3BARERFVBTk5QFgYsHv3g21BQaqFp93dbVcvawgJCcGSJUuwe/du3LlzR+cwgyNHjiArKwuNGjWy2HiTEydOAFD1zmnRooVFyqwqjApYWrRogRYtWmDgwIGabdnZ2eWCmB07dkAURchkMqtV2FrmzZuHmJgYODs7Y9myZfD39zc673PPPYdr165h9OjRGDt2rGb72bNnsWbNGjz//PNawU9paSm2bt2Kjz76CAAQFBRUoeMRERER2ZOwMCApSXtbUhIQHq5aeLo6ad26Ndq3b4+TJ09i+/btePbZZ8vtEx8fDwAYNGiQ2ZM25ebm4siRI5oZvUaNGoUGDRqYVWZVY/Kgew8PDwQGBiIwMFCz7c6dO5oApir566+/sGrVKgBAvXr18MUXX+jd97XXXtM6ZwC4du0asrKykJeXp7W9uLgY0dHRiI6OhqurKx599FHI5XJcuHABt2/fBgB07twZn3/+uWVPiIiIiKiSKJXaLStqJSVAYqIqvbotOj106FCcPHkSv/76a7mApbCwENu3b9fsV1Hvvvsu3n333XLbmzZtitmzZ+tcMqMs9fTG1YnJAcuqVau0WhMA1cxbXbp0QZcuXcytV6UqLCzU/J2dnY3s7Gy9+964ccPocps3b45p06ZpxvpkZmaisLAQDRs2RO/evTFkyBAMGTKkRs3yQERERNVLWprh9OoWsAQHB2P+/Pk4ePAgrl27pjWb7N69e3H79m20bNkSHTt2rHDZZac1BlQNApcuXcK1a9fw448/wtfXV7JnzuOPPw4HBwe96ZmZmRW6n7UHJgcs8+fPR1ZWFt577z1L1scmunbtitOnT5ucX99gqgYNGiAiIsLkcomIiIjsnZeXeelVkZubG3r06IG9e/di8+bNePnllzVp6u5gzzzzjEll65rWuLCwEKtXr8YXX3yBF198ET///DPatm2rM//ChQuNWjiyKjF6lrCHyWQyrF27FlOmTKnSA+2JiIiIyHS+vqoB9g93GJHLAYWi+rWuqKm7e/3666+abXl5edizZw8A1eB8tb179+K5554r9/Pdd98ZdSwHBwe88sor6NevH/Lz87VmLasJTA5YFi5cCAcHB+zatQtjxozBzZs3LVkvIiIiIqoiYmKAh4b4IjAQiI62TX0qShRFndvv3bunN0/fvn1Rr149pKamIu3ffnHbtm1DYWEhOnbsiJYtW2r2vXHjBv78889yP+fPn69QPTt16gQAOHbsWIXyVXUmByz9+/fHypUr0bBhQxw/fhwjR47ExYsXLVk3IiIiIqoC3N1Vs4GlpABxcarfCQn2P6Wxs7MzACAnJ0dnulRA4eTkhP79+wMA4uLiADzoDla2dQUAQkNDcfr06XI/6pm/jFVaWgoAuHXrVoXyVXUmByyAKsr76aef0Lx5c2RmZiI8PBzHjx+3VN2IiIiIqArx9QVCQqpONzB1K4iuFouLFy9i3759kvnV3cI2b96My5cv4/Dhw6hTpw4GDRpk8boCwNGjRwGgxq3DYlbAAqjmoo6JiUH79u2Rm5uLMWPGYOfOnZaoGxERERGR1fTp0wcA8M033+DSpUua7RcuXMC0adP0dhVT69q1K5o2bYrLly9j9uzZEEURPXv21JrlyxIKCwvxf//3f5qJnoYPH27R8u2dybOEleXm5oY1a9bgjTfewO7duzF16lTMmDEDY8aMsUTxREREREQWN27cOMTHxyM9PR0DBw5E69atUVpaivT0dLRt2xajRo3SrNWnS61atRAcHIwVK1boHGxviu+//x4bNmzQ/K+e1lg9nmbAgAE17h7b7BYWNScnJ3z77bd4/vnnUVpaivnz5+P111/HTz/9hBMnTmitdUJEREREZGsNGjTATz/9hNDQUDRs2BAZGRnIz8/Hyy+/jOjoaLi4uBgso+zikC4uLmYv3Hj+/HmtgfkZGRmoV68egoKCsHDhQixatAi1a1ukzaHKkImG2roq6O+//8bkyZNx7do1re1yuRytW7eGn58ffH194evri3bt2qFevXqWPDz9KzQ0FCkpKfDz88PGjRttXR0iIiIyAj+/icqzWHj2+++/Y/ny5Th06BAA1fRwbm5uuHnzJkRRRHFxMc6ePYu0tDTNTAq1atVCSkqKpapARERERETVjFkBS0lJCTZv3owVK1bgzJkzmoFJHTt2REREBAIDA3Hnzh0olUoolUqkpKRAqVQiIyMDpaWlmqnZiIiIiIiIdDE5YFm1ahVWr16NK1euaAKVLl26YOLEiejevbtmPxcXFwQEBCAgIECzLT8/H6mpqVAqlWZUnYiIiIiIqjuTA5ayC9306NEDERER6Ny5s1F5nZyc8MQTT+CJJ54w9fBERERERFQDmNUlLCgoCBMnTkT79u0tVR+yEPVc4unp6QgNDbVxbYiIiMgY6enpAKC1JghRTWdywLJp0yb4+PhYsi5kQQUFBQBU3e84sQEREVHVov4cJyIzApabN2+itLQUtWpZbCkXsiA3Nzfk5ubC0dERnp6eFis3PT0d+fn5cHJyQps2bSxWbnXEa1UxvF7G47UyHq+V8XitjGfNa3Xp0iUUFBRYfKV0oqrM5HVYfHx80LBhQwQGBkKhUKB3795wdna2dP3IznB+eOPxWlUMr5fxeK2Mx2tlPF4r4/FaEVUuk1tYvL29cfr0acTHx+PXX39FnTp10L17dygUCigUCnh4eFiynkREREREVAOZHLDExcXh8uXLSEhIwK5du3D06FHs3bsXSUlJmD17Nh5//HE8/fTT6Nu3L5uWiYiIiIjIJGbNEvboo4/ixRdfxIsvvoh//vkHe/bswa5du7Bv3z6cOHECJ0+exDfffIMWLVqgb9++UCgUePLJJyGTySxVfyIiIiIiqsbMCljKatCgAUJCQhASEoLCwkIkJydj165d2L17NzIzM7FixQqsXLkSjRo1QlBQEBQKBXr27AlHR0dLVYGIiIiIiKoZiwUsZTk4OKB3797o3bs3AODEiRPYtWsXEhISkJ6ejl9++QUbN26Ek5MTnnrqKfTt2xd9+/ZFw4YNrVEdIiIiIiKqoqwSsDzM398f/v7+ePPNN5GZmakZ93Ls2DEkJCQgMTERly9fxuTJkyujOkREREREVEVUSsBSVsuWLTFu3DiMGzcOubm5SExMRGJiIurWrVvZVSEiIiIiIjtX6QFLWW5ubvjvf/+L//73v7asBhERERER2SkuU09ERERERHbL4i0sGRkZOHbsGK5fv47c3FwUFBTA1dUVbm5uaNOmDTp16sTuX0REREREZBSLBCx//fUXYmJi8Pvvv+PGjRuS+8rlcvj5+eGZZ57B0KFDUb9+fUtUgSpJWFgYsrOz4eHhYeuq2D1eq4rh9TIer5XxeK2Mx2tlPF4rosolE0VRNDVzXFwcli9fjrS0NJQtxtnZGa6urnB1dYWjoyNu376N27dv4+bNmygtLVUdWCaDk5MTgoODMWnSJDRr1sz8syEiIiIiomrFpIDl4MGD+Oyzz5CamgpRFNGwYUMMGDAAnTt3RocOHdCyZUud+e7evYu///4bx48fR2JiIo4dOwYAcHR0xOjRozFhwgS4uLiYdUJERERERFR9mBSw+Pj4AAB69uyJkSNHIjAwEHXq1KnwwS9evIi4uDisXbsWt2/fxuTJkzFp0qQKl0NERERERNWTSQHLK6+8gilTpqBDhw4WqcT9+/exdu1aODs7Y9SoURYpk4iIiIiIqj6zxrAQERERERFZE9dhISIiIiIiu8WAhYiIiIiI7JZR67CcOHEC586dw9NPP81ZvKqIoKAg5ObmwtHREZ6enrauDhERERnh0qVLKCgogJubG3bv3m3r6hDZBaMClnXr1mHXrl0YMGCA1vaSkhL8+OOPOHr0KOrXr4/g4GB0797dKhWlisnNzUV+fj7y8/Nx+/ZtW1eHiIiIKiA3N9fWVSCyG0YFLMePH0e/fv1Qt25dre2ffvop1q1bp1k08pdffsHEiRMxZcoUy9eUKsTR0RH5+flwcnJCmzZtbF0dIiKiauN+0X0UlBTAUe6IunXqGs5QAenp6cjPz4ejo6NFyyWqyowKWK5fvw5BELS23b59GzExMWjUqBE++eQTODg4YPny5ViyZAmeeuopPPnkk1apMBnH09MTt2/fRps2bbBx40ZbV4eIiKjKy7mXg7ANYdh9/kFXraBWQYgZEQN3Z3eLHCM0NBQpKSnszk1UhlGD7ouLi+Hs7Ky1bd++fSgqKsJLL72Ep59+Gr1798by5cvRrFkzrFu3ziqVJSIiIrKVsA1hSMpM0tqWlJmE8A3hNqoRUc1gVMDy6KOP4ty5c1rbDhw4AJlMhqCgIM02BwcHPPPMMzh69Khla0lERERkQ8psJXaf340SsURre4lYgsTziVBmK21UM6Lqz6iApVevXti0aRNu3LgBQNXismfPHjRu3BheXl5a+3p6emr2IyIiIqoO0nLTzEonItMZNYbl5ZdfxqZNm/Df//4XAwcORHp6OnJzczFy5Mhy+xYWFpYbnE9ERERUlXm5eZmVTkSmM6qFpWnTpli2bBlkMhlWrlyJpKQkNG7cGOPHjy+3b0pKCjw8PCxeUSIiIiJb8fXwRVCrIMhlcq3tcpkcilYK+Hr42qhmRNWfUS0sANChQwfs3LkTx44dw/3799GhQwfUr19fa5979+5h165d6Nu3r8UrSmRvevfujccffxxLliyxdVWIiKgSxIyIQfiGcCSeT9RsC2wZiOgR0TasFVH1Z3TAAgByuVxyuuLU1FR4e3ujf//+ZleMyJ7dvHkT165dw4gRIyT3u3TpEkaPHo3ExETJ/YiIyP65O7sjYUwClNlKpOWmwcvNiy0rRJWgQgGLWnJyMpYtW4aMjAw4OzvD29sb/fr1Q//+/bFmzRpL15HI7pw6dQoA4OPjUy7t5s2buHDhAjp06FAube/evQgMDLR6/YiIyHp8PXwZqBBVogoHLHv37kVERIQmUBFFEfv27cOWLVvQtm1bLFmyBI899pg16kpkN6QClsuXL2P69Ono2rUrwsNVc/OnpaVh9uzZkMvl6NixIxo2bFip9SUiIiKqqiocsCxatAg+Pj5YtWoVGjRoAAAQRRGJiYn43//+hxdeeAFxcXFwdXW1dF2J7EZqaipcXFx0rkTs5+eHzZs3IyYmBlOnTsX169cxY8YMTJs2Db169bJBbYmIiIiqLqNmCSvr7NmzePbZZzXBCgDIZDL07dsX69evR3FxMb799luLVpLI3pw6dQo+Pj6QyWQ602Uymean7P9EREREVDEVDlhcXFxQUlKiM61p06YIDw/nAOMaQn3T7u3tjZUrVxrcf8eOHWjXrh28vb2xYsWKSqihdRQWFuLcuXM6u4MBgFKpREhICFJTU7FgwQI0adIE8+bNw/fff4+XXnoJt2/fruQaExEREVVdFQ5YOnfujLi4OJSWlupMb9asGa5fv252xcj++fj4oE+fPgCAqKgoFBUV6d33zz//xNtvv43S0lK88MILGDduXCXV0vLS09NRVFSkN2Bp1qwZ5s2bhzlz5mjGqrRt2xZr1qzBmDFjOH6FiKgKUGYrEX86Hspspa2rQlTjVThgee2113D69GlMmzYNubm55dKTk5O5cGQNMnHiRADAlStXsGXLFp37ZGRkICIiAgUFBejbty/ee++9yqyixUkNuAeARo0a6ZwhDIAmwCMiIvuUcy8HiigF/Jb4Yej6ofBb4gdFlAI593JsXTWiGqvCAYuvry8+//xz7N69G0FBQZg6dSoWLVqE7777Dq+++iq2bt2KZ5991hp1JTvk7++Pnj17AgB++OGHcum5ubl49dVXcevWLfj7++Orr75CrVoVftrZldTUVMjlcgiCYHBfT09PdpEkIqpCwjaEISkzSWtbUmYSwjeE26hGRGTSOiyDBw9G27Zt8d133yExMRHbt28HADg5OWHSpEmIiIiwaCXJvkVERGDfvn04c+aM1joj9+/fx4QJE3Dx4kW0aNEC33//PerWrWvj2pZXVFSEdevWITY2FhcuXEB+fj4aNGiAgIAAvPHGG2jdurXW/qdOnULr1q3h6OhooxoTEZE1KLOV2H1+d7ntJWIJEs8nQpmt5PorRDZgUsACqPrkf/XVVygpKcHFixchk8ng6ekJuVxuyfpRFdC5c2cEBATg0KFDWL58OQIDA1FSUoI333wTJ06cgKurK5YtWwY3NzdbV7WcjIwMTJ06FadPnwagmlRCLpfj5s2b2L59Ow4cOIANGzZoBS2nT5/WtCoREVH1kZabZjCdAQtR5TMqYHnqqafwxRdfoEePHuXS5HI5WrVqZel62YQoivjrr7+QmJiIo0eP4ty5c7hz5w7q168PX19fDBs2DM8880yFp6edOXMmYmNjJfdZtmwZevfubU71bSoiIgKHDh3CoUOHcPLkScTGxiIxMRGOjo5YunSpXT5Hzp07h+eeew63bt3CgAEDNK0pxcXF2Lx5M95//33k5eXh888/x9KlSwGoxurcunVL7/gVIiKqurzcvMxKJyLrMCpgyc3N1Rpgf+fOHcydOxeTJ09G8+bNrVa5ypacnIyxY8dq/n/sscfQvHlzZGVlYf/+/di/fz+2bNmCyMhIODg4VLj8Zs2aoVmzZjrTqvrMUU899RQ6duyIY8eOYfLkybh69SpkMhk+//xzdOrUyehyNm7ciHfffdfkeqxevRpdu3Y1uF9RURGmTp2KW7duITw8HJ988okmrXbt2hg2bBhOnz6NFStWICkpCfn5+XBycjI44J6IiKouXw9fBLUKQlJmEkrEB0s4yGVyBLYMZOsKkY2Y1CWsqKgImzZtQkhISLmA5bfffsOyZcuwceNGi1SwMomiCE9PT4wZMwbBwcFo3LixJm3Tpk344IMPsGfPHixcuBDvvPNOhct/9tlnMWXKFEtW2a5ERERgwoQJuHr1KgBgxowZGDhwYIXKcHJygru7u8l1qFOnjlH7bdy4EWfOnEHz5s3x/vvv69wnKCgIK1asQHFxMbKystCmTRsEBQVpuo8REVHVpcxWIi03DV5uXlqBSMyIGIRvCEfi+QcTpgS2DET0iGhbVJOIYMYYFlEUdW4vKipCamqqyRWyJX9/f2zbtk3nTe+wYcNw9epVfPPNN/j555/x1ltvVfnZriytT58+cHNzQ25uLvr374+XXnqpwmUMHjwYgwcPtkLttK1fvx4AMHr0aL2tZS4uLpq/9T3fiYioasm5l4OwDWFag+uDWgUhZkQM3J3d4e7sjoQxCXoDGiKqfLzjLsPFxUXyG3r1GJNbt27pXIOmpsvLy8PNmzcBAN26dbNxbfS7du0alErVQmB9+/bVu192drbm70ceecTq9SIiIuszdtpiXw9fhHiHMFghsgMmt7DURPn5+Zq/nZycKpz/4MGDOHv2LG7duoUGDRrAz89PZ7e6qkqpVGpaIvz8/GxcG/3+/PNPAICrqysee+wxvfv9/fffAIBWrVpptbYQEVHV8HArCactJqqajA5Y/v77b7Rv394uZ3uqLOqV3H18fEy6gT18+LDW/zt37sS3336LqVOn4tVXXzWYf/369YiJiTHqWOnp6RWun7nUrRZyudzkQelbt27F3LlzTa5DZGSkwUH+KSkpAAAPDw/J/RISEgBAs64MERFVDfq6fY17YpxkPk5bTGSfjA5YoqKisHr1atSvXx9eXl6QyWQ4duwYmjRpglatWlX79Vf+/vtvzbiH8ePHVyhvy5YtMXPmTHTr1g3NmzeHg4ODZgaqbdu24csvv4SzszNGjRolWU52drbmZtseqev2n//8x6QWKEDVipWTk2NyHYqKigzuow6s7ty5o3ef5ORkpKSkQCaTISwszOT6EBFR5dPX7ete4T3JfJy2mMg+GRWw7NixA0qlEqmpqZrfoihi4cKFWLRokWYtljZt2qCgoMDada50OTk5mDJlCoqLi9GvXz8EBwdXKH9ERES5bR06dMDChQsxe/ZsrFu3DgsWLMCwYcNQr149veV4eHgY3dUqPT1dqwtbZVAHAr6+pn87FRoaitDQUEtVSSd1YHXlyhWcOXMGgiBopefm5mpmDhs+fDi8vPgBRkRkj3QNjJfq9nXw8kEENA/A0ctHOW0xURViVMDSokULtGjRQmuK2uzs7HJBzI4dOyCKYoUXVrRneXl5ePXVV3H58mX4+flh/vz5Fi3/zTffxIYNG/DPP/8gOTlZchD4yJEjMXLkSKPKDQ0NrdTWmPv37yMjIwOAeQGLtWVlZeHWrVsAgPr16+Ptt9/G119/DS8vLxQXF2Pfvn2YO3cuLl68iDZt2mDWrFm2rTAREZUjNdOXodXqpwRMwcq/VnLaYqIqxORB9x4eHggMDNTq33/nzh1NAFMd3L17F6+88gqUSiXatm2LH374weKDr+vXr4+2bdtCqVQiMzPTomVXptTUVJSWlgKw7wH36uemh4cHpk2bhvfeew/BwcFo0KAB8vPzUVhYCEB1DkuXLkX9+vVtWV0iohpPVyuK1ExfkYMjJcvr1KwTXvB/gdMWE1UhJgcsq1at0loVHlBNC9ylSxd06dLF3HrZ3P379zFhwgQcO3YMrVq1wsqVK9GoUSOrHEs9lXJxcbFVyq8M6rV3ZDIZ2rVrZ+Pa6Kee+cvX1xf//e9/Ua9ePaxcuRJpaWmoXbs2fH19MXToUISFhaF2bU6iR0RkbfoCB32tKHOC5kjO9KXez9Bq9b4evgxUiKoIk+/I5s+fj6ysLLz33nuWrI9dKCgoQEREBA4fPozmzZtj1apVBmeUMlVxcTHOnTsHoGqv9TFq1CiDkwbYA3ULizqoGjRoEAYNGmTLKhER1UiGFnDU14oSsaX8uNCy0nLTuFo9UTVjcsAik8mwdu1aXL16FV9++SUcHR0tWS+bKSoqwpQpU/DHH3+gadOmiIqKQrNmzax2vOjoaOTl5aF27dp2vdhidWGJiQGIiKhiTOnWpa8V5eT1k5LH8nLz4mr1RNWMySvdL1y4EA4ODti1axfGjBmjWeG8KispKcFbb72FvXv3wsPDA1FRUZILC5alUCigUCiwbds2re379+/HF198gfPnz2ttLywsxJo1azBv3jwAqgH1TZo0sch5kG7Xrl3TTJnMgIWIyHKU2UrEn46HMlt7DGvOvRwoohTwW+KHoeuHwm+JHxRRCuy/sB+7z+/W6rIFPOjWlZiRCCntm7SHXKa9nIJcJoeilUIrMOFq9UTVg8ktLP3794e7uzsmTpyI48ePY+TIkVi+fLnRN/j26LfffsP27dsBAA4ODpIzRH3wwQdaN71ZWVkAgHv3tOd4v3//PpYvX47ly5fD3d0dTZs2BQBkZGRo9h0wYABmzJhh0XOh8tSzptWvXx+enp42rg0RkX0x1BqhK91a3boMWRq8FB/u/pBdvohqCLNGFXfq1Ak//fQTXn31VWRmZiI8PBxLly5Fhw4dLFW/SqWeIQpQBSDqIESXvLw8o8r08/PDxIkTcezYMWRmZiIjIwNFRUVwc3NDz549MXz4cCgUCrPrToaVHb9SnabeJiIylilBh1S6tbp1KVorJAfO92jRg12+iGoQmSiKormF5ObmYsKECTh58iScnJzwxRdfoF+/fpaoH5lIvQ6Ln58fNm7caOvqEBFRJajojFtlgw5dgUHCmAQoohQ60zs364yDlw/qrUvkoEhM+W2K3vT2TdpDma3Ue9yceznlBs4rWikQPSIa7s7uxl+UKoaf30TlmTyGpSw3NzesWbMGQUFByM/Px9SpUxEVFWWJoomIiGoUfeNBpNL0jRXJuacat6evJWTIj0Mkx5LEn47Xmy4VrBhjafBSBLYM1NpWtluXeuB8ysQUxI2MQ8rEFCSMSajWwQoR6WaxhSacnJzw7bff4n//+x/WrVuH+fPn4+jRo+jevTv8/Pzg4+MDBwcHSx2OiIioSjKlFQSASWNFDHXNMhR0HMwyPSixVLcurpdCRBZdGa9WrVoIDQ1FYmIirl27hp07d2Lnzp0AALlcjtatW8PPzw++vr7w9fVFu3btUK9ePUtWgYiIyOoqc4B6+IZwiBBNCkiMmXFLStfmXSXTA5oH4Ojlo3oXaDRmPRQGJERkiMUClt9//x3Lly/HoUOHAACiKMLNzQ03b96EKIooLi7G2bNnkZaWhri4OACqAEc9cxMREVFlskbQYY0B6mVv9nWlmROQANJBR4h3iGQrSfSIaMmAhOuhEJElmBWwlJSUYPPmzVixYgXOnDkD9fj9jh07IiIiAoGBgbhz5w6USiWUSiVSUlKgVCqRkZGB0tJSlJaWWuQkiIioZrKnoCNhTILkWBFd3a8sFXRIMdQ1y1DQIdVKYmxAwlYUIjKHyQHLqlWrsHr1aly5ckUTqHTp0gUTJ05E9+7dNfu5uLggICAAAQEBmm35+flITU3VTDNLREQ1V3UJOtQD1HWlmztAXYqhgMRQ1yxDQYcxQQkDEiKyJpMDlvnz52v+7tGjByIiItC5c2ej8jo5OeGJJ57AE088YerhiYiokkndsDLosO4AdfUYFlPHilgi6GBQQkS2YlaXsKCgIEycOBHt27e3VH2IiMiKTAk6zJm9qtoGHdfbAblegFsa0CQVwEMD1HWka8aKXBM0afKmZ8oHHYeuaNIDA5ppgg6pNHVAEr8vDQdP3kDX9o0R0tOrfL2zfYE0X8ALgId2klIJpKUBXl6AL+MSIrIjJgcsmzZtgo+PjyXrQkREMK21wlCatabMlZq9qlKCDh2BgVbQoSNdKs1Q0PFEg374a9G7wPmgB/u12o2eby1CiHcIejQeiv1fTdWZvrz/cnQbcAG3Tj3oXVDf5y8s2d5C9c89d4hRCUCZ0xZTAQT/+7e+NGcgJwcICwN27/aCKhoBgoKAmBjA3b1s+oP86nRAf5p7mSVPGNAQka2YHLAwWCGims6eukgB1gk6jJ69qszNfUmT1PJBx0PpZgcddxsDG2KA84oH+7VKBEaEqYIOifQnmnUyOegQN0QDF+Ra10J2oTfwcw9gMlTH1JMesdEBeWcba6XlnX0CE18CEhJUQUOS9sOApCQgPBwQRf1phvKaW7ZUsKMOaAwFMwx2iMgcFl2HpTpJTk7GypUrcfz4cdy7dw+PPvooBg4ciPHjx8PZ2dmkMrdv3461a9fi1KlTKCoqQsuWLRESEoLRo0ejTp06Fj4DourDGi0O5uS1ty5SFQo6dAQWGjrStGavqmDgcDDroP70sFBArG1y0FE/fhvyMjtqnS8ye8F18w6EfN4Jrr/uxK3M9jrTnT0eNynouBfVA38eKb8Aslgqx769csTHA/uT9KfrUlICJCYC8fHaAcHD6ebkNadspRKYPFl/QBMdLR3MGBPsEBEZwoBFhzVr1mDu3LkQRRGPPPIImjVrhrS0NCxduhQ7duzAunXr4OrqWqEyP/vsM6xYsQIA0KJFC9StWxdnz57F559/jt27d2PFihVwcCj/QWdv7O3GkXktm9fe6mXNFge77iJVwdYKo4IOfTf/I4cBJQ56AwMA0kHHhhggs7fW+SCzF7AhGl1fvgts6Ks7PeYX1HdsaFLQUf+XJOSd0/E1vVgHt1I7IT4eWt2uHk7fn6ojyYig488juoMOtYNmTARmzbzmlJ2YKB3sBAcDR49qp1Wk5Qdg6wsRGcaA5SF///03Pv30UwDAJ598grCwMMhkMly7dg0RERFISUnBBx98gMjISKPL3LlzpyYgWbBgAfr27QsASE9Px/jx43H48GF8/fXXmDlzplXOyRLs9caReS2T117rZa0WB6Pzlrn5T5KZ31phsIuUqa0VxgQd+gKL3xYAt1vpDToU7zSD6689dAcOPx9A3nndgQPO9wVOAzhfPlmdnqcjyZigQ2ewUoatAoeu0ovC2yyvOWUb8u9a0VqMbdnZvx/44AO2vhCRYTJRvYgKAQAmTpyIhIQEDBs2DJ999plW2vnz5zFo0CCUlpYiLi7O6HE8Q4cOxalTpzBp0iS8/vrrWml//PEHxo4dCwcHB+zduxdubm4WOY/Q0FCkpKTAz88PGzduNLs8RZRC75SaCWMSJNOlpuNkXvvIaxf1emjmpM7NOutscVB3RYobGYeh64fqTdcwJa9E4BD5348x5eePTQocZg2cgE+3fa+/tSJmoypwEMt8lyQrAlomIW7bXQwd6KI73X/Ng6BDV941LTG0l44Zo4wQFwcMHWpSVsyaBfz7/U+l5jWnzobydn2iEEf+kqMED1pb5ChBYM8SJPzuAEXPQiTt150uitCbZjDv3ylIuvU4SlCnTFoRAl1PIuFmJyga/WVyugiZ3rTI/Z3g51fx6wgYfgz92xUiJVX/9VBTxqch7eANeHVtDN8Q057HVYmlP7+JqgO2sJRx9+5d/P777wCAsLCwcumtWrVCt27dcODAAWzbts2ogOX8+fM4deoUACA8PLxcevfu3dGyZUtkZmYiISEBI0aMMPMsLE+ZrZQcdCs1m4/WN87m5LVwFxnmtaN6pZwANuzQuoEvaZWIgyOHASXWaXEwmFeimxP+m2pya4VkF6m124DL3VCOMa0Vx8fpSHiQ98Ix3cnGsNcWB6nAISTEAUE9TLv5DwnphCBX/Tf30c6fIByvIxEPnjeB2ItoRAKIRQzCJNJFk/L+fG8uSm4dRziikYi+ZdKSEH0rHIhfgZhb40xK//nWsyhBbb153dNWIAguSEKvctejM47iIHQ8Z9WPkYHH8ERq+a53JZAjcZ8cSiXQRH4DYd0uYPetJ6CZ+cz1L8Qkt4C797+TF7A/GVGNwICljNTUVBQWFsLBwQH+/v4693nyySdx4MABHD9+3Kgyjx07BgB47LHH0LRpU71lZmZm4vjx43YZsKTlpkmmmzOFqDkzAVn1hrUm5bV1vaxx829O3thV2nVV0wQOXsD5lrrTDQQOkkGHrmClDHMCB3MYuunsXf8v7M8z7eZf6pt9awUO5tz8/3zrWTTafxsJiIMS7ZAGL3ghDb5IBfYBiI+H+/44/emAaXn/VOd9unwaABw8CHfcMD3dQNkx+F739cCzeBYbdQYzgUhCCO7qDXb6YA8S0E/PswpIS7yAyR/cQNIt7a6ISbceR3i3k0g4KwJhYVDuvvqgzkGPcC5moupKJI2YmBhREASxf//+eveJi4sTBUEQAwMDjSrzm2++EQVBEF966SW9+yxZskQUBEF8/vnnK1plvYYPHy4KgiAOHz7c7LJSrqeI+Biqn4ntRIx8RvX7321xp+JEvNNYRKsEUTVB5r8/rRJETG+oP+2dxobztkoQISvSTpMVimi1S5VXX3qHH5jX2Lw2rFfk5oce9wr8xMWZls/cvLNm2SavOXVOSRHFINc/RTkKtbbLUSgqXI9Kpomi/rwv1d8gZqOxqMAurTQFdonZaCyKcXF603PR0Ky86g0paCfG4RkxBe10Xiyd6VJpZR4kqbxV6slhoReLrush+RjOmqU3/SA6Sx5266u/SKZntOsvBiFRa1sQEsXsnsNUH1zZ2aIYFKSdKShItd3OWfLzm6i6sGoLy759qq+UunfvDrlcenYVe3D79m0AQMOGDfXuo05T72vJMv/55x/JstavX48Y9SpfBqSnpxu1nzF8s4EeqY2xPzkGyCzzzXPLRPTsGoaQ04Drmhjculb+2+quK77G6dqtdKa5rolGSM+7evO2/78VOHlL/zfddVb/DpzvpTP9P8d74xx09HW2cV7szLTOt/Pm5LVm2YbyZuhONkZ1HFgt2Vrh5YQgXNX5bfVorMF5tNL7Tbdv2l2TuwRJtTgsyBuHBsiz2jf7hvICgC9Sy20r+wDrTJdKK/MgSeXVyZpPjoAA1XRcJQ/GgkEuBwIDgZAQ1Wj1pCTT0kXRqLy+JWWuh1wOdO4M94MH9T9GXbvCHZ/qTQ9Cot7nbJFM/6yZ7aDEuNQZSIL2+3ASeiJ8XykSDM3FzOnJiKqcWtYs/JVXXsH48eORl6dzLhi7U1BQAACSa6Kopx5W72vJMvPz8yXLys7ORkpKilE/hsqqkLS0f9cl0A4qZBd6AT9HQ7n5HG5dVQAPx79iHdTNaaU37dbVvti19rLedKdbzSWr9feebL1pjXHDLvOe+DVTb5onLkjnXXPMKnmtWbahvM4n/tCb9h9Id0Xsid+tkrcdlAhCIuQo0touRxEUSEAI4vWmv4QVZuX9Ja8fAqF9k6UKHPoDiYmIQZjO9AWYpjctGuFaN/8p8EUcQpACXyTgaTTCbb1p7rghmbdBmXm+fJGKEPyqfYP/0M1/uXQL5NXJmJv/h79Ek8sBheLBDbq+dKk0a+bdskUVQJQVGKhaCAVQdYUyNd3UvJs3a+qs9RjpOCdd6TE9FiHwoddiIH5HdM/F8ArWP0a0Ka5iNxQoeahXewnqIBF9kfZjsmrqsbIBGKA9PZlCAfj5qWZY8PNT/Z+To/eYRGRbVh/DIoqitQ9hMY6OjgCAoqIivfsUFhZq7WvJMp2cnCTL8vDwgJ+R07Wkp6dbLGhRwhf7S8u3GohiHewT++J3mavevGm6WhvKSBb199u/gcZ60wDg8T4ewIGqlbdbyyt607yQhktooT+vLBlAR4vntWbZhvI+LUtAEO7r/Jb1OfyEA+ih9xvYQUhEEIosnjcUv2AaFupucUA4cHCC3j79CzANhXAwOa9kawVgemuFka0GJrU4mPPNv5Hf7Fs8b3S06pv2sqsmPnyDLpVui7zu7qqWAX2tAuamm5rX0PlKpLsDSAgPhzJx8oPnrKKZKs3dXe8YJnldR+A+9LqRI0p/8kREqM6lrIdbXwC2wBDZE2v2N/P29hZ9fHzEmzdvWvMwFmONMSxff/11lR/DYqj7c2Sk9bpe965vWt96c/rlWzVvSooYhATd4wHwg940BXaJYlycVfJas2xj8lprjINdjo8wMq/On5QUVR98uVx7u1wuigqFdJooWi9vdrbqt9aFVDwYKyCVbqu8aikpqsckJUX3m59Uuq3y2isrXI/sUzmiwvWo9kPoelTct/mm5EvlbFyKea8zG49/4RgWovJgzcKrWsBy6NAhURAE8fHHHxcLCwt17hMZGSkKgiCOGTPGqDJjY2NFQRBEhfqDX4eZM2eKgiCIs2bNMqXaOll00H2K4ff3oB4FolxWrH0/IysWFT0LJNNEUTqvvg+s7FM5oijq/0DLPpVjv3l7DBUV0B5srkCCmN1zmGSaNfPasl7qm2GtG4uHbqR1plVC3kq/+TeUlzf/ls1LVUJK3FkxblaymBJ3VrPN0OdKdo+hOgfl327XVfoDLS7O8OvQyhiwEJXHgKWMvLw80c/PTxQEQTxy5IjOfcaOHSsKgiB+8803RpV57tw5URAEURAE8erVqzr36devnygIghgTE2Nq1cux9Buere6j1HR9YJUllW53ef89Ya0b5Yculs40a+a1g3rZ1U24vebVPLl48081m6GXSlCPAlGO8gHNS52OGQ5YpNIr4bnPgIWoPKuudO/j4wOZTIY//vgDrq6u1jqMRb322mvYvXu3RVe6f+aZZ3DmzBnJle7r1KmDpKQku13pPienfDdkheJB12o1qS6/hroD17juwta6WOZeaHusF/MSkQ66XipKpWocvT55AQq4HNUzvmnqVNVAfH3i4lRjpKyIK90TlceA5SEnTpzQrHI/e/ZshIWFQSaT4fr163jttdeQkpKCp59+Gt9++61WPoVCNf3u9OnTMXDgQK207du34/XXX4eDgwMWLlyo2ffcuXN49dVXcenSJYwZMwazZs2y2HlY6w2P91FERGTP4uOlY47f1uRg4Eo938Bdvy4d7aSkqD78rPhhyICFqDyudP8Qf39/zJw5E/Pnz8eHH36IpUuXolGjRkhLS0NhYSFat26NOXPmlMuXlZUFALh37165tAEDBmDMmDGIiopCREQEWrRoAWdnZ5w9exYlJSV48skn8dZbb1n93CzB15eBChER2S8v6ckp0aKTO/CCnlnP3N2lZ5hr0kQV3Oze/SAtKEg1G1rZ7gZEZFFWXYelqho7dixWrlyJ3r174/79+0hLS8Ojjz6K1157Db/88otJ3bZmzZqFBQsWICAgADdv3sT58+fRpk0bvP3224iKijJ6mmQiIiLSz9dXekkbTdcx+CIeIVDioW/hpNalCQvTvyAlEVkNW1j06N69O7p37270/qdPnza4z6BBgzBo0CBzqkVEREQGSC0Pk5Ojijv0NpLoW3dGqdTOpKZekFKpZBcEIithwEJERETVitRalwqF/kaSsutGlusDnZYmfdC0NAYsRFbCgIWIiIiqpYdjDrMaSQwNjjGUTkQm4xgWIiIiqhGMaSTRy9jBMURkcQxYiIiIqEYwu5FEakA+EVkNu4QRERFRjaBuJNE3a7HBRhKpwTFEZDVWDVjmzZsHAKhXr541D0NERERkFKkZxIzGRcmIKpVVA5bhw4dbs3giIiKiCmEjCVHVwy5hREREVOOwkYSo6uCgeyIiIiIislsMWIiIiIiIyG6xSxgRERHRQzjGhch+MGD516lTp7Br1y4cOnQIaWlpuH37NpydndG2bVsEBwcjLCwMderUqXC5kZGRWLx4seQ+H3/8MZ577jlTq05EREQWkpMDhIUBu3c/2BYUpJpdzN3ddvUiqskYsAC4cOEChg4dqvm/WbNm8PHxwbVr13D06FEcPXoUsbGx+OGHH9CwYUOTjtG4cWO0bNlSZ5qHh4dJZRIREZFlhYWp1mkpKylJNRVyQoJt6kRU0xkdsOTl5aF+/frWrIvNiKKIxo0b48UXX0RISAiaN2+uSdu7dy+mT5+OkydP4qOPPsKCBQtMOkbv3r0xf/58C9WYiIiILE2p1G5ZUSspUa3bolSyexiRLRg16D4lJQXdunXDRx99ZO362MQjjzyChIQEREREaAUrABAYGIj3338fALBjxw7cvHnTFlUkIiIiK0tLMy+diKzDqIBl7dq1qF+/Pt5++23J/f744w/8/fffEEXRIpWrLI6Ojqhbt67e9N69ewMASkpKcOHChcqqFhEREVUiLy/z0onIOozqEnbw4EEMGTLEYJcwmUyGESNGIDIyEk8//bRFKmgP8vPzNX87OTmZVMapU6fw1ltvITs7G/Xq1YO3tzeCg4PRtm1bS1WTiIiIzODrqxpgn5Sk6gamJpcDgYHsDkZkK0YFLNnZ2fD29ja4X7du3dCuXTskJCRUq4Bly5YtAABXV1d4mfj1SmpqKlJTUzX/JyYm4rvvvsPo0aMxY8YMyOVyg2WsX78eMTExRh0vPT3dpHoSERHVZDExqgH2iYkPtgUGAtHRtqsTUU1nVMDi7Oys1cogpVevXkioRtNoXL58GUuWLAEAvPzyy0YFFmU1adIEr7/+Onr16gVPT0+4uLggIyMD69atw/r16xEVFYXatWtj+vTpBsvKzs5GSkqKSedBREREhrm7q2YD4zosRPbDqIDF09MTJ0+eNKpAT09PXLt2zaxK2Yv79+9j0qRJyMvLg7+/P1566aUKlxEeHl5um7e3N2bPng1PT098+eWXiIqKwvPPPw9PT0/Jsjw8PODn52fUcdPT040OMomIiEibry8DFSJ7YVTA0qdPHyxbtgxTpkzBY489Jrnv3bt3UVhYaJHKGWPu3LlYvXp1hfMFBARgzZo1etMLCwsxefJkKJVKNG/eHIsXLzZp4Ugp48aNw+rVq3H9+nUkJiZi9OjRkvuPHDkSI0eONKrs0NBQtsYQERERUZVn1CxhL774IpydnTFhwgRcuXJFct9jx47h0UcftUjljOHs7AxXV9cK/7i4uOgts7i4GG+88Qb27duHJk2aICoqCk2bNrV43eVyOTp06AAAyMzMtHj5RERERERVnVEtLK6urvjqq68wceJEDB06FFOmTMGzzz4LZ2dnrf22bt2KHTt2YMyYMVaprC5vvPEG3njjDYuVV1JSgrfffhu7du2Cm5sbVq1aZbBVyRzqVpvi4mKrHYOIiIiIqKoyeqX7Hj164IcffsA777yDTz/9FF999RU6duyIli1bori4GKdPn0ZKSgo8PDzw6quvWrPOVlNaWop3330Xv/32Gxo2bIiVK1eiTZs2Vj3m2bNnAagWryQiIiIiIm1GBywA0LlzZ2zevBk//vgjfvnlFyQnJyM5OVmT3r17d3zyySdwc3OzeEUrw0cffYS4uDi4uLhg+fLl8PHxserx9uzZowlYevToYdVjERERERFVRRUKWACgXr16GD9+PMaPH4/r16/jypUrKCkpQcuWLdG4cWNr1LFSzJs3DzExMXB2dsayZcvg7+9vdN7nnnsO165dw+jRozF27FjN9rNnz2LNmjV4/vnntYKf0tJSbN26FR999BEAICgoqELHIyIiIiKqKYwKWL755hu0a9cOvr6+aNGihWZ7kyZN0KRJE6tVrrL89ddfWLVqFQBVQPbFF1/o3fe1115DYGCg1rZr164hKysLeXl5WtuLi4sRHR2N6OhouLq64tFHH4VcLseFCxdw+/ZtAKpWq88//9yyJ0REREREVE0YFbB8//33kMlkAFQ39D4+PpoApl27dmjbtm2FF1S0J2WnYc7OzkZ2drbefW/cuGF0uc2bN8e0adNw7NgxpKenIzMzE4WFhWjYsCF69+6NIUOGYMiQIVX62hERERERWZPRXcIcHBzQu3dv3L9/H6mpqThy5AgAQCaToU6dOvDy8tIEMO3atUOnTp2sVmlL69q1K06fPm1y/sTERJ3bGzRogIiICJPLJSIiIiKq6YwKWBYvXowvvvgCu3fvxnPPPYevvvoKBQUFUCqVSE1N1fz88ssvEEURMpkMqamp1q47ERERERFVc0YFLE8//TT69OmDtWvXYunSpYiPj8ekSZMwatQo9OnTR7PfnTt3NEEMERERERGRuYxa6R4AateujbFjx2LHjh145pln8Pnnn2Pw4MFISEjQ7OPi4oKAgIBKXTiSiIiIiIiqL6MDFrWGDRvi/fffx6+//orWrVtj0qRJGD16NE6dOmWN+hERERERUQ1W4YBFrXXr1vjuu++watUq/PPPPwgNDUVsbKwl60ZERERkd5RKID5e9ZuIrK/CC0devHgRaWlpOHv2LM6ePYu0tDScO3cOpaWlyMrKskYdiYiIiGwuJwcICwN2736wLSgIiIkB3N1tVy+i6s6ogOXdd9/F2bNnkZ6ejvz8fIiiCGdnZwiCAH9/f4SFhcHb21trNXciIiKi6iQsDEhK0t6WlASEhwNlhvQSkYUZFbDExsaibt26UCgUGDBgANq1a4fHHnvM2nUjIiIisgtKpXbLilpJCZCYqEr39a38ehHVBEZ3Cbt//z62bt2KPXv2aK107+Pjg7Zt26JOnTrWrCcRERGRzaSlGU5nwEJkHUYFLDt27NCsr6L+ffToUQCqle7lcjm8vLw0q9y3a9cOXbp0sWrFiYiIiCqLl5d56URkOqMClhYtWqBFixYYOHCgZlt2dna5IGbTpk2IjY3lSvdERERUrfj6qgbYJyWpuoGpyeVAYCBbV4isqcKzhKl5eHggMDAQgYGBmm1c6Z6IiIiqq5gY1QD7xMQH2wIDgeho29WJqCaQiaIompJx1apVGDt2rIWrQ5YSEBCA27dvw8nJCW3atLF1dYiIiKqN+/eBggLA0RGoW9eyZatnZG3YsCEOHTpk2cKJqiiTW1jmz5+PrKwsvPfee5asD1lIQUEBACA/Px8pKSk2rg0RERFVhPpznIjMCFhkMhnWrl2Lq1ev4ssvv4Sjo6Ml60VmcnNzQ25uLhwdHeHp6WmxctXf/LDlxjBeq4rh9TIer5XxeK2Mx2tlPGteq0uXLqGgoABubm4WLZeoKjO5S9iOHTvwzjvvoLCwEB06dMDSpUvRqFEjS9eP7ExoaChSUlLg5+eHjRs32ro6do3XqmJ4vYzHa2U8Xivj8VoZj9eKqHLVMjVj//79sXLlSjRs2BDHjx/HyJEjcfHiRUvWjYiIiIiIajiTAxYA6NSpE3766Sc0b94cmZmZCA8Px/Hjxy1VNyIiIiIiquHMClgAoHXr1oiJiUH79u2Rm5uLMWPGYOfOnZaoGxERERER1XBmByyAaoD3mjVrEBQUhPz8fEydOhVRUVGWKJqIiIiIiGowiwQsAODk5IRvv/0Wzz//PEpLSzF//ny8/vrr+Omnn3DixAkUFhZa6lBERERERFRDmDytsS61atVCaGgoEhMTce3aNezcuVPTPUwul6N169bw8/ODr68vfH190a5dO9SrV8+SVSAiIiIiomrEYgHL77//juXLl2tWZRVFEW5ubrh58yZEUURxcTHOnj2LtLQ0xMXFAVAFOFzUkIiIiIiI9DErYCkpKcHmzZuxYsUKnDlzBuolXTp27IiIiAgEBgbizp07UCqVUCqVSElJgVKpREZGBkpLS1FaWmqRkyAiIiIiourJ5IBl1apVWL16Na5cuaIJVLp06YKJEyeie/fumv1cXFwQEBCAgIAAzbb8/HykpqZCqVSaUXUiIiIiIqruTA5Y5s+fr/m7R48eiIiIQOfOnY3K6+TkhCeeeAJPPPGEqYcnIiIiIqIawKwuYUFBQZg4cSLat29vqfqQnQsLC0N2djY8PDxsXRW7x2tVMbxexuO1Mh6vlfF4rYzHa0VUuWSiuj9XBZ06dQo+Pj6Wrg8REREREZGGyQELERERERGRtVls4UgiIiIiIiJLY8BCRERERER2y6SAZfny5cjPz7doRU6ePIm9e/datEwiIiIiIqraTApYvvzySzz99NNYtWoV/vnnH7MqcOTIEUyYMAFhYWE4efKkWWUREREREVH1YtKg+2+++QZRUVEoKChAnTp10KdPHwQHB6Nz585o3LixZN6ioiKkpqYiMTERmzdvRlZWFkRRhL+/Pz755BPOPEZERERERBomzxJ27do1fP3119i8eTNKSkogk8kAAM2aNYO3tzfc3NzQsGFDODg44J9//sHt27dx8eJFnDp1CkVFRQAAURTRokULTJ06FcHBwZY7K0JQUBByc3Ph6OgIT09PW1eHiIiIjHDp0iUUFBTAzc0Nu3fvtnV1iOyC2dMaX7t2DTExMfjll19w9erVBwX/G8CUpT5U7dq1ERgYiPDwcPTq1UvnvmSeDh06WHycEREREVUOJycnHD9+3NbVILILFl2H5cyZMzh8+DBOnDiB69evIzc3FwUFBXB1dYWbmxu8vLzQuXNndOrUCS4uLpY6LOkQEBCA27dvw8nJCW3atLF1dYiIiMgI6enpyM/PR8OGDXHo0CFbV4fILtS2ZGGCIEAQBIwaNcqSxZIJPD09cfv2bbRp0wYbN260dXWIiIjICKGhoUhJSWF3bqIyuA4LERERERHZLQYsRERERERktyzaJQwA/vnnH1y/fh13794FANSrVw9NmjRBgwYNLH0oIiIiIiKq5iwSsCQnJyMuLg779u1DTk6Ozn3c3d3Rs2dPDB06FN26dbPEYYmIiIiIqJozK2DJy8vDO++8g7179wJ4MG2xLtnZ2di0aRM2bdqEwMBAfPHFF6hfv745hyciIiIiomrO5IClqKgIY8aMQWpqKkRRhKenJ3r16oW2bduiadOmqFu3LgDg/v37uHbtGs6ePYt9+/bh4sWL2Lt3L8aOHYvo6GjUrm3xXmlERERERFRNmBwtrF27FkqlEi4uLpg9e7bRK9Vv3boVH374IZRKJdauXYuxY8eaWgWiKunSpUsYPXo0EhMTbV0VIiIiIrtn8ixhW7ZsgUwmw5w5c4wOVgBg8ODBmDNnDkRRxObNm009PFGVcvPmTb0rFqu7VBIRERFReSYHLOfPn4eDgwMGDRpU4bwDBw6Eo6Mjzp8/b+rhiaqUy5cvY/r06fjwww9x+/ZtAEBaWhpefPFFrFy5UrONiIiIiLSZHLCUlJSgVi3TsstkMtSqVQulpaWmHp7IZqZNmwY/Pz8UFRWVS9u0aRO8vb2RkJCgtd3Pzw+bN2+Gt7c3pk6diuvXr2PGjBkYP348Vq1ahYYNG1ZW9YmIiIiqFJMDFk9PT+Tn5yM5ObnCef/44w/cv38fnp6eph6eyGYEQUBxcXG5FsLCwkIsWrQIXbp0Qd++fcvlk8lkmp+y/xMRERGRfiYHLP3794coipg+fTpOnDhhdL4TJ05g5syZkMlk6N+/v6mHJztw6tQp+Pj4wNvbGytXrjS4/44dO9CuXTt4e3tjxYoVlVBD6xAEAYCqS1dZ69atQ1ZWFt55551yeZRKJUJCQpCamooFCxagSZMmmDdvHr7//nu89NJL7BJGREREpIfJs4SNGzcOsbGxuHz5MsLDw9G1a1f07t1bclrj33//HQcPHkRpaSk8PT0xbtw4i50IVT4fHx/06dMHu3fvRlRUFF544QXUqVNH575//vkn3n77bZSWluKFF16o0o+9t7c3AO2A5c6dO1i6dCkGDBiADh06lMvTrFkzzJs3Dx06dMClS5cAAG3btsWaNWuwZ88edgkjIiIi0sPkgKVevXpYs2YNXnvtNZw9exYHDx7EwYMHJfOoF5YUBAFLly6Fs7OzqYcnOzFx4kTs3r0bV65cwZYtWzBs2LBy+2RkZCAiIgIFBQXo27cv3nvvvcqvqAV5enrC2dlZK2BZtmwZ7t69i7feektnnkaNGqFRo0Y60/r06WONahIRERFVCyZ3CQOA5s2bY9OmTZgzZw6efPJJyGQyiKKo80cmk6Fz58743//+h9jYWDRv3txS50A25O/vj549ewIAfvjhh3Lpubm5ePXVV3Hr1i34+/vjq6++MnmyBnshk8kgCALS09MBANevX0dUVBTCwsLQsmVLg/k9PT25BgsRERGRkcxeZl4ul2PEiBEYMWIE8vPzkZ6ejuvXr+Pu3bsAVC0xTZo0QZs2beDk5GR2hcn+REREYN++fThz5gz27t2LwMBAAKrugBMmTMDFixfRokULfP/995qugrb27bffYtGiRQgICMDSpUuxZs0aJCQkIDMzUzMhxPDhw/HKK69ALpeXyy8IAmJjY1FcXIzFixejVq1amDx5sg3OhIio5lJmK5GWmwYvNy/4evhWOJ2IqgazA5aynJyc4OfnBz8/P0sWS3auc+fOCAgIwKFDh7B8+XIEBgaipKQEb775Jk6cOAFXV1csW7YMbm5utq6qhlKpBKDqqjV06FBcunQJMpkMdevWRVFRETIyMvD111/j7Nmz+PLLL8vlFwQBRUVF2LNnD3755RdMmjTJrs6PiMjSpG7+zQkcTMmbcy8HYRvCsPv8bs1+Qa2CEDMiBu7O7gbTrV1nIrIsiwYsVZ0oivjrr7+QmJiIo0eP4ty5c7hz5w7q168PX19fDBs2DM8880yFp6KdOXMmYmNjJfdZtmwZevfubU71bSoiIgKHDh3CoUOHcPLkScTGxiIxMRGOjo5YunQpWrVqZesqalEHLNu3b0e9evXw/vvvIzQ0FPXq1cPFixfx3nvv4eDBg/j1118xcuRIdO7cWSu/eqawDz/8EI0aNcJLL71U6edARDWPuS0KptyES938AzA5cDAnb9iGMCRlJmnVPykzCeEbwpEwJkEyPXpEtNXqTETWIRPVI+Et5J9//tHZJaxBgwaWPIxV/PHHHxg7dqzm/8ceewwNGjRAVlYWbt26BUA1QDoyMhIODg5Gl6sOWJo1a4ZmzZrp3UfX7FKmCg0NRUpKCvz8/LBx40aLlSslPDwcx44dwyOPPIKrV69CJpNhwYIFGDhwoNFlbNy4Ee+++67JdVi9ejW6du0quc+tW7c0+zg7O2PNmjV4/PHHtfa5efMm+vbti7t372LcuHGYMWNGufRu3boBAObMmYOwsDCT60xENYstWhTMuQlXRCmQlJmEErFEky6XyRHYMhAiRL1pCWMSrJK3c7POOHhZ/yQ/cSPjMHT9UL3pAc0DcPTyUavU2RJs8flNZO8s0sKSnJyMuLg47Nu3Dzk5OTr3cXd3R8+ePTF06FDNjZ69EUURnp6eGDNmDIKDg9G4cWNN2qZNm/DBBx9gz549WLhwoc61Ngx59tlnMWXKFEtW2a5ERERgwoQJuHr1KgBgxowZFQpWAFW3Qnd307+l0jetclnq1hUAmDp1arlgBVB1FXviiSewb98+zTTED6efPn3a5HoSkf2zp25M5rQoGEpX34TrSoscHKlVH7USsQSJ53VPHqJOiz8db5W8UsEKABzMkk4/lHXIKnVWZivZPYzISswKWPLy8vDOO+9g7969AB5MW6xLdnY2Nm3ahE2bNiEwMBBffPEF6tevb87hLc7f3x/btm3TedM7bNgwXL16Fd988w1+/vlnvPXWW1V+titL69OnD9zc3JCbm4v+/fub1E1q8ODBGDx4sBVq90BKSgoAoGHDhnjuuef07tekSROr1oOIzFeVukCZGlQM+XGIzpt0Y2+yzbkJT8wwfUZDQ4GDtfJ2bS7dym6t46blpjFgIbISkwOWoqIijBkzBqmpqZqWiV69ekkuHLlv3z5cvHgRe/fuxdixYxEdHY3ate1nGI2Li4tkeu/evfHNN9/g1q1byM3NNasloDrKy8vDzZs3AcBuW9EAIDU1FYAqwHJ0dNS7n/pcyra0EZHlVXZrBSAddJjaGmGtoMPcFgVzbsLNYU7gYCivVLeuEO8QBLUKMqk7mTl19nLzMjkvEUkzOVpYu3YtlEolXFxcMHv2bAQHBxuVb+vWrfjwww+hVCqxdu1arTEj9i4/P1/ztylTNB88eBBnz57FrVu30KBBA/j5+SEkJKTarEmjVCo1rWz2PFOcuoVFV1ewsk6cOAEA8PXlN2ZEQPXpImWLLlDmBh1SDN1km3MTrmit0Hvzb2hMh1TgYG7e6BHRCN8QrvWYqLcDQMyIGL3p6ueGpevM1hUi6zE5YNmyZQtkMhnmzJmDQYMGGZ1v8ODBkMlkeOONN7B58+YqFbBs2bIFAODj42OwNUaXw4cPa/2/c+dOfPvtt5g6dSpeffVVi9TRltRjQ+RyOXx8fEwqY+vWrZg7d67JdYiMjESnTp30pt+9exeZmZkAoHfleUAVXN64cQMymUyzrgxRdcAuUvbZBcpaLQqWuAmXuvkHYHLgYE5ed2d3JIxJ0PuclUo3VCdz6kxE1mFywHL+/Hk4ODhUKFhRGzhwIGbOnInz58+bevhK9/fff2P9+vUAgPHjx1cob8uWLTFz5kx069YNzZs3h4ODA06fPo0VK1Zg27Zt+PLLL+Hs7IxRo0ZJlrN+/XrExMQYdUz1KuyVSd1y8Z///MfkRULz8/P1TtxgjKKiIsl0dRdGAMjNzdW737JlywAAAwYMQNOmTU2uD5Ep7G1cRnXrImUt1gw6zGlRMCZdKs1QcGBq4GBuXgDw9fCVbNnQlW5OsGOozkRkHSZPa/zEE08AAP766y+TDvzEE09AJpPhzz//NCl/ZcrJycGIESNw+fJl9OvXD4sXL7ZY2bNnz8a6devQoEED7NmzB/Xq1dO7b2RkZIWPXZnTIg4ePBjp6ekYOnQoPv/880o5ZkWtXr1a04LTs2dP/PDDD+X2iY6OxocffghHR0fExsaiTZs2lV1NqgbsbVyGqVO1Rg6OhN8S07p4GppeVsqsXrPw6e+fVvpxUyamYPLWyVaZxldX0KFopdC0GOTcy5FMB2yzDgtVLk5rTFSeyS0snp6eSEtLQ3JycoUHWP/xxx+4f/++ZvE9e5aXl4dXX30Vly9fhp+fH+bPn2/R8t98801s2LAB//zzD5KTk9G3b1+9+3p4eBg9NiQ9PV1rzI213b9/HxkZGQDse8yHuttagwYNsG/fPixYsACvvPIKXFxccP36daxcuRKrVq0CAHzyyScMVmoAjsuoeV2kbNUFytxv9gHTWhSMTTeUl4jIVkwOWPr374+zZ89i+vTpWLx4Mfz9/Y3Kd+LECcycORMymQz9+/c39fCV4u7du3jllVegVCrRtm1b/PDDDyaNXZFSv359tG3bFkqlUjO2Qp+RI0di5MiRRpWr/oamsqSmpqK0tBSAfQ+4VwcskydPxs8//4ylS5fiu+++Q7169XDnzh0AqjE4s2bNwrBhw2xYU6oIjsuwXtBhDnvuImWrLlCA+UEHEVFNY3LAMm7cOMTGxuLy5csIDw9H165d0bt3b8lpjX///XccPHgQpaWl8PT0xLhx4yx2IpZ2//59TJgwAceOHUOrVq2wcuVKyUHa5lCv+1JcXGyV8iuDeqpgmUyGdu3a2bg2uhUWFmrG9nTs2BHDhg3DokWLkJCQgJycHDRt2hTdunXDuHHjTJ40gPTjuIyqOS7DmrNEmRN0VMY4BHNaIxh0EBFZjsljWAAgKysLr732Gs6ePQuZTGZwf/WhBEHA0qVL7XY634KCAkyYMAF//PEHmjdvjh9//BHNmjWzyrGKi4vRrVs35OXl4YsvvkBISIhFymUf2PJOnDiBESNGQC6X488//zR5YoCajOMyaua4DKmxFUD51orKHpdBVJ3w85uoPLNWbWzevDk2bdqEjRs3Ii4uDn/++aemW9DDatWqhSeffBLDhg3D8OHDIZfLzTm01RQVFWHKlCn4448/0LRpU0RFRVktWAFUA7zz8vJQu3Ztu15ssTpQtwK1bt26RgcrHJfBcRlq7CJFRERVgdnLzMvlcowYMQIjRoxAfn4+0tPTcf36ddy9excAUK9ePTRp0gRt2rSx+5vEkpISvPXWW9i7dy88PDwQFRWFxx57zKi8CoUCADB9+nQMHDhQs33//v04cOAARowYgVatWmm2FxYWIjo6Gp999hkA1fiUJk2aWO5kqBz1mJ7q3t3LlO5THJdhvJo4LkONXaSIiMgWzA5YynJycoKfn59dD7qW8ttvv2H79u0AAAcHB8yaNUvvvh988IHWbFhZWVkAgHv37mntd//+fSxfvhzLly+Hu7u7Zk2PjIwMzb4DBgzAjBkzLHouVJ56wL09z2KmZo1WEFsEHRyXoVJdxmUQERHZgkUDlqqusLBQ83dWVpYmCNElLy/PqDL9/PwwceJEHDt2DJmZmcjIyEBRURHc3NzQs2dPDB8+XNM6Q9ZTXFyMM2fOAIDdTApQmV2vDHWfslXQYai1Qoo5QUd1nrqWQQcREVU3Zg26N9W9e/cwZ84cyGQyfPqpaQNQSRoH7dmeKV2z1EFHRRel69yss2RgETkoElN+m6I33ZqDwaW6SBlaaM+ag8HVLL0OC5FVKZVAWhrg5QXoai02J5157QI/v4nKs0kLS0FBAWJjYxmwUJVnya5Z1ux6ZQjHZXBcRo1krzfKutJzcoCwMGB3mfeAoCAgJgZwdzcvHWDesnmlHgdj0ojI4mzSwnLz5k10794dMplMM3MTWRa/obEMS7eSmDOdrjmtIIamtTXU0qEr6KjMqWvZklENVJebf8A2ecPCgKQkoOTB6xNyORAYCCQkAAqF6emiyLxl81oi2DEDP7+JymPAUk3xDc94prSSWKtrlhRzu14ZCiq4XkY1YW+tBtXt5t8WN9mdOwMHJVpR4+KAoRJr9BhKl1LT8qakAJMnm/4YWgA/v4nKM7lL2OLFi00+aH5+vsl5iSrKnFaSsowZwG5u1yxrdr2y9WDwaomtBobzqoODspKSgPDwBzd/utISEqyTd8gQ3Tf/JSVAYiIQH699Lg+n62LtvFLBCmB+OvM+kJho+mOoVLJ7GJGVmBWwGLO6PVFlqMyxJOas/2FoZitrTomrVi2DDrYaSN/cW+vm31DeyMjqd/Nvj3m7Gphtz1A681pGWhoDFiIrMXvQfePGjeHg4FChPKIo4sqVK+YemmqQ6tJKYmg63cpoBbGqmhI4sNXAuLz60o1hrzf/tsobEAAcPaq7K1JIiOr5qa+rkqF0qW5ONS2vOcsMeHmZnpeIpIkmCgoKEn18fMQtW7ZUOO+NGzdEb29v0cfHx9TDkwHDhw8XBUEQhw8fbuuqmCX7brYYtCpIxMfQ/AStChKz72aLoiiKQauCRPlsuVa6fLZc7Pp/XbW2PfwTeTBSMl3qJ+V6it7jKlYpxOy72aJilUIrTb29rJTrKWLcqTgx5XqKLS6tfikpohgXp/ptbFp2tigGBYmi6lZA9RMUpNoulWZu3qAgUZTLtdPlclFUKKTTzMmbkqK9vSI/cXG2yTtrlm3yRkba57UKCLDOc8OaebOzVb/Lpqm3q19HpqYzr3Zecx5DC6gun99ElgRTM06ePFn08fERv/jiiwrnzc3NZcBiZVXxDU/XDbxUYJByPcXkoMNQwBKwLEDvcUVRNCoosVlAIhVwSKUzcDDux5ybcFsFDrYKlFJSqt/Nv63ymvv6NiadeVXMeQwtoCp+fhNZm8mzhC1duhQLFy7EU089hRUrVlQoL2cJsz57nGWkot265gTNQc+VPfWWZ86MW4am+TU0ja+hc7I6a6zTYOrsRpGRgJ9pUzWbNZtPZCQwxbTHH7NmAaauAWXOca0585FUlyFbTxEbHq7dPUyhAKJV47L0pqmfs9bIq55+1t5mVDM2nSqHjdZhscfPbyJbM3kMi9+/NygpKSkVziuXy/Hoo49y0H4VZMq0tqYOfo/YEmFWXa05lkTNrPEilh6zYc6ga3MGR9tqnII5zBlroFDYZ7/86OjyN+jq7YDqOSKVbq287u6q55++57RUmjXzAqr/pW42pdJtlZcqjzmPIRFZlMktLPn5+Thx4gQAoEuXLgw+7Iylv6ExFHTYYiFFu28lscZAcWut02BOq4GtWhzMXS+BrQaV22pAREZhCwtReTZZOLIqSE5OxsqVK3H8+HHcu3cPjz76KAYOHIjx48fD2dnZpDK3b9+OtWvX4tSpUygqKkLLli0REhKC0aNHo06dOhatv6Xf8KRWQZdaJd3chRTbN2kPZbbS5MUQASt32zKla5Ytul4Z6gJlTtBREwMHNXYZIiILY8BCVB4DFh3WrFmDuXPnQhRFPPLII3Bzc0NaWhoKCwvRpk0brFu3Dq6urhUq87PPPtOM9WnRogXq1q2LtLQ0lJSUoEuXLlixYkWFp4eWYsk3PGW2UrIVxNAK7FIMBSz7XtqHD3d/WLVaSaRW0TYn6LBmS4a5QUdNDRyqGXttnGFey+SlqoEBC5EONhvub6dOnjwp+vj4iN7e3uL69evF0tJSURRF8erVq5qZOyZPnlyhMnfs2CEKgiA+/vjj4q5duzTb09LSRIVCIQqCIM6bN8+i52HJWUbiTsVJzqg1K2GW1aYIVrPqjFu6ZooxdVasrl2lZ00yZ4YpQ3nNmapVfc7mzoxjq5mAbKQqTXwklW7NmaeZ1/Z57eF5R8bjLGFE5TFgeUhERIQoCII4ffr0cmkZGRmij4+PKAiCmJqaanSZISEhoiAI4sKFC8ulHThwQBPM3Lhxw6y6l2XJNzxD0wcbCmgsMUWweSdgwjS+1ppO15yAxdAUsZaYMlXqehlKsyFbzHpqbzel5uS11ezCzFs5eW35vLP2a7Q6YsBCVB4DljLu3LkjPv7446IgCOKRI0d07jN27FhREATxm2++MarMjIwMURAEURAE8erVqzr36devnygIghgTE2Nq1cux9BueoVYQmy+kWFVaScxdl6Iy1mmwkuoUONjjTampeQ093W21hAvzWi6vLZfDsXarkZ2+3ZmFAQtRebB1BezJ4cOHNa0dhYWFOveJjIwUBUEQx44da1SZsbGxoiAIYt++ffXuM3PmTFEQBPG9994zqd66WPoNz1DQYfWFFKtSK4mhrlnW7nplRfbW3cgWN2FVcaF7c/Laaq1L5rVcXnO+Y7HXdUOrc7DDgIWoPJPXYamOMjIyAACPPvqo3lm7WrRoobWvIefPn9fKZ06Z69evR4x66lsD0tPTjdrPWIbWJTFm3RKDa5aYMuOWvrVFhgzRPc2vJdYOMbQOh6H1MMxZW0LNjDUATBm0a86alOYsDyOK1lk6Jj7e9Ly2WnbGVnnNWbKGee0/ryHmPHcSE633Gg0OVq2TWpax7yvR0eatsQtwcgOiSmfriMmeLFu2TBQEQRwxYoTeffbs2SMKgiB27NjRqDI//vhjURAEcdq0aXr3+fHHH0VBEMQhQ4ZIlrVo0SJN9zJjf+zqG5qa0kpi6HytzJTLbCjdHrsbmfOtsTnfZtvq22pr5jVnvoaq1gWuJua1VaugrV6j1ny+GztmxxxsYSEqD7augD1ZvHixKAiC+Pzzz+vdRz1Ivl27dkaV+e6774qCIIjvvPOO3n02bNggCoIgPv3005Jl/fTTT+Lw4cON+vH397fNG151GUtSBbtmmdN9SirdmkFHVQwcbDkewJrda0ydr4F57T+vrZ53tgqUbBnsWAIDFqLyYOsK2BN7b2GpCKu94bGVpFJU9mW215sDqR9bDyS2t5tSS0wSV5WmYmbeiuW11fOuqk0UYc77maU+JhiwEJUHW1fAnsTExIiCIIj9+/fXu09cXJwoCIIYGBhoVJlff/21KAiC+NJLL+ndZ8mSJQZbdirK4m94bCWxOHtqjLLX7hf2GjhIPYbGpNlrXqr+bDEFuDVeo/YY7MTFmf64lMWAhag82LoC9uTQoUNGzxI2ZswYo8pUzxKmkGgvVs8SNmvWLFOqrZPF3/DYSlJhVakxytp9vqtr4EBExrH0a9Qegx22sBBZDwOWMvLy8kQ/Pz+LrsNy7ty5qr8Oi6E7ZbaS2EUriTmXWape5gYdUtfK0LU0Ni8R1Uz2FuxYAgMWovIYsDxkwoQJFl/pfsiQIQZXuvfz87Pble4Nfv3OVhKtoKSqNkZZO+ggIrIn1gh2LIEBC1F5DFgecvz4cdHb21v09vYW169fL5aWloqiKIrXrl3TvIlMnDixXL6goCAxKChI/O2338qlbdu2TdPVLCEhQbM9PT1dVCgUoiAI4ty5cy16HpXawsJWErtoJbHUZWbQQUQkzZrvkwxYiMqTiaIo2notGHuzatUqzJ8/H6IoolmzZmjUqBHS0tJQWFiI1q1bY926dXBzc9PK4+3tDQCYN28eQkNDy5X56aefIioqCoBqoUhnZ2ecPXsWJSUlePLJJ7Fy5Uo4Ojpa7BxCQ0ORkpICPz8/bNy40fwCFQr9CyUmJKhW2np4sUSFQrVCl52utGXMYoe6TjcyEvDzM+2YkZHAlCn60wMCVIuhVaPLTEREFWDxz2+iaoAr3eswduxYeHt7Y8WKFThx4gRu3LiBRx99FAMHDsT48eNRr169Cpc5a9YsPPHEE1i3bh1SU1Nx/fp1tGnTBiEhIRg7dizq1KljhTOxoJgY81ZvB8xand0c+qqkbyXkIUN0r+5siZXOFQpVUKQvGIqOrrKXmYiIiMgqGLDo0b17d3Tv3t3o/U+fPm1wn0GDBmHQoEHmVMt2jLlTBuwqKJFqQbl+XXu7WkmJ7mClIqRaSXx9pWM/O7/MRERERJWOAQtVjJ3dKRvTrauspCRVsDB1qunHZCsJERERUeWpZesKEBlDqQTi41W/y5Lq1rV7t3ZAATzo1mVIQIAqAClLLlcFK+pWksBA7fSHW0lSUoC4ONXvhIQHY0zUfH2BkBAGJkRERERS2MJCdqOyu3WxlYSIiIjI/jFgIZuzRbcuLy+OJSEiIiKqChiwUKWx9GxdhgIWQ4PfAbaSEBEREdk7jmEhq8vJUY398PMDhg5V/VYoVNuVSv1jTYzt1qVvrMmWLfrHmZTFsSRERERE9osBC1mUrsHxUt260tJMP5a6W5e5g9+JiIiIyH6xSxhViL7uU/rGocyZo39gPLt1EREREZEhbGEho0h16wL0t6JERBgum926iIiIiEgfBixkFKluXVLjUE6elC6X3bqIiIiISAq7hP3r1KlT2LVrFw4dOoS0tDTcvn0bzs7OaNu2LYKDgxEWFoY6depUuNzIyEgsXrxYcp+PP/4Yzz33nKlVtzp1QPIwdbcuQwsxtm+vKoPduoiIiIioohiwALhw4QKGDh2q+b9Zs2bw8fHBtWvXcPToURw9ehSxsbH44Ycf0LBhQ5OO0bhxY7Rs2VJnmoeHh0llVhZzBsYDwNKlwIcf6l+EUY1BCRERERE9jAELAFEU0bhxY7z44osICQlB8+bNNWl79+7F9OnTcfLkSXz00UdYsGCBScfo3bs35s+fb6EaVy4vL+l0hUJ61fgePYxbhJGIiIiI6GEcwwLgkUceQUJCAiIiIrSCFQAIDAzE+++/DwDYsWMHbt68aYsq2pSvr/TAeF9f6XEoZcvhwHgiIiIiqggGLAAcHR1Rt25dvem9e/cGAJSUlODChQuVVS27Yigg4eB4IiIiIrIGdgkzQn5+vuZvJycnk8o4deoU3nrrLWRnZ6NevXrw9vZGcHAw2rZta6lqWpU6IDHUrYvjUIiIiIjIkhiwGGHLli0AAFdXV3gZGtChR2pqKlJTUzX/JyYm4rvvvsPo0aMxY8YMyB/ub2WnGJAQERERUWViwGLA5cuXsWTJEgDAyy+/XOHAokmTJnj99dfRq1cveHp6wsXFBRkZGVi3bh3Wr1+PqKgo1K5dG9OnTzdY1vr16xETE2PUcdPT0ytUTyIiIiIie8SARcL9+/cxadIk5OXlwd/fHy/9f3v3HhTVef9x/LPlkoSscjErCtiAViReUKsDbZOaiDYxTdpapo2m6RibRBIz2kalaUlr0miMTpuxOrHJOG0EZCattjXaMaO2lWJrGy9JvUTAC2CUBUSqggjKcjm/P/wtDQFSLrt7zrLv14wz7rk85/t8Zw/wPed5zvne93rdxpw5czotGzNmjF5++WXFxcXptddeU25urr7zne8oLi7uU9uqqalRYWFhr2MAAAAA/JXfFyyrVq3S5s2be71fSkqK8vLyul3vcrm0aNEiFRUVKTY2Vhs2bOjTiyM/zRNPPKHNmzfr4sWLys/P17x58z51e4fDoXHjxvWo7dLS0g5zbwAAAAB/5PcFS1hYmCIiInq9n91u73ZdS0uLlixZov3792vo0KHKzc1VdHR0P6LsWlBQkCZOnKi//OUvOnfu3P/cfu7cuZo7d26P2k5PT+duDAAAAPye3xcsS5Ys0ZIlSzzWXmtrqzIzM/XXv/5VUVFRysnJ0YgRIzzW/ie579q0tLR47RgAAACAv+I9LB/T1tamrKws7dq1S+Hh4crOztaoUaO8eswzZ85IuvnySgAAAAAdUbB8zEsvvaQdO3bIbrfrN7/5jZKSkrx6vIKCgvaC5e677/bqsQAAAAB/RMHy/1avXq2tW7cqLCxMv/71r5WcnNzjfR999FGlpaUpJyenw/IzZ87oxRdf1MmTJzssb2tr086dO7Vs2TJJ0vTp03t1PAAAACBQ+P0cFk84cuRIe7Fx++236xe/+EW32z7zzDO69957Oyyrrq5WRUWF6uvrOyxvaWnRli1btGXLFkVERCgmJkZBQUE6f/686urqJElTp07Vz3/+c892CAAAABggKFh08xHGbjU1Naqpqel220uXLvW43djYWD333HM6evSoSktLde7cOblcLoWHh2vatGl6+OGH9fDDD/vNW+4BAAAAX6NgkZSamqpTp071ef/8/Pwulw8ePFgLFy7sc7sAAABAoGMOCwAAAADLomABAAAAYFkULAAAAAAsi4IFAAAAgGVRsAAAAACwLAoWAAAAAJZFwQIAAADAsihYAAAAAFgWBQsAAAAAy6JgAQAAAGBZFCwAAAAALIuCBQAAAIBlUbAAAAAAsKxgswOAdzidTklSaWmp0tPTTY4GAAD0RGlpqaT//h4HQMEyYDU1NUmSbty4ocLCQpOjAQAAveH+PQ6AgmXAioqK0uXLl3XLLbcoLi7OY+2Wlpbqxo0buvXWWzVq1CiPtTsQkaveIV89R656jlz1HLnqOW/myul0qqmpSVFRUR5tF/BnNsMwDLODgP9IT09XYWGhxo0bp23btpkdjqWRq94hXz1HrnqOXPUcueo5cgX4FpPuAQAAAFgWBQsAAAAAy6JgAQAAAGBZFCwAAAAALIuCBQAAAIBlUbAAAAAAsCwKFgAAAACWRcECAAAAwLIoWAAAAABYFgULAAAAAMsKNjsA+JdHHnlENTU1cjgcZodieeSqd8hXz5GrniNXPUeueo5cAb5lMwzDMDsIAAAAAOgKQ8IAAAAAWBYFCwAAAADLomABAAAAYFkULAAAAAAsi6eEBbgDBw4oOztbx44dU2Njo2JiYjRr1ixlZGQoLCysx+0cPHhQ8+bN69G2ixcv1qJFi/oasmk8lSu3yspKbdq0Sfv371dVVZXa2trkcDiUmpqq+fPna8yYMV7ohW94OldXrlxRdna29u7dK6fTqeDgYH3uc59Tenq6vv3tb+szn/G/ay81NTX65z//qRMnTujDDz9UcXGxmpqalJKSory8vH617en8m80bufJm/s3k6X4ZhqEjR44oPz9fH3zwgcrKynTt2jUNGjRIY8eO1ezZs/W1r31NNpvNC73xPm98D3bt2qV//etfKiws1MWLF1VbW6uQkBDFx8fr3nvv1eOPP67IyEgP9wQY2HhKWADLy8vTqlWrZBiGhg0bpqioKJWUlMjlcmnUqFF6++23FRER0aO2ioqKtHLlym7XX7t2TadPn5Ykbdq0SXfffbcnuuAznsyVJB05ckRPPvmkGhoaFBISori4OIWEhOj8+fO6ceOGgoOD9dprr+nBBx/0Xqe8xNO5Kisr0xNPPKGqqiqFhIRo9OjRampqUllZmQzD0PTp07VhwwYFB/vX9ZecnBytXr260/L+/sHs6fxbgTdy5a38m83T/Xrvvfc0f/789s8jRozQ4MGDVVFRodraWknSfffdp9dff12hoaF9Dds03vgefOMb39DJkycVGhoqh8OhyMhIXb58WZWVlZKkIUOGaNOmTUpKSupX7EAg8a/f8PCYEydO6NVXX5UkrVixQo888ohsNpuqq6u1cOFCFRYWavny5Xr99dd71N7YsWP129/+ttv1GzZs0OnTpzV8+HB98Ytf9EgffMXTuTIMQz/60Y/U0NCgyZMna+3atYqJiZEk1dfX62c/+5l27typn/70p7rnnns0aNAgr/XN0zydq9bWVn3/+99XVVWVpkyZovXr17e/9+DUqVN65pln9Le//U2/+tWv9IMf/MBr/fIGu92uL33pS5owYYImTJigoqIivfHGG/1q09P5twpv5MobbVqBp/tlGIbi4uL0+OOP66GHHtKQIUPa123fvl3Lly9XQUGB1q9frx/+8Iee6IJPeeN78NhjjykhIUGTJk1SSEhI+/JTp04pMzNTp0+f1rJly/Tuu+/2N3wgcBgISAsXLjQSExON559/vtO6s2fPGklJSUZiYqJRXFzc72O1tbUZM2bMMBITE421a9f2uz1f83SuTp8+bSQmJna7T1NTkzFp0iQjMTHRyM/P73f8vuTpXO3du9dITEw0xo8fb5SXl3dan5+fbyQmJhoTJ0406urq+h2/mfLy8ozExETju9/9bp/b8OV5bSZP5MoXbVpBf/tVX19vuFyubte/+eabRmJiopGSkmK0trb2NUzL8Pb34NixY+0//0tKSrxyDGAg8r+B3+i3hoYG/eMf/5B08229nxQfH68vfOELkqTdu3f3+3iHDx9WeXm5JCk9Pb3f7fmSN3J148aN9v+PGDGi0/rQ0FBFR0dLklpaWnods1m8kasPPvhAkjR+/HjFxcV1Wj99+nSFhYXp+vXr2rt3b19DHxB8fV4jMNjt9g53CT5p2rRpkqTa2lpdvnzZV2H5rZEjR7b///r16yZGAvgXCpYAVFxcLJfLpdDQUCUnJ3e5zZQpUyRJx44d6/fx3nnnnfY277zzzn6350veyFVCQoJuvfVWSTfnsnzSxYsX5XQ6FRQUpLFjx/Yxct/zRq7q6uokqb2A68rQoUMldZ3LQOLr8xqQOl6Acf9cQ/fcF2HCwsKUkJBgcjSA/6BgCUBnz56VJMXExHR75eyzn/1sh237qrGxsf1q7je/+c1+tWUGb+TKbrfr2WeflSRlZWVp9+7dunLliq5du6YDBw4oIyNDzc3NysjIUGxsrAd64RveyJV7/k51dXW321y8eFHSzcn5gcyX5zXg5p6HkZSUJLvdbnI01tTW1qbq6mpt27ZNWVlZkqTMzEzdfvvtJkcG+A8m3Qcg91Xr8PDwbrdxr3Nv21e7d+9WY2OjbrvtNr984pW3cvX000/L4XDorbfe6jRZPD4+Xr/85S/11a9+tQ8Rm8cbuZowYYKkm5PJKyoqOhVw+/btU2NjY6/aHKh8eV4D0s3z8ne/+50kKSMjw+RorKerJ5AlJydrzZo17UPpAPQMd1gCUFNTkyR96rhk9+Mp3dv2lXs42P333++XV9+8lavm5maVl5errq5OwcHBio+P1+jRoxUaGqpz587pD3/4gy5cuNC/4H3MG7maOXOmhg0bJpfLpaVLl6qqqqp93fHjx/XSSy+1f/740JRA5MvzGvjPf/6jxYsXq6WlRV/5ylf00EMPmR2S5URHR+vzn/+8Jk6cKIfDIZvNpuLiYu3YsUNXr141OzzAr3CHJQDdcsstkm7+0dwdl8vVYdu+KC8v1+HDhyX553AwyXu5WrRokQoKCjRt2jS98sor7XM06urq9Morr+hPf/qT5syZo3fffddvCj1v5Co0NFTr1q3TggULdPToUc2YMUN33nmnmpqaVFFRoYiICN1///3685//HPDDK3x1XgP19fVasGCBKisrNW7cOK1Zs8bskCzpwQcf7DCy4OTJk1q5cqV27typ0tJS/fGPf1RQUJCJEQL+gzssAagnw0J6Mrzkf9m+fbsMw1BsbGz704n8jTdylZ+fr4KCAkVGRmrt2rUdJpSHh4fr1Vdf1ciRI3XhwgW9/fbb/Yjet7z1vZo8ebLeeecdzZkzR8OGDVN5ebmampqUnp6u7du3KyoqSpJ0xx139CN6/+er8xqBraGhQU899ZSKioo0evRovfXWW35zUcVsSUlJ2rhxoyIjI1VcXMx7WIBe4A5LAIqPj5ckVVZWqrm5ucshJOfPn++wbW8ZhqHt27dLkmbPni2bzdandszmjVy9//77km6OZe7qpZAhISFKTU1VWVmZTpw40bfATeDN79WIESO0YsWKLteVlJRI+u98l0Dli/Mage369et6+umndfToUcXHxys7O1uRkZFmh+VX7Ha7UlJStGfPHhUWFurrX/+62SEBfoE7LAHorrvuUkhIiFwul44fP97lNu5HL06aNKlPxzh06JCcTqdsNpvfDgeTvJOrhoaGHh/fn+Ya+OJ79UmXL1/W0aNHJUkzZszwSJv+yoz8I3A0NTVp4cKFOnz4sGJjY5WTkyOHw2F2WH7J/X6t1tZWkyMB/AcFSwCy2+265557JElbt27ttP6jjz7SgQMHJEmzZs3q0zHck+2nTp3a5csR/YU3cuV+9v7x48dVX1/faX1zc7MOHjzYYVt/4Ivv1SetW7dOLS0tmjp1qsaPH++RNv2VGflHYGhubtbixYv13nvvKTo6Wrm5uRo+fLjZYfml2tpaHTp0SNLNiwwAeoaCJUA9++yzstls2rFjh7Zs2SLDMCTdfKfF0qVL1dbWppkzZyopKanDfmlpaUpLS/vUN2U3NDRoz549kvzvzfZd8XSuZs2apdDQUF25ckVLly7t8I6Ruro6vfDCCyorK5PNZvO74QLe+F7t27ev/c6A29WrV7Vq1Spt2bJFYWFh3Q4XG4geffRRpaWlKScnp9O6vuZ/oPq0XKGj7nLV2tqqZcuWad++fXI4HMrNzfXri1Ce0l2+Dh06pDfeeENOp7PTPoWFhXryySdVX1+v6OhoLhwAvcAclgCVnJysH//4x1qzZo1efPFFvfnmm4qMjFRJSYlcLpcSEhK0cuXKTvtVVFRIUvu7L7qyZ88eNTY2KiwsTA888IDX+uArns7VsGHDtHLlSv3kJz/R3//+d6WlpSkuLk4hISE6d+6cXC6XbDabMjMz/epN95J3vlf79+/X5s2bZbfb29/DUlZWpubmZkVERGjDhg0aNWqUdzvmBVVVVZo9e3b7Z/cTvP79738rNTW1fflTTz2lBQsWtH+urq5WRUVFl3fn+pp/q/NGrvraptV5Ole7du1qvwAVGhqqF154odtjL1++3O9+Znk6X1evXtX69eu1fv16ORwODR06VEFBQaqqqlJNTY2km4873rhxY8A/2RDoDQqWADZ//nyNGTNGmzZt0vHjx3Xp0iXFxMRo1qxZysjI6PMPU/dwsAceeGDA/ED2dK5mz56tpKQk5ebm6v3331dlZaUMw5DD4dDkyZP12GOPacqUKV7qjXd5OlczZ87UpUuX9OGHH+r8+fOy2WxKSEhQWlqa5s+f77eTfltbW1VbW9tpeUtLS4flvX2/jLfOazN5I1feyr/ZPN0v9x/w0s0LC+6LC13pqjC0Ok/na/LkycrKytLBgwdVUlKijz76SC6XS4MHD1ZqaqrS0tL0rW99iyerAb1kM9xjBgAAAADAYpjDAgAAAMCyKFgAAAAAWBYFCwAAAADLomABAAAAYFkULAAAAAAsi4IFAAAAgGVRsAAAAACwLAoWABiAnE6n0tLSzA4DAIB+o2ABgAHiypUrOnbsWJfr9u3b5+NoAADwjGCzAwAAeEZlZaWef/55paamas6cOZKkkpISvfzyywoKCtKkSZMUHh5ucpQAAPSOzTAMw+wgAACe0dzcrK1btyo7O1sXLlzQmDFj9Nxzz+nLX/6y2aEBANAnDAkDgAHEZrO1//v4ZwAA/BV3WADARFlZWdq2bVuf9k1OTtbvf//79s9FRUXKzMzUlClTNHfuXC1evFgbN27UihUrFBwcrHXr1jEkDADgd5jDAgAmcjqduuOOOzotb2xsVGNjoyR1uV6SUlJSOnwePny4Vq9erYkTJ8rpdEqSRo8erby8PBUUFFCsAAD8EndYAMCCli9frq1bt2r48OEqKCjo9f5Op1Pz5s1Tfn6+54MDAMCHmMMCABZUWFgoSRo7dmyf9o+Li6NYAQAMCBQsAGAxLS0tOnPmjKS+FywAAAwUFCwAYDElJSVyuVySKFgAAKBgAQCLcQ8Hk6Rx48aZGAkAAOajYAEAiykuLpYkDRkyRNHR0SZHAwCAuShYAMBi3HdY7rrrLpMjAQDAfBQsAGAhbW1tOnnypCSGgwEAIFGwAIClnD17tv2FkUy4BwCAggUALMU9f0XiDgsAABIFCwBYinv+yqBBgxQXF2dyNAAAmI+CBQAspKioSNLNCfc2m83kaAAAMB8FCwBYCBPuAQDoiIIFACzC6XSqtrZWEo80BgDAjYIFACzCPRxM4g4LAABuFCwAYBHuguW2227TyJEjTY4GAABrsBmGYZgdBAAAAAB0hTssAAAAACyLggUAAACAZVGwAAAAALAsChYAAAAAlkXBAgAAAMCyKFgAAAAAWBYFCwAAAADLomABAAAAYFkULAAAAAAsi4IFAAAAgGVRsAAAAACwLAoWAAAAAJZFwQIAAADAsihYAAAAAFgWBQsAAAAAy/o/9YdFfs76hhAAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "def plot_vle_errors():\n", + " nist_data_subset = nist_data.loc[nist_data['t']< 1.30977] #use only data with temperatures where all EoS are subcritical\n", + "\n", + " fig, axs = plt.subplots(3, 1, sharex=True, sharey=True)\n", + "\n", + " for i, row in nist_data_subset.iterrows():\n", + " temp = row['t']\n", + " rhov = row['rhov']\n", + " rhol = row['rhol']\n", + " psat = row['p']\n", + "\n", + " vle_uvb3 = PhaseEquilibrium.pure(uvtheory_b3, temp * eps_k_k)\n", + " rhov_uvb3 = vle_uvb3.vapor.density * NAV * (sigma * ANGSTROM)**3\n", + " rhol_uvb3 = vle_uvb3.liquid.density * NAV * (sigma * ANGSTROM)**3\n", + " ps_uvb3 = vle_uvb3.vapor.pressure() / (KB * eps_k_k ) * (sigma * ANGSTROM)**3\n", + " err_uvb3_rhov = (rhov - rhov_uvb3) / rhov * 100\n", + " err_uvb3_rhol = (rhol - rhol_uvb3) / rhol * 100\n", + " err_uvb3_ps = (psat - ps_uvb3) / psat * 100\n", + "\n", + " vle_uvwca = PhaseEquilibrium.pure(uvtheory_wca, temp * eps_k_k)\n", + " rhov_uvwca = vle_uvwca.vapor.density * NAV * (sigma * ANGSTROM)**3\n", + " rhol_uvwca = vle_uvwca.liquid.density * NAV * (sigma * ANGSTROM)**3\n", + " ps_uvwca = vle_uvwca.vapor.pressure() / (KB * eps_k_k ) * (sigma * ANGSTROM)**3\n", + " err_uvwca_rhov = (rhov - rhov_uvwca) / rhov * 100\n", + " err_uvwca_rhol = (rhol - rhol_uvwca) / rhol * 100\n", + " err_uvwca_ps = (psat - ps_uvwca) / psat * 100\n", + "\n", + "\n", + " vle_uvbh = PhaseEquilibrium.pure(uvtheory_bh, temp * eps_k_k)\n", + " rhov_uvbh = vle_uvbh.vapor.density * NAV * (sigma * ANGSTROM)**3\n", + " rhol_uvbh = vle_uvbh.liquid.density * NAV * (sigma * ANGSTROM)**3\n", + " ps_uvbh = vle_uvbh.vapor.pressure() / (KB * eps_k_k ) * (sigma * ANGSTROM)**3\n", + " err_uvbh_rhov = (rhov - rhov_uvbh) / rhov * 100\n", + " err_uvbh_rhol = (rhol - rhol_uvbh) / rhol * 100\n", + " err_uvbh_ps = (psat - ps_uvbh) / psat * 100\n", + "\n", + "\n", + " axs[0].plot(temp, err_uvb3_rhov, 'r.')\n", + " axs[0].plot(temp, err_uvwca_rhov, 'g.')\n", + " axs[0].plot(temp, err_uvbh_rhov, 'b.')\n", + "\n", + " axs[1].plot(temp, err_uvb3_rhol, 'r.')\n", + " axs[1].plot(temp, err_uvwca_rhol, 'g.')\n", + " axs[1].plot(temp, err_uvbh_rhol, 'b.')\n", + " \n", + " axs[2].plot(temp, err_uvb3_ps, 'r.')\n", + " axs[2].plot(temp, err_uvwca_ps, 'g.')\n", + " axs[2].plot(temp, err_uvbh_ps, 'b.')