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nist-gov/www.nist.gov/chemical-informatics-research-group/hard-sphere-thermodynamic-and-transport-properties
Scott Williams 4063bef310 Initital commit.
2025-03-05 18:59:57 +00:00

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<h1 class="nist-page__title">Hard Sphere Thermodynamic and Transport Properties</h1>
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<p><strong>BULK-SLIT-HS: properties of the hard-sphere fluid in bulk and confined to a slit pore</strong>&nbsp;<br>
This page gives some results for hard-sphere fluids [1]</p>
<p><strong>Methods:</strong>&nbsp;<br>
Event-driven molecular dynamics (MD) [1] and Transition-matrix Monte Carlo (TMMC) [2, 7-12].</p>
<p><strong>Remarks:</strong>&nbsp;</p>
<p>TMMC data is taken from Refs.[5,6].&nbsp; Data for MD simulations was produced using N=4000 particles. All systems were equilibrated for 1000 reduced time units. Productions runs of time t&gt;100,000 reduced time units were used. Self-diffusivities were calculated from the Einstein relation D_x=dx(t)^2, t-&gt;infinity, were dx(t)^2 is the mean square displacement in direction x. For the bulk self-diffusivity, all three directions where averaged together.&nbsp; For the slit-pore self-diffusivity, only the periodic x and y directions (see schematic below) were averaged together. Mean-squared displacements were measured over times windows exceeding 5000 reduced units, using standard block averaging [1]. No less than 5 independent (different random seeds) were conducted at each state point.&nbsp; This data