\n", + " \n", + " \n", + " \n", + " \n", + " axs[0].plot(temp, err_uvb3_rhov, 'r.', label='uv-B3')\n", + " axs[0].plot(temp, err_uvwca_rhov, 'g.', label='uv-WCA')\n", + " axs[0].plot(temp, err_uvbh_rhov, 'b.', label='uv-BH')\n", + "\n", + "\n", + " axs[0].text(0.7, 2.1, '$Y=\\\\rho^{v*}$')\n", + " axs[1].text(0.7, 2, '$Y=\\\\rho^{l*}$')\n", + " axs[2].text(0.7, 2, '$Y=p^{v*}$')\n", + "\n", + " axs[0].legend(frameon=False, bbox_to_anchor=(1.01, 1.05))\n", + " axs[1].set_ylabel('100$(Y^{MC}-Y^{EoS}) / Y^{EoS}$')\n", + "\n", + " plt.xlabel('$T^*$') \n", + " return\n", + "\n", + "plot_vle_errors() " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compare Third Virial Coefficients" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "jupyter": { + "source_hidden": true + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_third_virial_coeff():\n", + " tvec = np.linspace(0.5, 20, 800)\n", + " \n", + " b3_uv_wca = []\n", + " b3_uv_b3 = []\n", + " b3_thol = []\n", + " for temp in tvec:\n", + " b3_uv_wca.append(uvtheory_wca.third_virial_coefficient(temp * eps_k_k) / (sigma * ANGSTROM)**6 / NAV**2)\n", + " b3_uv_b3.append(uvtheory_b3.third_virial_coefficient(temp * eps_k_k) / (sigma * ANGSTROM)**6 / NAV**2)\n", + " b3_thol.append(thol.third_virial_coefficient(temp * eps_k_k) / (sigma * ANGSTROM)**6 / NAV**2)\n", + "\n", + " plt.plot(1/tvec, b3_uv_wca, '-', label='uv-WCA')\n", + " plt.plot(1/tvec, b3_uv_b3, label='uv-$B_3$')\n", + " plt.plot(1/tvec, b3_thol, '-', label='Thol')\n", + " plt.ylim(-10, 10)\n", + " plt.ylabel('$B_3 / \\\\sigma^6$')\n", + " plt.xlabel('$\\\\varepsilon/(k_BT)$')\n", + " plt.legend(frameon=False)\n", + " return\n", + "plot_third_virial_coeff()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compare isochoric heat capacity isotherms" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "jupyter": { + "source_hidden": true + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_heat_capcities(temp):\n", + " dimensionless_density = np.linspace(0.01, 1.0, 100)\n", + " cv_thol = []\n", + " cv_uv_b3 = []\n", + " cv_uv_wca = []\n", + " cv_uv_bh = []\n", + " for rho in dimensionless_density:\n", + " density = rho / (sigma * ANGSTROM)**3 / NAV\n", + " temperature = temp * eps_k_k\n", + " s_thol = State(thol, density = density, temperature = temperature)\n", + " cv_thol.append(s_thol.c_v(Contributions.ResidualNvt) / (RGAS) + 3.0 / 2.0)\n", + " s_uv_b3 = State(uvtheory_b3, density = density, temperature = temperature)\n", + " cv_uv_b3.append(s_uv_b3.c_v(Contributions.ResidualNvt) / (RGAS) + 3.0 / 2.0)\n", + " s_uv_wca = State(uvtheory_wca, density = density, temperature = temperature)\n", + " cv_uv_wca.append(s_uv_wca.c_v(Contributions.ResidualNvt) / (RGAS) + 3.0 / 2.0)\n", + " s_uv_bh = State(uvtheory_bh, density = density, temperature = temperature)\n", + " cv_uv_bh.append(s_uv_bh.c_v(Contributions.ResidualNvt) / (RGAS) + 3.0 / 2.0)\n", + " \n", + " \n", + " plt.plot(dimensionless_density, cv_thol, '-', label='Thol')\n", + " plt.plot(dimensionless_density, cv_uv_b3, '-', label='uv-$B_3$')\n", + " plt.plot(dimensionless_density, cv_uv_wca, '-', label='uv-WCA')\n", + " plt.plot(dimensionless_density, cv_uv_bh, '-', label='uv-BH')\n", + " \n", + " plt.xlabel('$\\\\rho^*$')\n", + " plt.ylabel('$C_v/Nk_B$')\n", + " plt.title('$T^*={}$'.format(temp))\n", + " plt.legend(frameon=False)\n", + " return\n", + "plot_heat_capcities(1.5)\n", + " " + ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "venv_feos05", "language": "python", - "name": "python3" + "name": "venv_feos05" }, "language_info": { "codemirror_mode": { @@ -402,7 +803,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.12" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/examples/uvtheory.ipynb b/examples/uvtheory.ipynb deleted file mode 100644 index 80bfcf264..000000000 --- a/examples/uvtheory.ipynb +++ /dev/null @@ -1,390 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from feos.si import *\n", - "from feos.uvtheory import UVParameters, Perturbation\n", - "from feos.pets import PetsParameters\n", - "from feos.eos import State, PhaseEquilibrium, PhaseDiagram, EquationOfState, Contributions\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# Parameters for Thol EoS:\n", - "A = np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0,\n", - " 2.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0])\n", - "N = np.array([0.005208073, 2.186252000, -2.161016000, 1.452700000, -2.041792000, 0.186952860, -0.090988445, \n", - " -0.497456100, 0.109014310, -0.800559220, -0.568839000, -0.620862500, -1.466717700, 1.891469000, \n", - " -0.138370100, -0.386964500, 0.126570200, 0.605781000, 1.179189000, -0.477326790, -9.921857500, -0.574793200, 0.003772923])\n", - "T = np.array([1.000, 0.320, 0.505, 0.672, 0.843, 0.898, 1.294, 2.590, 1.786, 2.770, 1.786,\n", - " 1.205, 2.830, 2.548, 4.650, 1.385, 1.460, 1.351, 0.660, 1.496, 1.830, 1.616, 4.970])\n", - "D = np.array([4.0, 1.0, 1.0, 2.0, 2.0, 3.0, 5.0, 2.0, 2.0, 3.0, 1.0,\n", - " 1.0, 1.0, 1.0, 2.0, 3.0, 3.0, 2.0, 1.0, 2.0, 3.0, 1.0, 1.0])\n", - "L = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 2.0, 1.0, 2.0, 2.0,\n", - " 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n", - "ETA = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.067, 1.522,\n", - " 8.82, 1.722, 0.679, 1.883, 3.925, 2.461, 28.2, 0.753, 0.82])\n", - "BETA = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.625,\n", - " 0.638, 3.91, 0.156, 0.157, 0.153, 1.16, 1.73, 383, 0.112, 0.119])\n", - "GAMMA = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.71,\n", - " 0.86, 1.94, 1.48, 1.49, 1.945, 3.02, 1.11, 1.17, 1.33, 0.24])\n", - "EPSILON = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2053,\n", - " 0.409, 0.6, 1.203, 1.829, 1.397, 1.39, 0.539, 0.934, 2.369, 2.43])\n", - "\n", - "class Thol:\n", - " def __init__(self):\n", - " self.sigma = 3.7039 * ANGSTROM\n", - " self.eps_k = 150.03 * KELVIN\n", - " self.tc = 1.32 * self.eps_k / KELVIN\n", - " self.rhoc = 0.31 / self.sigma**3 * ANGSTROM**3\n", - " \n", - " def components(self): \n", - " return 1\n", - " \n", - " def subset(self, components):\n", - " return self\n", - " \n", - " def molar_weight(self):\n", - " return np.array([1.0])\n", - " \n", - " def max_density(self, moles):\n", - " return 0.04\n", - " \n", - " def helmholtz_energy(self, state):\n", - " \"\"\"\n", - " state (StateHD):\n", - " temperature in Kelvin als Float, Dual oder HD oder HD3, HDD, HDD3,\n", - " partial_density in # / Angstrom^3\n", - " volume in Angstrom^3\n", - " moles in mol\n", - " \"\"\"\n", - " tau = self.tc / state.temperature\n", - " delta = np.sum(state.partial_density) / self.rhoc\n", - " a = 0.0 #zero(state)\n", - " \n", - " # print(\"v\", state.volume)\n", - " # print(\"n\", state.moles)\n", - " #print(\"partial density\", state.partial_density)\n", - " #print(\"1\")\n", - " # print(\"delta: {}\".format(delta))\n", - " # print(\"tau: {}\".format(tau))\n", - " \n", - " for i in range(6):\n", - " a = a + N[i] * delta**D[i] * tau**T[i]\n", - " \n", - " # print(\"2\")\n", - " for i in range(6, 12):\n", - " a = a + N[i] * delta**D[i] * tau**T[i] * np.exp(-1.0 * delta**L[i])\n", - " # print(\"3\")\n", - " for i in range(12, 23):\n", - " a = a + N[i] * delta**D[i] * tau**T[i] * np.exp(- 1.0 * ETA[i] * (delta - EPSILON[i])**2.0 - 1.0 * BETA[i] * (tau - 1.0 * GAMMA[i])**2.0)\n", - " return a * np.sum(state.moles)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "sigma = 3.7039\n", - "sigma_a = sigma * ANGSTROM\n", - "eps_k = 150.03\n", - "eps_k_k = eps_k * KELVIN\n", - "\n", - "parameters = UVParameters.from_lists([12.0], [6.0], [sigma], [eps_k])\n", - "uvtheory_wca = EquationOfState.uvtheory(parameters)\n", - "uvtheory_bh = EquationOfState.uvtheory(parameters, perturbation=Perturbation.BarkerHenderson)\n", - "\n", - "parameters = PetsParameters.from_values(sigma, eps_k)\n", - "pets = EquationOfState.pets(parameters)\n", - "\n", - "thol = EquationOfState.python(Thol())\n", - "s3 = State(thol, temperature=300*KELVIN, pressure=1*BAR)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "s1 = State(uvtheory_wca, temperature=300*KELVIN, pressure=1*BAR)\n", - "s2 = State(pets, temperature=300*KELVIN, pressure=1*BAR)\n", - "s3 = State(thol, temperature=300*KELVIN, pressure=1*BAR)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.0016213224956115704" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "s1.molar_helmholtz_energy(Contributions.ResidualNvt) / (RGAS * 300 * KELVIN)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.0009407040108813868" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "s2.molar_helmholtz_energy(Contributions.ResidualNvt) / (RGAS * 300 * KELVIN)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.0016144150962601586" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "s3.molar_helmholtz_energy(Contributions.ResidualNvt) / (RGAS * 300 * KELVIN)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(1.3200003469821506, 1.3097658041494302, 1.3208296613277393)" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "State.critical_point(thol).temperature / eps_k_k, State.critical_point(uvtheory_wca).temperature / eps_k_k, State.critical_point(uvtheory_bh).temperature / eps_k_k" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 52.5 ms, sys: 1.45 ms, total: 54 ms\n", - "Wall time: 54.2 ms\n" - ] - } - ], - "source": [ - "%%time\n", - "vle_uv = PhaseDiagram.pure(uvtheory_wca, 150*KELVIN, 500)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "vle_uv.liquid" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 49 ms, sys: 1.77 ms, total: 50.7 ms\n", - "Wall time: 52.6 ms\n" - ] - } - ], - "source": [ - "%%time\n", - "vle_uv_bh = PhaseDiagram.pure(uvtheory_bh, 150*KELVIN, 500)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/3s/t93ws1md04qdbbq5d1jdz8640000gn/T/ipykernel_78968/174117960.py:65: RuntimeWarning: overflow encountered in exp\n", - " a = a + N[i] * delta**D[i] * tau**T[i] * np.exp(-1.0 * delta**L[i])\n", - "/var/folders/3s/t93ws1md04qdbbq5d1jdz8640000gn/T/ipykernel_78968/174117960.py:65: RuntimeWarning: invalid value encountered in exp\n", - " a = a + N[i] * delta**D[i] * tau**T[i] * np.exp(-1.0 * delta**L[i])\n", - "/var/folders/3s/t93ws1md04qdbbq5d1jdz8640000gn/T/ipykernel_78968/174117960.py:68: RuntimeWarning: overflow encountered in exp\n", - " a = a + N[i] * delta**D[i] * tau**T[i] * np.exp(- 1.0 * ETA[i] * (delta - EPSILON[i])**2.0 - 1.0 * BETA[i] * (tau - 1.0 * GAMMA[i])**2.0)\n", - "/var/folders/3s/t93ws1md04qdbbq5d1jdz8640000gn/T/ipykernel_78968/174117960.py:68: RuntimeWarning: invalid value encountered in exp\n", - " a = a + N[i] * delta**D[i] * tau**T[i] * np.exp(- 1.0 * ETA[i] * (delta - EPSILON[i])**2.0 - 1.0 * BETA[i] * (tau - 1.0 * GAMMA[i])**2.0)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 1.9 s, sys: 16.4 ms, total: 1.92 s\n", - "Wall time: 1.93 s\n" - ] - } - ], - "source": [ - "%%time\n", - "vle_thol = PhaseDiagram.pure(thol, 150*KELVIN, 500)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 27 ms, sys: 1.68 ms, total: 28.7 ms\n", - "Wall time: 32.6 ms\n" - ] - } - ], - "source": [ - "%%time\n", - "vle_pets = PhaseDiagram.pure(pets, 150*KELVIN, 500)" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "s3 = NAV * sigma_a**3\n", - "plt.plot(vle_uv.vapor.density * s3 , vle_uv.vapor.temperature / eps_k_k, color='black')\n", - "plt.plot(vle_uv.liquid.density * s3, vle_uv.vapor.temperature / eps_k_k, color='black')\n", - "\n", - "plt.plot(vle_uv_bh.vapor.density * s3 , vle_uv_bh.vapor.temperature / eps_k_k, color='black', linestyle='dashed')\n", - "plt.plot(vle_uv_bh.liquid.density * s3, vle_uv_bh.vapor.temperature / eps_k_k, color='black', linestyle='dashed')\n", - "\n", - "plt.plot(vle_thol.vapor.density * s3, vle_thol.vapor.temperature / eps_k_k, color='red')\n", - "plt.plot(vle_thol.liquid.density * s3, vle_thol.vapor.temperature / eps_k_k, color='red')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "vle_thol = PhaseDiagram.pure(thol, 150*KELVIN, 500)\n", - "s3 = NAV * sigma_a**3\n", - "plt.plot(vle_uv.vapor.density * s3 , vle_uv.vapor.temperature / eps_k_k, color='black')" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "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": "3.9.7" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/feos-core/CHANGELOG.md b/feos-core/CHANGELOG.md index 75dd1b99c..1741b4d10 100644 --- a/feos-core/CHANGELOG.md +++ b/feos-core/CHANGELOG.md @@ -9,6 +9,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0 - Added `PhaseDiagram::par_pure` that uses rayon to calculate phase diagrams in parallel. [#57](https://github.com/feos-org/feos/pull/57) - Added `StateVec::moles` getter. [#113](https://github.com/feos-org/feos/pull/113) - Added public constructors `PhaseDiagram::new` and `StateVec::new` that allow the creation of the respective structs from a list of `PhaseEquilibrium`s or `State`s in Rust and Python. [#113](https://github.com/feos-org/feos/pull/113) +- Added new variant `EosError::Error` which allows dispatching generic errors that are not covered by the existing variants. [#98](https://github.com/feos-org/feos/pull/98) ### Changed - Added `Sync` and `Send` as supertraits to `EquationOfState`. [#57](https://github.com/feos-org/feos/pull/57) diff --git a/feos-core/src/errors.rs b/feos-core/src/errors.rs index 0da42ea27..37936a4e6 100644 --- a/feos-core/src/errors.rs +++ b/feos-core/src/errors.rs @@ -6,6 +6,8 @@ use thiserror::Error; /// Error type for improperly defined states and convergence problems. #[derive(Error, Debug)] pub enum EosError { + #[error("{0}")] + Error(String), #[error("`{0}` did not converge within the maximum number of iterations.")] NotConverged(String), #[error("`{0}` encountered illegal values during the iteration.")] diff --git a/src/python/eos.rs b/src/python/eos.rs index 8207c72a0..6d4fb92bf 100644 --- a/src/python/eos.rs +++ b/src/python/eos.rs @@ -24,7 +24,7 @@ use crate::saftvrqmie::{FeynmanHibbsOrder, SaftVRQMie, SaftVRQMieOptions}; #[cfg(feature = "uvtheory")] use crate::uvtheory::python::PyUVParameters; #[cfg(feature = "uvtheory")] -use crate::uvtheory::{Perturbation, UVTheory, UVTheoryOptions}; +use crate::uvtheory::{Perturbation, UVTheory, UVTheoryOptions, VirialOrder}; use feos_core::cubic::PengRobinson; use feos_core::python::cubic::PyPengRobinsonParameters; @@ -213,6 +213,9 @@ impl PyEosVariant { /// Maximum packing fraction. Defaults to 0.5. /// perturbation : Perturbation, optional /// Division type of the Mie potential. Defaults to WCA division. + /// virial_order : VirialOrder, optional + /// Highest order of virial coefficient to consider. + /// Defaults to second order (original uv-theory). /// /// Returns /// ------- @@ -220,17 +223,26 @@ impl PyEosVariant { /// The UV-Theory equation of state that can be used to compute thermodynamic /// states. #[cfg(feature = "uvtheory")] - #[args(max_eta = "0.5", perturbation = "Perturbation::WeeksChandlerAndersen")] + #[args( + max_eta = "0.5", + perturbation = "Perturbation::WeeksChandlerAndersen", + virial_order = "VirialOrder::Second" + )] #[staticmethod] - #[pyo3(text_signature = "(parameters, max_eta, perturbation)")] - fn uvtheory(parameters: PyUVParameters, max_eta: f64, perturbation: Perturbation) -> Self { + #[pyo3(text_signature = "(parameters, max_eta, perturbation, virial_order)")] + fn uvtheory( + parameters: PyUVParameters, + max_eta: f64, + perturbation: Perturbation, + virial_order: VirialOrder, + ) -> PyResult { let options = UVTheoryOptions { max_eta, perturbation, + virial_order, }; - Self(Arc::new(EosVariant::UVTheory(UVTheory::with_options( - parameters.0, - options, + Ok(Self(Arc::new(EosVariant::UVTheory( + UVTheory::with_options(parameters.0, options)?, )))) } diff --git a/src/uvtheory/eos/attractive_perturbation_bh.rs b/src/uvtheory/eos/attractive_perturbation_bh.rs index a157724fc..c99580cb5 100644 --- a/src/uvtheory/eos/attractive_perturbation_bh.rs +++ b/src/uvtheory/eos/attractive_perturbation_bh.rs @@ -1,3 +1,4 @@ +//use super::attractive_perturbation_wca::one_fluid_properties; use super::hard_sphere_bh::diameter_bh; use crate::uvtheory::parameters::*; use feos_core::{HelmholtzEnergyDual, StateHD}; @@ -133,37 +134,6 @@ fn activation>(c: D, one_fluid_beta: D) -> D { one_fluid_beta * c.sqrt() / (one_fluid_beta.powi(2) * c + 1.0).sqrt() } -// fn one_fluid_properties>( -// p: &UVParameters, -// x: &Array1, -// t: D, -// ) -> (D, D, D, D, D, D) { -// let d = diameter_bh(p, t) / &p.sigma; -// let mut epsilon_k = D::zero(); -// let mut weighted_sigma3_ij = D::zero(); -// let mut rep = D::zero(); -// let mut att = D::zero(); -// for i in 0..p.ncomponents { -// let xi = x[i]; -// for j in 0..p.ncomponents { -// let _y = xi * x[j] * p.sigma_ij[[i, j]].powi(3); -// weighted_sigma3_ij += _y; -// epsilon_k += _y * p.eps_k_ij[[i, j]]; -// rep += xi * x[j] * p.rep_ij[[i, j]]; -// att += xi * x[j] * p.att_ij[[i, j]]; -// } -// } -// let dx = (x * &d.mapv(|v| v.powi(3))).sum().powf(1.0 / 3.0); -// ( -// rep, -// att, -// (x * &p.sigma.mapv(|v| v.powi(3))).sum().powf(1.0 / 3.0), -// weighted_sigma3_ij, -// epsilon_k / weighted_sigma3_ij, -// dx, -// ) -// } - fn one_fluid_properties>( p: &UVParameters, x: &Array1, diff --git a/src/uvtheory/eos/attractive_perturbation_uvb3.rs b/src/uvtheory/eos/attractive_perturbation_uvb3.rs new file mode 100644 index 000000000..c703dee6a --- /dev/null +++ b/src/uvtheory/eos/attractive_perturbation_uvb3.rs @@ -0,0 +1,435 @@ +use super::attractive_perturbation_wca::one_fluid_properties; +use super::hard_sphere_wca::{ + diameter_wca, dimensionless_diameter_q_wca, WCA_CONSTANTS_ETA_A_UVB3, WCA_CONSTANTS_ETA_B_UVB3, +}; +use crate::uvtheory::parameters::*; +use feos_core::{HelmholtzEnergyDual, StateHD}; +use ndarray::Array1; +use num_dual::DualNum; +use std::{f64::consts::PI, fmt, sync::Arc}; + +const C_WCA: [[f64; 6]; 6] = [ + [ + -0.2622378162, + 0.6585817423, + 5.5318022309, + 0.6902354794, + -3.6825190645, + -1.7263213318, + ], + [ + -0.1899241690, + -0.5555205158, + 9.1361398949, + 0.7966155658, + -6.1413017045, + 4.9553415149, + ], + [ + 0.1169786415, + -0.2216804790, + -2.0470861617, + -0.3742261343, + 0.9568416381, + 10.1401796764, + ], + [ + 0.5852642702, + 2.0795520346, + 19.0711829725, + -2.3403594600, + 2.5833371420, + 432.3858674425, + ], + [ + -0.6084232211, + -7.2376034572, + 19.0412933614, + 3.2388986513, + 75.4442555789, + -588.3837110653, + ], + [ + 0.0512327656, + 6.6667943569, + 47.1109947616, + -0.5011125797, + -34.8918383146, + 189.5498636006, + ], +]; + +// Constants for delta B2 RSAP +const C_B2_RSAP: [[f64; 4]; 4] = [ + [-0.063550989, 6.206829830, -37.45829549, 40.72849774], + [1.519053409, 13.14989643, 85.35058674, 374.1906360], + [0.693456220, 9.459946180, -53.28984218, 315.8199084], + [0.007492596, 0.546171170, 7.979562575, -119.6126395], +]; + +// // Constants for B3 Model for Mie nu-6 fluids +const K_LJ_B3: [f64; 16] = [ + -3.9806, 79.565, 0.5489, 5.3632, 1.4245, 57.292, 0.0, 1.0031, -39.755, -81.213, 0.6987, 30.156, + -23.692, -85.006, 0.7762, 12.798, +]; + +const P_B3: [f64; 4] = [0.80844, -0.09541, 0.47525, -2.83283]; +const L_B3: [f64; 4] = [4.9485, -21.3, 7.0, 3.2162]; +const M_B3: [f64; 4] = [0.11853, 0.078556, -0.55039, 0.009163]; + +const CU_WCA: [f64; 8] = [26.454, 1.8045, 1.7997, 161.96, 11.605, 12., 0.4, 2.0]; + +#[derive(Debug, Clone)] +pub struct AttractivePerturbationUVB3 { + pub parameters: Arc, +} + +impl fmt::Display for AttractivePerturbationUVB3 { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Attractive Perturbation") + } +} + +impl> HelmholtzEnergyDual for AttractivePerturbationUVB3 { + /// Helmholtz energy for attractive perturbation + fn helmholtz_energy(&self, state: &StateHD) -> D { + let p = &self.parameters; + let t = state.temperature; + let density = state.partial_density.sum(); + let d = diameter_wca(p, t); + let x = &state.molefracs; + // vdw effective one fluid properties + let (rep_x, att_x, sigma_x, weighted_sigma3_ij, epsilon_k_x, d_x) = + one_fluid_properties(p, x, t); + let t_x = state.temperature / epsilon_k_x; + let rho_x = density * sigma_x.powi(3); + let rm_x = (rep_x / att_x).powd((rep_x - att_x).recip()); + let mean_field_constant_x = mean_field_constant(rep_x, att_x, rm_x); + let q_vdw = dimensionless_diameter_q_wca(t_x, rep_x, att_x); + let i_wca = + correlation_integral_wca(rho_x, mean_field_constant_x, rep_x, att_x, d_x, q_vdw, rm_x); + + let delta_a1u = state.partial_density.sum() / t_x * i_wca * 2.0 * PI * weighted_sigma3_ij; + + let u_fraction_wca = u_fraction_wca( + rep_x, + density * (x * &p.sigma.mapv(|s| s.powi(3))).sum(), + t_x, + ); + + let b21u = delta_b12u(t_x, mean_field_constant_x, weighted_sigma3_ij, q_vdw, rm_x); + let b2bar = residual_virial_coefficient(p, x, state.temperature); + + let b3bar = residual_third_virial_coefficient(p, x, state.temperature, &d); + let db31u = delta_b31u(t_x, weighted_sigma3_ij, rm_x, rep_x, att_x, d_x); + let alpha = + (-rho_x * rep_x.recip() * CU_WCA[0] * (t_x.powi(2).recip() * CU_WCA[1] + 1.0)).exp(); + state.moles.sum() + * (delta_a1u + + (-u_fraction_wca + 1.0) + * ((b2bar - b21u) * density + density.powi(2) * alpha * (b3bar - db31u) * 0.5)) + } +} + +fn delta_b12u>( + t_x: D, + mean_field_constant_x: D, + weighted_sigma3_ij: D, + q_x: D, + rm_x: D, +) -> D { + (-mean_field_constant_x - (rm_x.powi(3) - q_x.powi(3)) * 1.0 / 3.0) / t_x + * 2.0 + * PI + * weighted_sigma3_ij +} + +fn residual_virial_coefficient>(p: &UVParameters, x: &Array1, t: D) -> D { + let mut delta_b2bar = D::zero(); + + for i in 0..p.ncomponents { + let xi = x[i]; + + for j in 0..p.ncomponents { + let t_ij = t / p.eps_k_ij[[i, j]]; + let rep_ij = p.rep_ij[[i, j]]; + let att_ij = p.att_ij[[i, j]]; + + let q_ij = dimensionless_diameter_q_wca(t_ij, D::from(rep_ij), D::from(att_ij)); + + delta_b2bar += + xi * x[j] * p.sigma_ij[[i, j]].powi(3) * delta_b2(t_ij, rep_ij, att_ij, q_ij); + } + } + delta_b2bar +} +fn residual_third_virial_coefficient>( + p: &UVParameters, + x: &Array1, + t: D, + d: &Array1, +) -> D { + let mut delta_b3bar = D::zero(); + + for i in 0..p.ncomponents { + let xi = x[i]; + + for j in 0..p.ncomponents { + let t_ij = t / p.eps_k_ij[[i, j]]; + let rep_ij = p.rep_ij[[i, j]]; + let att_ij = p.att_ij[[i, j]]; + let q_ij = dimensionless_diameter_q_wca(t_ij, D::from(rep_ij), D::from(att_ij)); + + // No mixing rule defined for B3 yet! The implemented rule is just taken from B2 and not correct! + let rm_ij = (rep_ij / att_ij).powd((rep_ij - att_ij).recip()); + let d_ij = (d[i] / p.sigma[i] + d[j] / p.sigma[j]) * 0.5; + // Recheck mixing rule! + delta_b3bar += xi + * x[j] + * p.sigma_ij[[i, j]].powi(6) + * delta_b3(t_ij, rm_ij, rep_ij, att_ij, d_ij, q_ij); + } + } + delta_b3bar +} +fn correlation_integral_wca>( + rho_x: D, + mean_field_constant_x: D, + rep_x: D, + att_x: D, + d_x: D, + q_x: D, + rm_x: D, +) -> D { + let c = coefficients_wca(rep_x, att_x, d_x); + + (q_x.powi(3) - rm_x.powi(3)) * 1.0 / 3.0 - mean_field_constant_x + + mie_prefactor(rep_x, att_x) * (c[0] * rho_x + c[1] * rho_x.powi(2) + c[2] * rho_x.powi(3)) + / (c[3] * rho_x + c[4] * rho_x.powi(2) + c[5] * rho_x.powi(3) + 1.0) +} + +/// U-fraction with low temperature correction omega +fn u_fraction_wca>(rep_x: D, reduced_density: D, t_x: D) -> D { + let omega = if t_x.re() < 175.0 { + (-t_x * CU_WCA[5] * (reduced_density - CU_WCA[6]).powi(2)).exp() + * ((t_x * CU_WCA[7]).tanh().recip() - 1.0).powi(2) + } else { + (-t_x * CU_WCA[5] * (reduced_density - CU_WCA[6]).powi(2)).exp() * 0.0 + }; + + -(-(reduced_density.powi(2) * ((rep_x + CU_WCA[4]).recip() * CU_WCA[3] + CU_WCA[2]) + omega)) + .exp() + + 1.0 +} + +// Coefficients for IWCA +fn coefficients_wca>(rep: D, att: D, d: D) -> [D; 6] { + let rep_inv = rep.recip(); + let rs_x = (rep / att).powd((rep - att).recip()); + let tau_x = -d + rs_x; + let c1 = rep_inv.powi(2) * C_WCA[0][2] + + C_WCA[0][0] + + rep_inv * C_WCA[0][1] + + (rep_inv.powi(2) * C_WCA[0][5] + rep_inv * C_WCA[0][4] + C_WCA[0][3]) * tau_x; + let c2 = rep_inv.powi(2) * C_WCA[1][2] + + C_WCA[1][0] + + rep_inv * C_WCA[1][1] + + (rep_inv.powi(2) * C_WCA[1][5] + rep_inv * C_WCA[1][4] + C_WCA[1][3]) * tau_x; + let c3 = rep_inv.powi(2) * C_WCA[2][2] + + C_WCA[2][0] + + rep_inv * C_WCA[2][1] + + (rep_inv.powi(2) * C_WCA[2][5] + rep_inv * C_WCA[2][4] + C_WCA[2][3]) * tau_x; + let c4 = rep_inv.powi(2) * C_WCA[3][2] + + C_WCA[3][0] + + rep_inv * C_WCA[3][1] + + (rep_inv.powi(2) * C_WCA[3][5] + rep_inv * C_WCA[3][4] + C_WCA[3][3]) * tau_x; + let c5 = rep_inv.powi(2) * C_WCA[4][2] + + C_WCA[4][0] + + rep_inv * C_WCA[4][1] + + (rep_inv.powi(2) * C_WCA[4][5] + rep_inv * C_WCA[4][4] + C_WCA[4][3]) * tau_x; + let c6 = rep_inv.powi(2) * C_WCA[5][2] + + C_WCA[5][0] + + rep_inv * C_WCA[5][1] + + (rep_inv.powi(2) * C_WCA[5][5] + rep_inv * C_WCA[5][4] + C_WCA[5][3]) * tau_x; + + [c1, c2, c3, c4, c5, c6] +} + +// Residual second virial coefficient from Revised series approximation RSAP + +fn factorial(num: u64) -> u64 { + (1..=num).product() +} + +fn delta_b2>(reduced_temperature: D, rep: f64, att: f64, q: D) -> D { + let rm = (rep / att).powd((rep - att).recip()); + let beta = reduced_temperature.recip(); + let b20 = q.powi(3) * 2.0 / 3.0 * PI; + let y = beta.exp() - 1.0; + + let c1 = rep.recip() * C_B2_RSAP[0][1] + + (rep.powi(2)).recip() * C_B2_RSAP[0][2] + + (rep.powi(3)).recip() * C_B2_RSAP[0][3] + + C_B2_RSAP[0][0]; + + let c2 = rep.recip() * C_B2_RSAP[1][1] + + (rep.powi(2)).recip() * C_B2_RSAP[1][2] + + (rep.powi(3)).recip() * C_B2_RSAP[1][3] + + C_B2_RSAP[1][0]; + let c3 = rep.recip() * C_B2_RSAP[2][1] + + (rep.powi(2)).recip() * C_B2_RSAP[2][2] + + (rep.powi(3)).recip() * C_B2_RSAP[2][3] + + C_B2_RSAP[2][0]; + let c4 = rep.recip() * C_B2_RSAP[3][1] + + (rep.powi(2)).recip() * C_B2_RSAP[3][2] + + (rep.powi(3)).recip() * C_B2_RSAP[3][3] + + C_B2_RSAP[3][0]; + + let mut sum_beta = beta; + + for i in 2..16 { + let k = factorial(i as u64) as f64 * i as f64; + sum_beta += beta.powi(i as i32) / k + } + + (b20 - rm.powi(3) * 2.0 / 3.0 * PI - c1) * y - sum_beta * c2 - beta * c3 - beta.powi(2) * c4 +} + +fn delta_b31u>( + t_x: D, + weighted_sigma3_ij: D, + rm_x: D, + rep_x: D, + att_x: D, + d_x: D, +) -> D { + let nu = rep_x; + let tau = rm_x - d_x; + + let k1 = nu.recip() * C_WCA[0][1] + + (nu.powi(2)).recip() * C_WCA[0][2] + + C_WCA[0][0] + + (nu.recip() * C_WCA[0][4] + (nu.powi(2)).recip() * C_WCA[0][5] + C_WCA[0][3]) * tau; + t_x.recip() * 4.0 * mie_prefactor(rep_x, att_x) * PI * k1 * weighted_sigma3_ij.powi(2) +} + +fn delta_b3>(t_x: D, rm_x: f64, rep_x: f64, _att_x: f64, d_x: D, q_x: D) -> D { + let beta = t_x.recip(); + let b30 = (q_x.powi(3) * PI / 6.0).powi(2) * 10.0; + + let b31 = ((t_x + K_LJ_B3[2]) + .powf(((rep_x - 12.0) / (rep_x - 6.0) * M_B3[0] + 1.0) * K_LJ_B3[3])) + .recip() + * K_LJ_B3[1] + * ((rep_x - 12.0) / (rep_x - L_B3[0]) * P_B3[0] + 1.0) + + K_LJ_B3[0]; + + let b32 = ((t_x + K_LJ_B3[6]) + .powf(((rep_x - 12.0) / (rep_x - 6.0) * M_B3[1] + 1.0) * K_LJ_B3[7])) + .recip() + * K_LJ_B3[5] + * ((rep_x - 12.0) / (rep_x - L_B3[1]) * P_B3[1] + 1.0) + + K_LJ_B3[4]; + + let b33 = ((t_x + K_LJ_B3[10]) + .powf(((rep_x - 12.0) / (rep_x - 6.0) * M_B3[2] + 1.0) * K_LJ_B3[11])) + .recip() + * K_LJ_B3[9] + * ((rep_x - 12.0) / (rep_x - L_B3[2]) * P_B3[2] + 1.0) + + K_LJ_B3[8]; + + let b34 = ((t_x + K_LJ_B3[14]) + .powf(((rep_x - 12.0) / (rep_x - 6.0) * M_B3[3] + 1.0) * K_LJ_B3[15])) + .recip() + * K_LJ_B3[13] + * ((rep_x - 12.0) / (rep_x - L_B3[3]) * P_B3[3] + 1.0) + + K_LJ_B3[12]; + + let b3 = b30 + b31 * beta + b32 * beta.powi(2) + b33 * beta.powi(3) + b34 * beta.powi(4); + + // Watch out: Not defined for mixtures! + let tau = -d_x + rm_x; + let tau2 = tau * tau; + let rep_inv = rep_x.recip(); + + let c1_eta_a = tau + * (rep_inv * WCA_CONSTANTS_ETA_A_UVB3[0][1] + WCA_CONSTANTS_ETA_A_UVB3[0][0]) + + tau2 * (rep_inv * WCA_CONSTANTS_ETA_A_UVB3[0][3] + WCA_CONSTANTS_ETA_A_UVB3[0][2]); + + let c1_eta_b = tau * WCA_CONSTANTS_ETA_B_UVB3[0][0] + tau2 * WCA_CONSTANTS_ETA_B_UVB3[0][1]; + + let b30_uv = (d_x.powi(3) * PI / 6.0).powi(2) * 10.0 + - d_x.powi(3) * 5.0 / 9.0 + * PI.powi(2) + * ((-q_x.powi(3) + rm_x.powi(3)) * (c1_eta_a + 1.0) + - (-d_x.powi(3) + rm_x.powi(3)) * (c1_eta_b + 1.0)); + + b3 - b30_uv +} + +#[cfg(test)] +mod test { + use super::*; + use crate::uvtheory::parameters::utils::methane_parameters; + use approx::assert_relative_eq; + use ndarray::arr1; + + #[test] + fn test_attractive_perturbation_uvb3() { + let moles = arr1(&[2.0]); + let reduced_temperature = 4.0; + let reduced_density = 0.5; + let reduced_volume = moles[0] / reduced_density; + + let p = methane_parameters(12.0, 6.0); + let pt = AttractivePerturbationUVB3 { + parameters: Arc::new(p.clone()), + }; + let state = StateHD::new( + reduced_temperature * p.epsilon_k[0], + reduced_volume * p.sigma[0].powi(3), + moles.clone(), + ); + let x = &state.molefracs; + let (rep_x, att_x, sigma_x, weighted_sigma3_ij, epsilon_k_x, d_x) = + one_fluid_properties(&p, &state.molefracs, state.temperature); + + let t_x = state.temperature / epsilon_k_x; + let rho_x = state.partial_density.sum() * sigma_x.powi(3); + let rm_x = (rep_x / att_x).powd((rep_x - att_x).recip()); + let mean_field_constant_x = mean_field_constant(rep_x, att_x, rm_x); + + // Effective Diameters: + let q_vdw = dimensionless_diameter_q_wca(t_x, rep_x, att_x); + assert_relative_eq!(q_vdw.re(), 0.9606854684075393, epsilon = 1e-10); + assert_relative_eq!(d_x.re(), 0.934655265184067, epsilon = 1e-10); + + //u-fraction: + let u_fraction_wca = u_fraction_wca( + rep_x, + state.partial_density.sum() * (x * &p.sigma.mapv(|s| s.powi(3))).sum(), + t_x, + ); + assert_relative_eq!(u_fraction_wca.re(), 0.8852775506870431, epsilon = 1e-10); + // delta a1u + let i_wca = + correlation_integral_wca(rho_x, mean_field_constant_x, rep_x, att_x, d_x, q_vdw, rm_x); + let delta_a1u = state.partial_density.sum() / t_x * i_wca * 2.0 * PI * weighted_sigma3_ij; + assert!(delta_a1u.re() == -0.8992910890819197); + // Virial coeffecients: + let b2bar = residual_virial_coefficient(&p, x, state.temperature) / p.sigma[0].powi(3); + assert_relative_eq!(b2bar.re(), -1.6142316456384618, epsilon = 1e-12); + + let b21u = delta_b12u(t_x, mean_field_constant_x, weighted_sigma3_ij, q_vdw, rm_x) + / p.sigma[0].powi(3); + assert_relative_eq!(b21u.re(), -1.5103749286162982, epsilon = 1e-10); + + let db3 = delta_b3(t_x, rm_x, rep_x, att_x, d_x, q_vdw); + assert_relative_eq!(db3.re(), -0.6591980196661884, epsilon = 1e-10); + + // Full attractive perturbation: + let a = pt.helmholtz_energy(&state) / moles[0]; + + assert_relative_eq!(-0.9027781694834115, a.re(), epsilon = 1e-5); + } +} diff --git a/src/uvtheory/eos/attractive_perturbation_wca.rs b/src/uvtheory/eos/attractive_perturbation_wca.rs index 99d304a46..9904e61a4 100644 --- a/src/uvtheory/eos/attractive_perturbation_wca.rs +++ b/src/uvtheory/eos/attractive_perturbation_wca.rs @@ -155,17 +155,6 @@ fn correlation_integral_wca>( rm_x: D, ) -> D { let c = coefficients_wca(rep_x, att_x, d_x); - // dbg!(q_x.re()); - // dbg!(rm_x.re()); - // dbg!(mean_field_constant_x.re()); - // dbg!(mie_prefactor(rep_x, att_x).re()); - // dbg!(rho_x.re()); - // dbg!(c[0].re()); - // dbg!(c[1].re()); - // dbg!(c[2].re()); - // dbg!(c[3].re()); - // dbg!(c[4].re()); - // dbg!(d_x.re()); (q_x.powi(3) - rm_x.powi(3)) * 1.0 / 3.0 - mean_field_constant_x + mie_prefactor(rep_x, att_x) * (c[0] * rho_x + c[1] * rho_x.powi(2) + c[2] * rho_x.powi(3)) @@ -180,7 +169,7 @@ fn u_fraction_wca>(rep_x: D, reduced_density: D) -> D { .tanh() } -fn one_fluid_properties>( +pub(super) fn one_fluid_properties>( p: &UVParameters, x: &Array1, t: D, @@ -326,7 +315,6 @@ mod test { let q_vdw = dimensionless_diameter_q_wca(t_x, rep_x, att_x); let b21u = delta_b12u(t_x, mean_field_constant_x, weighted_sigma3_ij, q_vdw, rm_x) / p.sigma[0].powi(3); - //assert!(b21u.re() == -1.02233216); assert_relative_eq!(b21u.re(), -1.02233215790525, epsilon = 1e-12); let i_wca = @@ -334,8 +322,6 @@ mod test { let delta_a1u = state.partial_density.sum() / t_x * i_wca * 2.0 * PI * weighted_sigma3_ij; - //dbg!(delta_a1u); - //assert!(delta_a1u.re() == -1.1470186919354); assert_relative_eq!(delta_a1u.re(), -1.52406840346272, epsilon = 1e-6); let u_fraction_wca = u_fraction_wca( @@ -347,10 +333,8 @@ mod test { dbg!(b2bar); assert_relative_eq!(b2bar.re(), -1.09102560732964, epsilon = 1e-12); dbg!(u_fraction_wca); - //assert!(u_fraction_WCA.re() == 0.743451055308332); - assert_relative_eq!(u_fraction_wca.re(), 0.997069754340431, epsilon = 1e-5); - //assert!(b2bar.re() == -1.00533412744652); + assert_relative_eq!(u_fraction_wca.re(), 0.997069754340431, epsilon = 1e-5); let a_test = delta_a1u + (-u_fraction_wca + 1.0) diff --git a/src/uvtheory/eos/hard_sphere_bh.rs b/src/uvtheory/eos/hard_sphere_bh.rs index 4453310b9..a3001cb4b 100644 --- a/src/uvtheory/eos/hard_sphere_bh.rs +++ b/src/uvtheory/eos/hard_sphere_bh.rs @@ -1,31 +1,29 @@ use crate::uvtheory::parameters::UVParameters; use feos_core::{HelmholtzEnergyDual, StateHD}; -use lazy_static::lazy_static; use ndarray::prelude::*; use num_dual::DualNum; use std::fmt; use std::sync::Arc; -lazy_static! { - static ref BH_CONSTANTS_ETA_B: Array2 = arr2(&[ - [-0.960919783, -0.921097447], - [-0.547468020, -3.508014069], - [-2.253750186, 3.581161364], - ]); - static ref BH_CONSTANTS_ETA_A: Array2 = arr2(&[ - [-1.217417282, 6.754987582, -0.5919326153, -28.99719604], - [1.579548775, -26.93879416, 0.3998915410, 106.9446266], - [-1.993990512, 44.11863355, -40.10916106, -29.6130848], - [0.0, 0.0, 0.0, 0.0], - ]); -} +const BH_CONSTANTS_ETA_B: [[f64; 2]; 3] = [ + [-0.960919783, -0.921097447], + [-0.547468020, -3.508014069], + [-2.253750186, 3.581161364], +]; + +const BH_CONSTANTS_ETA_A: [[f64; 4]; 4] = [ + [-1.217417282, 6.754987582, -0.5919326153, -28.99719604], + [1.579548775, -26.93879416, 0.3998915410, 106.9446266], + [-1.993990512, 44.11863355, -40.10916106, -29.6130848], + [0.0, 0.0, 0.0, 0.0], +]; #[derive(Debug, Clone)] -pub struct HardSphere { +pub struct HardSphereBH { pub parameters: Arc, } -impl> HelmholtzEnergyDual for HardSphere { +impl> HelmholtzEnergyDual for HardSphereBH { /// Helmholtz energy for hard spheres, eq. 19 (check Volume) fn helmholtz_energy(&self, state: &StateHD) -> D { let d = diameter_bh(&self.parameters, state.temperature); @@ -39,7 +37,7 @@ impl> HelmholtzEnergyDual for HardSphere { } } -impl fmt::Display for HardSphere { +impl fmt::Display for HardSphereBH { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { write!(f, "Hard Sphere") } @@ -48,7 +46,7 @@ impl fmt::Display for HardSphere { /// Dimensionless Hard-sphere diameter according to Barker-Henderson division. /// Eq. S23 and S24. /// -pub fn diameter_bh>(parameters: &UVParameters, temperature: D) -> Array1 { +pub(super) fn diameter_bh>(parameters: &UVParameters, temperature: D) -> Array1 { parameters .cd_bh_pure .iter() @@ -63,7 +61,7 @@ pub fn diameter_bh>(parameters: &UVParameters, temperature: D) - .collect() } -pub fn zeta>(partial_density: &Array1, diameter: &Array1) -> [D; 4] { +pub(super) fn zeta>(partial_density: &Array1, diameter: &Array1) -> [D; 4] { let mut zeta: [D; 4] = [D::zero(), D::zero(), D::zero(), D::zero()]; for i in 0..partial_density.len() { for k in 0..4 { @@ -74,13 +72,16 @@ pub fn zeta>(partial_density: &Array1, diameter: &Array1) zeta } -pub fn packing_fraction>(partial_density: &Array1, diameter: &Array1) -> D { +pub(super) fn packing_fraction>( + partial_density: &Array1, + diameter: &Array1, +) -> D { (0..partial_density.len()).fold(D::zero(), |acc, i| { acc + partial_density[i] * diameter[i].powi(3) * (std::f64::consts::PI / 6.0) }) } -pub fn zeta_23>(molefracs: &Array1, diameter: &Array1) -> D { +pub(super) fn zeta_23>(molefracs: &Array1, diameter: &Array1) -> D { let mut zeta: [D; 2] = [D::zero(), D::zero()]; for i in 0..molefracs.len() { for k in 0..2 { @@ -90,16 +91,7 @@ pub fn zeta_23>(molefracs: &Array1, diameter: &Array1) -> zeta[0] / zeta[1] } -//#[inline] -//pub fn dimensionless_length_scale>( -// parameters: &UVParameters, -//temperature: D, -//rep: f64, -//) -> Array1 { -// -diameter_bh(parameters, temperature) + 1.0 -//} - -pub fn packing_fraction_b>( +pub(super) fn packing_fraction_b>( parameters: &UVParameters, diameter: &Array1, eta: D, @@ -109,16 +101,17 @@ pub fn packing_fraction_b>( let tau = -(diameter[i] / parameters.sigma[i] + diameter[j] / parameters.sigma[j]) * 0.5 + 1.0; //dimensionless let tau2 = tau * tau; + let c = arr1(&[ - tau * BH_CONSTANTS_ETA_B[[0, 0]] + tau2 * BH_CONSTANTS_ETA_B[[0, 1]], - tau * BH_CONSTANTS_ETA_B[[1, 0]] + tau2 * BH_CONSTANTS_ETA_B[[1, 1]], - tau * BH_CONSTANTS_ETA_B[[2, 0]] + tau2 * BH_CONSTANTS_ETA_B[[2, 1]], + tau * BH_CONSTANTS_ETA_B[0][0] + tau2 * BH_CONSTANTS_ETA_B[0][1], + tau * BH_CONSTANTS_ETA_B[1][0] + tau2 * BH_CONSTANTS_ETA_B[1][1], + tau * BH_CONSTANTS_ETA_B[2][0] + tau2 * BH_CONSTANTS_ETA_B[2][1], ]); eta + eta * c[0] + eta * eta * c[1] + eta.powi(3) * c[2] }) } -pub fn packing_fraction_a>( +pub(super) fn packing_fraction_a>( parameters: &UVParameters, diameter: &Array1, eta: D, @@ -126,19 +119,21 @@ pub fn packing_fraction_a>( let n = parameters.att.len(); Array2::from_shape_fn((n, n), |(i, j)| { let tau = - -(diameter[i] / parameters.sigma[i] + diameter[j] / parameters.sigma[j]) * 0.5 + 1.0; //dimensionless//-(diameter[i] + diameter[j]) * 0.5 + 1.0; + -(diameter[i] / parameters.sigma[i] + diameter[j] / parameters.sigma[j]) * 0.5 + 1.0; let tau2 = tau * tau; let rep_inv = 1.0 / parameters.rep_ij[[i, j]]; + let c = arr1(&[ - tau * (BH_CONSTANTS_ETA_A[[0, 0]] + BH_CONSTANTS_ETA_A[[0, 1]] * rep_inv) - + tau2 * (BH_CONSTANTS_ETA_A[[0, 2]] + BH_CONSTANTS_ETA_A[[0, 3]] * rep_inv), - tau * (BH_CONSTANTS_ETA_A[[1, 0]] + BH_CONSTANTS_ETA_A[[1, 1]] * rep_inv) - + tau2 * (BH_CONSTANTS_ETA_A[[1, 2]] + BH_CONSTANTS_ETA_A[[1, 3]] * rep_inv), - tau * (BH_CONSTANTS_ETA_A[[2, 0]] + BH_CONSTANTS_ETA_A[[2, 1]] * rep_inv) - + tau2 * (BH_CONSTANTS_ETA_A[[2, 2]] + BH_CONSTANTS_ETA_A[[2, 3]] * rep_inv), - tau * (BH_CONSTANTS_ETA_A[[3, 0]] + BH_CONSTANTS_ETA_A[[3, 1]] * rep_inv) - + tau2 * (BH_CONSTANTS_ETA_A[[3, 2]] + BH_CONSTANTS_ETA_A[[3, 3]] * rep_inv), + tau * (BH_CONSTANTS_ETA_A[0][0] + BH_CONSTANTS_ETA_A[0][1] * rep_inv) + + tau2 * (BH_CONSTANTS_ETA_A[0][2] + BH_CONSTANTS_ETA_A[0][3] * rep_inv), + tau * (BH_CONSTANTS_ETA_A[1][0] + BH_CONSTANTS_ETA_A[1][1] * rep_inv) + + tau2 * (BH_CONSTANTS_ETA_A[1][2] + BH_CONSTANTS_ETA_A[1][3] * rep_inv), + tau * (BH_CONSTANTS_ETA_A[2][0] + BH_CONSTANTS_ETA_A[2][1] * rep_inv) + + tau2 * (BH_CONSTANTS_ETA_A[2][2] + BH_CONSTANTS_ETA_A[2][3] * rep_inv), + tau * (BH_CONSTANTS_ETA_A[3][0] + BH_CONSTANTS_ETA_A[3][1] * rep_inv) + + tau2 * (BH_CONSTANTS_ETA_A[3][2] + BH_CONSTANTS_ETA_A[3][3] * rep_inv), ]); + eta + eta * c[0] + eta * eta * c[1] + eta.powi(3) * c[2] + eta.powi(4) * c[3] }) } @@ -167,27 +162,4 @@ mod test { 0.95583586434435486 ); } - - // #[test] - // fn helmholtz_energy() { - // let p = methane_parameters(12); - // let p = test_parameters(12, 1.0, 1.0); - // let reduced_density = 1.0; - // let reduced_temperature = 4.0; - - // let hs = HardSphere { - // parameters: Arc::new(p.clone()), - // }; - // let particles = arr1(&[1000.0]); - // let n = &particles / 6.02214076e23; - // let volume = particles[0] / reduced_density * p.sigma[0].powi(3); - // let temperature = reduced_temperature * p.epsilon_k[0]; - // let s = StateHD::new(temperature, volume, n.clone()); - // dbg!(particles[0] / volume * p.sigma[0].powi(3)); - // dbg!(&s.temperature); - // dbg!(&s.volume); - // dbg!(&s.moles); - // let a = hs.helmholtz_energy(&s); - // assert_relative_eq!(a / particles[0], 1.9859860794723039, epsilon = 1e-10) - // } } diff --git a/src/uvtheory/eos/hard_sphere_wca.rs b/src/uvtheory/eos/hard_sphere_wca.rs index 5d256fa2b..8a8e57270 100644 --- a/src/uvtheory/eos/hard_sphere_wca.rs +++ b/src/uvtheory/eos/hard_sphere_wca.rs @@ -1,41 +1,53 @@ use crate::uvtheory::parameters::UVParameters; use feos_core::{HelmholtzEnergyDual, StateHD}; -use lazy_static::lazy_static; use ndarray::prelude::*; use num_dual::DualNum; use std::f64::consts::PI; use std::fmt; use std::sync::Arc; -lazy_static! { - static ref WCA_CONSTANTS_ETA_B: Array2 = arr2(&[ - [-0.883143456, -0.618156214], - [-0.589914255, -3.015264636], - [-2.152046477, 4.7038689542], - ]); - static ref WCA_CONSTANTS_ETA_A: Array2 = arr2(&[ - [-0.888512176, 0.265207151, -0.851803291, -1.380304110], - [-0.395548410, -0.626398537, -1.484059291, -3.041216688], - [-2.905719617, -1.778798984, -1.556827067, -4.308085347], - [0.429154871, 20.765871545, 9.341250676, -33.787719418], - ]); - pub static ref WCA_CONSTANTS_Q: Array2 = arr2(&[ - [1.92840364363978, 4.43165896265079E-01, 0.0, 0.0], - [ - 5.20120816141761E-01, - 1.82526759234412E-01, - 1.10319989659929E-02, - -7.97813995328348E-05 - ], - [ - 0.0, - 1.29885156087242E-02, - 6.41039871789327E-03, - 1.85866741090323E-05 - ], - ]); -} +pub(super) const WCA_CONSTANTS_Q: [[f64; 4]; 3] = [ + [1.92840364363978, 4.43165896265079E-01, 0.0, 0.0], + [ + 5.20120816141761E-01, + 1.82526759234412E-01, + 1.10319989659929E-02, + -7.97813995328348E-05, + ], + [ + 0.0, + 1.29885156087242E-02, + 6.41039871789327E-03, + 1.85866741090323E-05, + ], +]; + +const WCA_CONSTANTS_ETA_A: [[f64; 4]; 4] = [ + [-0.888512176, 0.265207151, -0.851803291, -1.380304110], + [-0.395548410, -0.626398537, -1.484059291, -3.041216688], + [-2.905719617, -1.778798984, -1.556827067, -4.308085347], + [0.429154871, 20.765871545, 9.341250676, -33.787719418], +]; + +const WCA_CONSTANTS_ETA_B: [[f64; 2]; 3] = [ + [-0.883143456, -0.618156214], + [-0.589914255, -3.015264636], + [-2.152046477, 4.7038689542], +]; +// New Fit to numerical integrals for uv-B3-theory +pub(super) const WCA_CONSTANTS_ETA_A_UVB3: [[f64; 4]; 4] = [ + [2.64043218, -1.2184421, -22.90786387, 0.96433414], + [-16.75643936, 30.83929771, 73.08711814, -166.57701616], + [19.53170162, -88.87955657, -76.51387192, 443.68942745], + [-3.77740877, 83.04694547, 21.62502721, -304.8643176], +]; + +pub(super) const WCA_CONSTANTS_ETA_B_UVB3: [[f64; 2]; 3] = [ + [2.19821588, -20.45005484], + [-13.47050687, 56.65701375], + [12.90119266, -42.71680606], +]; #[derive(Debug, Clone)] pub struct HardSphereWCA { pub parameters: Arc, @@ -62,7 +74,10 @@ impl fmt::Display for HardSphereWCA { } /// Dimensionless Hard-sphere diameter according to Weeks-Chandler-Andersen division. -pub fn diameter_wca>(parameters: &UVParameters, temperature: D) -> Array1 { +pub(super) fn diameter_wca>( + parameters: &UVParameters, + temperature: D, +) -> Array1 { parameters .sigma .iter() @@ -81,59 +96,21 @@ pub fn diameter_wca>(parameters: &UVParameters, temperature: D) .collect() } -// Hard sphere diameter q for WCA division from eq. (S28) -// pub fn diameter_q_wca>(parameters: &UVParameters, temperature: D) -> Array1 { -// parameters -// .sigma -// .iter() -// .enumerate() -// .map(|(i, _c)| { -// let nu = parameters.rep[i]; -// let n = parameters.att[i]; -// let t = temperature / parameters.epsilon_k[i]; -// let rs = (nu / n).powf(1.0 / (nu - n)); -// let coeffs = arr1(&[ -// (nu * 2.0 * PI / n).sqrt(), -// WCA_CONSTANTS_Q[[0, 0]] + WCA_CONSTANTS_Q[[0, 1]] * (nu - 7.0), -// WCA_CONSTANTS_Q[[1, 0]] -// + WCA_CONSTANTS_Q[[1, 1]] * (nu - 7.0) -// + WCA_CONSTANTS_Q[[1, 2]] * (nu - 7.0).powi(2) -// + WCA_CONSTANTS_Q[[1, 3]] * (nu - 7.0).powi(3), -// WCA_CONSTANTS_Q[[2, 0]] -// + WCA_CONSTANTS_Q[[2, 1]] * (nu - 7.0) -// + WCA_CONSTANTS_Q[[2, 2]] * (nu - 7.0).powi(2) -// + WCA_CONSTANTS_Q[[2, 3]] * (nu - 7.0).powi(3), -// ]); - -// (t.powf(2.0) * coeffs[3] -// + t.powf(3.0 / 2.0) * coeffs[2] -// + t * coeffs[1] -// + t.powf(1.0 / 2.0) * coeffs[0] -// + 1.0) -// .powf(-1.0 / (2.0 * nu)) -// * rs -// * parameters.sigma[i] -// }) -// .collect() -// } - -// - -pub fn dimensionless_diameter_q_wca>(t_x: D, rep_x: D, att_x: D) -> D { +pub(super) fn dimensionless_diameter_q_wca>(t_x: D, rep_x: D, att_x: D) -> D { let nu = rep_x; let n = att_x; let rs = (nu / n).powd((nu - n).recip()); let coeffs = arr1(&[ (nu * 2.0 * PI / n).sqrt(), - (nu - 7.0) * WCA_CONSTANTS_Q[[0, 1]] + WCA_CONSTANTS_Q[[0, 0]], - (nu - 7.0) * WCA_CONSTANTS_Q[[1, 1]] - + (nu - 7.0).powi(2) * WCA_CONSTANTS_Q[[1, 2]] - + (nu - 7.0).powi(3) * WCA_CONSTANTS_Q[[1, 3]] - + WCA_CONSTANTS_Q[[1, 0]], - (nu - 7.0) * WCA_CONSTANTS_Q[[2, 1]] - + (nu - 7.0).powi(2) * WCA_CONSTANTS_Q[[2, 2]] - + (nu - 7.0).powi(3) * WCA_CONSTANTS_Q[[2, 3]] - + WCA_CONSTANTS_Q[[2, 0]], + (nu - 7.0) * WCA_CONSTANTS_Q[0][1] + WCA_CONSTANTS_Q[0][0], + (nu - 7.0) * WCA_CONSTANTS_Q[1][1] + + (nu - 7.0).powi(2) * WCA_CONSTANTS_Q[1][2] + + (nu - 7.0).powi(3) * WCA_CONSTANTS_Q[1][3] + + WCA_CONSTANTS_Q[1][0], + (nu - 7.0) * WCA_CONSTANTS_Q[2][1] + + (nu - 7.0).powi(2) * WCA_CONSTANTS_Q[2][2] + + (nu - 7.0).powi(3) * WCA_CONSTANTS_Q[2][3] + + WCA_CONSTANTS_Q[2][0], ]); (t_x.powf(2.0) * coeffs[3] @@ -145,7 +122,7 @@ pub fn dimensionless_diameter_q_wca>(t_x: D, rep_x: D, att_x: D) * rs } -pub fn zeta>(partial_density: &Array1, diameter: &Array1) -> [D; 4] { +pub(super) fn zeta>(partial_density: &Array1, diameter: &Array1) -> [D; 4] { let mut zeta: [D; 4] = [D::zero(), D::zero(), D::zero(), D::zero()]; for i in 0..partial_density.len() { for k in 0..4 { @@ -156,13 +133,16 @@ pub fn zeta>(partial_density: &Array1, diameter: &Array1) zeta } -pub fn packing_fraction>(partial_density: &Array1, diameter: &Array1) -> D { +pub(super) fn packing_fraction>( + partial_density: &Array1, + diameter: &Array1, +) -> D { (0..partial_density.len()).fold(D::zero(), |acc, i| { acc + partial_density[i] * diameter[i].powi(3) * (std::f64::consts::PI / 6.0) }) } -pub fn zeta_23>(molefracs: &Array1, diameter: &Array1) -> D { +pub(super) fn zeta_23>(molefracs: &Array1, diameter: &Array1) -> D { let mut zeta: [D; 2] = [D::zero(), D::zero()]; for i in 0..molefracs.len() { for k in 0..2 { @@ -173,7 +153,7 @@ pub fn zeta_23>(molefracs: &Array1, diameter: &Array1) -> } #[inline] -pub fn dimensionless_length_scale>( +pub(super) fn dimensionless_length_scale>( parameters: &UVParameters, temperature: D, ) -> Array1 { @@ -192,7 +172,29 @@ pub fn dimensionless_length_scale>( #[inline] -pub fn packing_fraction_b>( +pub(super) fn packing_fraction_b>( + parameters: &UVParameters, + eta: D, + temperature: D, +) -> Array2 { + let n = parameters.att.len(); + let dimensionless_lengths = dimensionless_length_scale(parameters, temperature); + Array2::from_shape_fn((n, n), |(i, j)| { + let tau = (dimensionless_lengths[i] + dimensionless_lengths[j]) + / parameters.sigma_ij[[i, j]] + * 0.5; //dimensionless + let tau2 = tau * tau; + + let c = arr1(&[ + tau * WCA_CONSTANTS_ETA_B[0][0] + tau2 * WCA_CONSTANTS_ETA_B[0][1], + tau * WCA_CONSTANTS_ETA_B[1][0] + tau2 * WCA_CONSTANTS_ETA_B[1][1], + tau * WCA_CONSTANTS_ETA_B[2][0] + tau2 * WCA_CONSTANTS_ETA_B[2][1], + ]); + eta + eta * c[0] + eta * eta * c[1] + eta.powi(3) * c[2] + }) +} + +pub(super) fn packing_fraction_b_uvb3>( parameters: &UVParameters, eta: D, temperature: D, @@ -206,15 +208,44 @@ pub fn packing_fraction_b>( let tau2 = tau * tau; let c = arr1(&[ - tau * WCA_CONSTANTS_ETA_B[[0, 0]] + tau2 * WCA_CONSTANTS_ETA_B[[0, 1]], - tau * WCA_CONSTANTS_ETA_B[[1, 0]] + tau2 * WCA_CONSTANTS_ETA_B[[1, 1]], - tau * WCA_CONSTANTS_ETA_B[[2, 0]] + tau2 * WCA_CONSTANTS_ETA_B[[2, 1]], + tau * WCA_CONSTANTS_ETA_B_UVB3[0][0] + tau2 * WCA_CONSTANTS_ETA_B_UVB3[0][1], + tau * WCA_CONSTANTS_ETA_B_UVB3[1][0] + tau2 * WCA_CONSTANTS_ETA_B_UVB3[1][1], + tau * WCA_CONSTANTS_ETA_B_UVB3[2][0] + tau2 * WCA_CONSTANTS_ETA_B_UVB3[2][1], ]); eta + eta * c[0] + eta * eta * c[1] + eta.powi(3) * c[2] }) } -pub fn packing_fraction_a>( +pub(super) fn packing_fraction_a>( + parameters: &UVParameters, + eta: D, + temperature: D, +) -> Array2 { + let dimensionless_lengths = dimensionless_length_scale(parameters, temperature); + let n = parameters.att.len(); + Array2::from_shape_fn((n, n), |(i, j)| { + let tau = (dimensionless_lengths[i] + dimensionless_lengths[j]) + / parameters.sigma_ij[[i, j]] + * 0.5; //dimensionless + + let tau2 = tau * tau; + let rep_inv = 1.0 / parameters.rep_ij[[i, j]]; + + let c = arr1(&[ + tau * (WCA_CONSTANTS_ETA_A[0][0] + WCA_CONSTANTS_ETA_A[0][1] * rep_inv) + + tau2 * (WCA_CONSTANTS_ETA_A[0][2] + WCA_CONSTANTS_ETA_A[0][3] * rep_inv), + tau * (WCA_CONSTANTS_ETA_A[1][0] + WCA_CONSTANTS_ETA_A[1][1] * rep_inv) + + tau2 * (WCA_CONSTANTS_ETA_A[1][2] + WCA_CONSTANTS_ETA_A[1][3] * rep_inv), + tau * (WCA_CONSTANTS_ETA_A[2][0] + WCA_CONSTANTS_ETA_A[2][1] * rep_inv) + + tau2 * (WCA_CONSTANTS_ETA_A[2][2] + WCA_CONSTANTS_ETA_A[2][3] * rep_inv), + tau * (WCA_CONSTANTS_ETA_A[3][0] + WCA_CONSTANTS_ETA_A[3][1] * rep_inv) + + tau2 * (WCA_CONSTANTS_ETA_A[3][2] + WCA_CONSTANTS_ETA_A[3][3] * rep_inv), + ]); + eta + eta * c[0] + eta * eta * c[1] + eta.powi(3) * c[2] + eta.powi(4) * c[3] + }) +} + +pub(super) fn packing_fraction_a_uvb3>( parameters: &UVParameters, eta: D, temperature: D, @@ -229,14 +260,18 @@ pub fn packing_fraction_a>( let tau2 = tau * tau; let rep_inv = 1.0 / parameters.rep_ij[[i, j]]; let c = arr1(&[ - tau * (WCA_CONSTANTS_ETA_A[[0, 0]] + WCA_CONSTANTS_ETA_A[[0, 1]] * rep_inv) - + tau2 * (WCA_CONSTANTS_ETA_A[[0, 2]] + WCA_CONSTANTS_ETA_A[[0, 3]] * rep_inv), - tau * (WCA_CONSTANTS_ETA_A[[1, 0]] + WCA_CONSTANTS_ETA_A[[1, 1]] * rep_inv) - + tau2 * (WCA_CONSTANTS_ETA_A[[1, 2]] + WCA_CONSTANTS_ETA_A[[1, 3]] * rep_inv), - tau * (WCA_CONSTANTS_ETA_A[[2, 0]] + WCA_CONSTANTS_ETA_A[[2, 1]] * rep_inv) - + tau2 * (WCA_CONSTANTS_ETA_A[[2, 2]] + WCA_CONSTANTS_ETA_A[[2, 3]] * rep_inv), - tau * (WCA_CONSTANTS_ETA_A[[3, 0]] + WCA_CONSTANTS_ETA_A[[3, 1]] * rep_inv) - + tau2 * (WCA_CONSTANTS_ETA_A[[3, 2]] + WCA_CONSTANTS_ETA_A[[3, 3]] * rep_inv), + tau * (WCA_CONSTANTS_ETA_A_UVB3[0][0] + WCA_CONSTANTS_ETA_A_UVB3[0][1] * rep_inv) + + tau2 + * (WCA_CONSTANTS_ETA_A_UVB3[0][2] + WCA_CONSTANTS_ETA_A_UVB3[0][3] * rep_inv), + tau * (WCA_CONSTANTS_ETA_A_UVB3[1][0] + WCA_CONSTANTS_ETA_A_UVB3[1][1] * rep_inv) + + tau2 + * (WCA_CONSTANTS_ETA_A_UVB3[1][2] + WCA_CONSTANTS_ETA_A_UVB3[1][3] * rep_inv), + tau * (WCA_CONSTANTS_ETA_A_UVB3[2][0] + WCA_CONSTANTS_ETA_A_UVB3[2][1] * rep_inv) + + tau2 + * (WCA_CONSTANTS_ETA_A_UVB3[2][2] + WCA_CONSTANTS_ETA_A_UVB3[2][3] * rep_inv), + tau * (WCA_CONSTANTS_ETA_A_UVB3[3][0] + WCA_CONSTANTS_ETA_A_UVB3[3][1] * rep_inv) + + tau2 + * (WCA_CONSTANTS_ETA_A_UVB3[3][2] + WCA_CONSTANTS_ETA_A_UVB3[3][3] * rep_inv), ]); eta + eta * c[0] + eta * eta * c[1] + eta.powi(3) * c[2] + eta.powi(4) * c[3] }) diff --git a/src/uvtheory/eos/mod.rs b/src/uvtheory/eos/mod.rs index 8b59fd532..143b859c0 100644 --- a/src/uvtheory/eos/mod.rs +++ b/src/uvtheory/eos/mod.rs @@ -2,23 +2,27 @@ #![allow(clippy::needless_range_loop)] use super::parameters::UVParameters; -use feos_core::{parameter::Parameter, EquationOfState, HelmholtzEnergy}; +use feos_core::{parameter::Parameter, EosError, EosResult, EquationOfState, HelmholtzEnergy}; use ndarray::Array1; use std::f64::consts::FRAC_PI_6; use std::sync::Arc; pub(crate) mod attractive_perturbation_bh; +pub(crate) mod attractive_perturbation_uvb3; pub(crate) mod attractive_perturbation_wca; pub(crate) mod hard_sphere_bh; pub(crate) mod hard_sphere_wca; pub(crate) mod reference_perturbation_bh; +pub(crate) mod reference_perturbation_uvb3; pub(crate) mod reference_perturbation_wca; pub(crate) mod ufraction; use attractive_perturbation_bh::AttractivePerturbationBH; +use attractive_perturbation_uvb3::AttractivePerturbationUVB3; use attractive_perturbation_wca::AttractivePerturbationWCA; -use hard_sphere_bh::HardSphere; +use hard_sphere_bh::HardSphereBH; use hard_sphere_wca::HardSphereWCA; use reference_perturbation_bh::ReferencePerturbationBH; +use reference_perturbation_uvb3::ReferencePerturbationUVB3; use reference_perturbation_wca::ReferencePerturbationWCA; /// Type of perturbation. @@ -29,11 +33,20 @@ pub enum Perturbation { WeeksChandlerAndersen, } +/// Order of the highest virial coefficient included in the model. +#[derive(Clone)] +#[cfg_attr(feature = "python", pyo3::pyclass)] +pub enum VirialOrder { + Second, + Third, +} + /// Configuration options for uv-theory #[derive(Clone)] pub struct UVTheoryOptions { pub max_eta: f64, pub perturbation: Perturbation, + pub virial_order: VirialOrder, } impl Default for UVTheoryOptions { @@ -41,6 +54,7 @@ impl Default for UVTheoryOptions { Self { max_eta: 0.5, perturbation: Perturbation::WeeksChandlerAndersen, + virial_order: VirialOrder::Second, } } } @@ -54,44 +68,79 @@ pub struct UVTheory { impl UVTheory { /// uv-theory with default options (WCA). - pub fn new(parameters: Arc) -> Self { + pub fn new(parameters: Arc) -> EosResult { Self::with_options(parameters, UVTheoryOptions::default()) } /// uv-theory with provided options. - pub fn with_options(parameters: Arc, options: UVTheoryOptions) -> Self { + pub fn with_options( + parameters: Arc, + options: UVTheoryOptions, + ) -> EosResult { let mut contributions: Vec> = Vec::with_capacity(3); match options.perturbation { - Perturbation::BarkerHenderson => { - contributions.push(Box::new(HardSphere { - parameters: parameters.clone(), - })); - contributions.push(Box::new(ReferencePerturbationBH { - parameters: parameters.clone(), - })); - contributions.push(Box::new(AttractivePerturbationBH { - parameters: parameters.clone(), - })); - } + Perturbation::BarkerHenderson => match options.virial_order { + VirialOrder::Second => { + contributions.push(Box::new(HardSphereBH { + parameters: parameters.clone(), + })); + contributions.push(Box::new(ReferencePerturbationBH { + parameters: parameters.clone(), + })); + contributions.push(Box::new(AttractivePerturbationBH { + parameters: parameters.clone(), + })); + } + VirialOrder::Third => { + return Err(EosError::Error( + "Third virial coefficient is not implemented for Barker-Henderson" + .to_string(), + )) + } + }, Perturbation::WeeksChandlerAndersen => { contributions.push(Box::new(HardSphereWCA { parameters: parameters.clone(), })); - contributions.push(Box::new(ReferencePerturbationWCA { - parameters: parameters.clone(), - })); - contributions.push(Box::new(AttractivePerturbationWCA { - parameters: parameters.clone(), - })); + match options.virial_order { + VirialOrder::Second => { + contributions.push(Box::new(ReferencePerturbationWCA { + parameters: parameters.clone(), + })); + contributions.push(Box::new(AttractivePerturbationWCA { + parameters: parameters.clone(), + })); + } + VirialOrder::Third => { + if parameters.sigma.len() > 1 { + return Err(EosError::Error( + "Third virial coefficient is not implemented for mixtures!" + .to_string(), + )); + } + if parameters.att[0] != 6.0 { + return Err(EosError::Error( + "Third virial coefficient is not implemented for attractive exponents other than 6!" + .to_string(), + )); + } + contributions.push(Box::new(ReferencePerturbationUVB3 { + parameters: parameters.clone(), + })); + contributions.push(Box::new(AttractivePerturbationUVB3 { + parameters: parameters.clone(), + })); + } + } } } - Self { + Ok(Self { parameters, options, contributions, - } + }) } } @@ -105,6 +154,7 @@ impl EquationOfState for UVTheory { Arc::new(self.parameters.subset(component_list)), self.options.clone(), ) + .expect("Not defined for mixture") } fn compute_max_density(&self, moles: &Array1) -> f64 { @@ -130,20 +180,14 @@ mod test { use quantity::si::{ANGSTROM, KELVIN, MOL, NAV, RGAS}; #[test] - fn helmholtz_energy_pure_wca() { - let eps_k = 150.03; + fn helmholtz_energy_pure_wca() -> EosResult<()> { let sig = 3.7039; - let r = UVRecord::new(24.0, 6.0, sig, eps_k); - //let r = UVRecord::new(12.0, 6.0, sig, eps_k); - let i = Identifier::new(None, None, None, None, None, None); - let pr = PureRecord::new(i, 1.0, r, None); - let parameters = UVParameters::new_pure(pr); - let eos = Arc::new(UVTheory::new(Arc::new(parameters))); + let eps_k = 150.03; + let parameters = UVParameters::new_simple(24.0, 6.0, sig, eps_k); + let eos = Arc::new(UVTheory::new(Arc::new(parameters))?); let reduced_temperature = 4.0; - //let reduced_temperature = 1.0; let reduced_density = 1.0; - //let reduced_density = 0.9; let temperature = reduced_temperature * eps_k * KELVIN; let moles = arr1(&[2.0]) * MOL; let volume = (sig * ANGSTROM).powi(3) / reduced_density * NAV * 2.0 * MOL; @@ -152,23 +196,23 @@ mod test { .molar_helmholtz_energy(Contributions::ResidualNvt) .to_reduced(RGAS * temperature) .unwrap(); - assert_relative_eq!(a, 2.972986567516, max_relative = 1e-12) //wca - //assert_relative_eq!(a, -7.0843443690046017, max_relative = 1e-12) // bh: assert_relative_eq!(a, 2.993577305779432, max_relative = 1e-12) + assert_relative_eq!(a, 2.972986567516, max_relative = 1e-12); //wca + Ok(()) } + #[test] - fn helmholtz_energy_pure_bh() { + fn helmholtz_energy_pure_bh() -> EosResult<()> { let eps_k = 150.03; let sig = 3.7039; - let r = UVRecord::new(24.0, 6.0, sig, eps_k); - let i = Identifier::new(None, None, None, None, None, None); - let pr = PureRecord::new(i, 1.0, r, None); - let parameters = UVParameters::new_pure(pr); - + let rep = 24.0; + let att = 6.0; + let parameters = UVParameters::new_simple(rep, att, sig, eps_k); let options = UVTheoryOptions { max_eta: 0.5, perturbation: Perturbation::BarkerHenderson, + virial_order: VirialOrder::Second, }; - let eos = Arc::new(UVTheory::with_options(Arc::new(parameters), options)); + let eos = Arc::new(UVTheory::with_options(Arc::new(parameters), options)?); let reduced_temperature = 4.0; let reduced_density = 1.0; @@ -176,17 +220,48 @@ mod test { let moles = arr1(&[2.0]) * MOL; let volume = (sig * ANGSTROM).powi(3) / reduced_density * NAV * 2.0 * MOL; let s = State::new_nvt(&eos, temperature, volume, &moles).unwrap(); + let a = s .molar_helmholtz_energy(Contributions::ResidualNvt) .to_reduced(RGAS * temperature) .unwrap(); - assert_relative_eq!(a, 2.993577305779432, max_relative = 1e-12) + assert_relative_eq!(a, 2.993577305779432, max_relative = 1e-12); + Ok(()) + } + + #[test] + fn helmholtz_energy_pure_uvb3() -> EosResult<()> { + let eps_k = 150.03; + let sig = 3.7039; + let rep = 12.0; + let att = 6.0; + let parameters = UVParameters::new_simple(rep, att, sig, eps_k); + let options = UVTheoryOptions { + max_eta: 0.5, + perturbation: Perturbation::WeeksChandlerAndersen, + virial_order: VirialOrder::Third, + }; + let eos = Arc::new(UVTheory::with_options(Arc::new(parameters), options)?); + + let reduced_temperature = 4.0; + let reduced_density = 0.5; + let temperature = reduced_temperature * eps_k * KELVIN; + let moles = arr1(&[2.0]) * MOL; + let volume = (sig * ANGSTROM).powi(3) / reduced_density * NAV * 2.0 * MOL; + let s = State::new_nvt(&eos, temperature, volume, &moles).unwrap(); + let a = s + .molar_helmholtz_energy(Contributions::ResidualNvt) + .to_reduced(RGAS * temperature) + .unwrap(); + dbg!(a); + assert_relative_eq!(a, 0.37659379124271003, max_relative = 1e-12); + Ok(()) } #[test] - fn helmholtz_energy_mixtures_bh() { - // Mixture of equal components --> result must be the same as fpr pure fluid /// + fn helmholtz_energy_mixtures_bh() -> EosResult<()> { + // Mixture of equal components --> result must be the same as for pure fluid /// // component 1 let rep1 = 24.0; let eps_k1 = 150.03; @@ -219,9 +294,10 @@ mod test { let options = UVTheoryOptions { max_eta: 0.5, perturbation: Perturbation::BarkerHenderson, + virial_order: VirialOrder::Second, }; - let eos_bh = Arc::new(UVTheory::with_options(Arc::new(uv_parameters), options)); + let eos_bh = Arc::new(UVTheory::with_options(Arc::new(uv_parameters), options)?); let state_bh = State::new_nvt(&eos_bh, t_x, volume, &moles).unwrap(); let a_bh = state_bh @@ -230,9 +306,11 @@ mod test { .unwrap(); assert_relative_eq!(a_bh, 2.993577305779432, max_relative = 1e-12); + Ok(()) } + #[test] - fn helmholtz_energy_wca_mixture() { + fn helmholtz_energy_wca_mixture() -> EosResult<()> { let p = test_parameters_mixture( arr1(&[12.0, 12.0]), arr1(&[6.0, 6.0]), @@ -249,18 +327,19 @@ mod test { let volume = (p.sigma[0] * ANGSTROM).powi(3) / reduced_density * NAV * total_moles; // EoS - let eos_wca = Arc::new(UVTheory::new(Arc::new(p))); + let eos_wca = Arc::new(UVTheory::new(Arc::new(p))?); let state_wca = State::new_nvt(&eos_wca, t_x, volume, &moles).unwrap(); let a_wca = state_wca .molar_helmholtz_energy(Contributions::ResidualNvt) .to_reduced(RGAS * t_x) .unwrap(); - assert_relative_eq!(a_wca, -0.597791038364405, max_relative = 1e-5) + assert_relative_eq!(a_wca, -0.597791038364405, max_relative = 1e-5); + Ok(()) } #[test] - fn helmholtz_energy_wca_mixture_different_sigma() { + fn helmholtz_energy_wca_mixture_different_sigma() -> EosResult<()> { let p = test_parameters_mixture( arr1(&[12.0, 12.0]), arr1(&[6.0, 6.0]), @@ -278,12 +357,13 @@ mod test { let volume = NAV * total_moles / density; // EoS - let eos_wca = Arc::new(UVTheory::new(Arc::new(p))); + let eos_wca = Arc::new(UVTheory::new(Arc::new(p))?); let state_wca = State::new_nvt(&eos_wca, t_x, volume, &moles).unwrap(); let a_wca = state_wca .molar_helmholtz_energy(Contributions::ResidualNvt) .to_reduced(RGAS * t_x) .unwrap(); - assert_relative_eq!(a_wca, -0.034206207363139396, max_relative = 1e-5) + assert_relative_eq!(a_wca, -0.034206207363139396, max_relative = 1e-5); + Ok(()) } } diff --git a/src/uvtheory/eos/reference_perturbation_uvb3.rs b/src/uvtheory/eos/reference_perturbation_uvb3.rs new file mode 100644 index 000000000..30d79d126 --- /dev/null +++ b/src/uvtheory/eos/reference_perturbation_uvb3.rs @@ -0,0 +1,104 @@ +use super::hard_sphere_wca::{ + diameter_wca, dimensionless_diameter_q_wca, packing_fraction, packing_fraction_a_uvb3, + packing_fraction_b_uvb3, +}; +use crate::uvtheory::parameters::*; +use feos_core::{HelmholtzEnergyDual, StateHD}; +use num_dual::DualNum; +use std::fmt; +use std::{f64::consts::PI, sync::Arc}; + +#[derive(Debug, Clone)] +pub struct ReferencePerturbationUVB3 { + pub parameters: Arc, +} + +impl fmt::Display for ReferencePerturbationUVB3 { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Reference Perturbation") + } +} + +impl> HelmholtzEnergyDual for ReferencePerturbationUVB3 { + /// Helmholtz energy for perturbation reference (Mayer-f), eq. 29 + fn helmholtz_energy(&self, state: &StateHD) -> D { + let p = &self.parameters; + let n = p.sigma.len(); + let x = &state.molefracs; + let d = diameter_wca(p, state.temperature); + //let q = diameter_q_wca(&p, state.temperature); + let eta = packing_fraction(&state.partial_density, &d); + let eta_a = packing_fraction_a_uvb3(p, eta, state.temperature); + let eta_b = packing_fraction_b_uvb3(p, eta, state.temperature); + let mut a = D::zero(); + + for i in 0..n { + for j in 0..n { + let rs_ij = ((p.rep[i] / p.att[i]).powf(1.0 / (p.rep[i] - p.att[i])) + + (p.rep[j] / p.att[j]).powf(1.0 / (p.rep[j] - p.att[j]))) + * 0.5; // MIXING RULE not clear!!! + let d_ij = (d[i] + d[j]) * 0.5; // (d[i] * p.sigma[i] + d[j] * p.sigma[j]) * 0.5; + + let t_ij = state.temperature / p.eps_k_ij[[i, j]]; + let rep_ij = p.rep_ij[[i, j]]; + let att_ij = p.att_ij[[i, j]]; + let q_ij = dimensionless_diameter_q_wca(t_ij, D::from(rep_ij), D::from(att_ij)) + * p.sigma_ij[[i, j]]; + + a += x[i] + * x[j] + * ((-eta_a[[i, j]] * 0.5 + 1.0) / (-eta_a[[i, j]] + 1.0).powi(3) + * (-q_ij.powi(3) + (rs_ij * p.sigma_ij[[i, j]]).powi(3)) + - ((-eta_b[[i, j]] * 0.5 + 1.0) / (-eta_b[[i, j]] + 1.0).powi(3)) + * (-d_ij.powi(3) + (rs_ij * p.sigma_ij[[i, j]]).powi(3))) + } + } + + -a * state.moles.sum().powi(2) * 2.0 / 3.0 / state.volume * PI + } +} + +#[cfg(test)] +mod test { + use super::*; + use crate::uvtheory::parameters::utils::test_parameters; + use approx::assert_relative_eq; + use ndarray::arr1; + + #[test] + fn test_delta_a0_uvb3_pure() { + let moles = arr1(&[2.0]); + // #temp = 2.0, rho = 0.5, nu = 12 + // Hard sphere adhs 1.3491645849732654 + // Delta a0 0.1130778070897391 + + let reduced_temperature = 2.0; + let reduced_density = 0.5; + let reduced_volume = moles[0] / reduced_density; + + let p = test_parameters(12.0, 6.0, 1.0, 1.0); + let pt = ReferencePerturbationUVB3 { + parameters: Arc::new(p), + }; + let state = StateHD::new(reduced_temperature, reduced_volume, moles.clone()); + let a = pt.helmholtz_energy(&state) / moles[0]; + dbg!(a.re()); + assert_relative_eq!(a, 0.1130778070897391, epsilon = 1e-10); + + // #temp = 3.0, rho = 1.1, nu = 20 + // Hard sphere adhs 5.458989212531771 + //Delta a0 0.3405167374787895 + let reduced_temperature = 3.0; + let reduced_density = 1.1; + let reduced_volume = moles[0] / reduced_density; + + let p = test_parameters(20.0, 6.0, 1.0, 1.0); + let pt = ReferencePerturbationUVB3 { + parameters: Arc::new(p), + }; + let state = StateHD::new(reduced_temperature, reduced_volume, moles.clone()); + let a = pt.helmholtz_energy(&state) / moles[0]; + + assert_relative_eq!(a, 0.3405167374787895, epsilon = 1e-10); + } +} diff --git a/src/uvtheory/mod.rs b/src/uvtheory/mod.rs index 481932928..f24a800a4 100644 --- a/src/uvtheory/mod.rs +++ b/src/uvtheory/mod.rs @@ -1,10 +1,71 @@ -//! uv-theory equation of state +//! uv-theory for fluids interacting with a Mie potential. //! -//! [van Westen et al. (2021)](https://doi.org/10.1063/5.0073572) +//! # Implementations +//! +//! ## uv-theory +//! +//! [van Westen et al. (2021)](https://doi.org/10.1063/5.0073572): utilizing second virial coeffients and Barker-Henderson or Weeks-Chandler-Andersen perturbation. +//! +//! ```ignore +//! # use feos_core::EosError; +//! use feos::uvtheory::{Perturbation, UVTheory, UVTheoryOptions, UVParameters, VirialOrder}; +//! use std::sync::Arc; +//! +//! let parameters = Arc::new( +//! UVParameters::new_simple(24.0, 7.0, 3.0, 150.0) +//! ); +//! +//! let default_options = UVTheoryOptions { +//! max_eta = 0.5, +//! perturbation = Perturbation::WeeksChandlerAndersen, +//! virial_order = VirialOrder::Second +//! }; +//! // Define equation of state. +//! let uv_wca = Arc::new(UVTheory::new(parameters)); +//! // this is identical to above +//! let uv_wca = Arc::new( +//! UVTheory::with_options(parameters, default_options) +//! ); +//! +//! // use Barker-Henderson perturbation +//! let options = UVTheoryOptions { +//! max_eta = 0.5, +//! perturbation = Perturbation::BarkerHenderson, +//! virial_order = VirialOrder::Second +//! }; +//! let uv_bh = Arc::new( +//! UVTheory::with_options(parameters, options) +//! ); +//! ``` +//! +//! ## uv-B3-theory +//! +//! - utilizing third virial coefficients for pure fluids with attractive exponent of 6 and Weeks-Chandler-Andersen perturbation. Manuscript submitted. +//! +//! ```ignore +//! # use feos_core::EosError; +//! use feos::uvtheory::{Perturbation, UVTheory, UVTheoryOptions, UVParameters, VirialOrder}; +//! use std::sync::Arc; +//! +//! let parameters = Arc::new( +//! UVParameters::new_simple(24.0, 6.0, 3.0, 150.0) +//! ); +//! +//! // use uv-B3-theory +//! let options = UVTheoryOptions { +//! max_eta = 0.5, +//! perturbation = Perturbation::WeeksChandlerAndersen, +//! virial_order = VirialOrder::Third +//! }; +//! // Define equation of state. +//! let uv_b3 = Arc::new( +//! UVTheory::with_options(parameters, options) +//! ); +//! ``` mod eos; mod parameters; -pub use eos::{Perturbation, UVTheory, UVTheoryOptions}; +pub use eos::{Perturbation, UVTheory, UVTheoryOptions, VirialOrder}; pub use parameters::{UVBinaryRecord, UVParameters, UVRecord}; #[cfg(feature = "python")] diff --git a/src/uvtheory/parameters.rs b/src/uvtheory/parameters.rs index 20d16fc51..4b54c22a7 100644 --- a/src/uvtheory/parameters.rs +++ b/src/uvtheory/parameters.rs @@ -1,3 +1,4 @@ +use feos_core::parameter::Identifier; use feos_core::parameter::{Parameter, PureRecord}; use lazy_static::lazy_static; use ndarray::concatenate; @@ -203,6 +204,14 @@ impl Parameter for UVParameters { } impl UVParameters { + /// Parameters for a single substance with molar weight one and no (default) ideal gas contributions. + pub fn new_simple(rep: f64, att: f64, sigma: f64, epsilon_k: f64) -> Self { + let model_record = UVRecord::new(rep, att, sigma, epsilon_k); + let pure_record = PureRecord::new(Identifier::default(), 1.0, model_record, None); + Self::new_pure(pure_record) + } + + /// Markdown representation of parameters. pub fn to_markdown(&self) -> String { let mut output = String::new(); let o = &mut output; diff --git a/src/uvtheory/python.rs b/src/uvtheory/python.rs index b442971d7..08c135a18 100644 --- a/src/uvtheory/python.rs +++ b/src/uvtheory/python.rs @@ -1,5 +1,5 @@ use super::parameters::{NoRecord, UVBinaryRecord, UVParameters, UVRecord}; -use super::Perturbation; +use super::{Perturbation, VirialOrder}; use feos_core::parameter::{ BinaryRecord, Identifier, IdentifierOption, Parameter, ParameterError, PureRecord, }; @@ -100,6 +100,34 @@ impl PyUVParameters { let binary = Array2::from_shape_fn((n, n), |(_, _)| UVBinaryRecord { k_ij: 0.0 }); Self(Arc::new(UVParameters::from_records(pure_records, binary))) } + + /// Create UV Theory parameters for pure substance. + /// + /// Parameters + /// ---------- + /// rep : float + /// repulsive exponents + /// att : float + /// attractive exponents + /// sigma : float + /// Mie diameter in units of Angstrom + /// epsilon_k : float + /// Mie energy parameter in units of Kelvin + /// + /// Returns + /// ------- + /// UVParameters + /// + /// # Info + /// + /// Molar weight is one. No ideal gas contribution is considered. + #[pyo3(text_signature = "(rep, att, sigma, epsilon_k)")] + #[staticmethod] + fn new_simple(rep: f64, att: f64, sigma: f64, epsilon_k: f64) -> Self { + Self(Arc::new(UVParameters::new_simple( + rep, att, sigma, epsilon_k, + ))) + } } impl_pure_record!(UVRecord, PyUVRecord, NoRecord, PyNoRecord); @@ -112,6 +140,7 @@ pub fn uvtheory(_py: Python<'_>, m: &PyModule) -> PyResult<()> { m.add_class::()?; m.add_class::()?; + m.add_class::()?; m.add_class::()?; m.add_class::()?; m.add_class::()?;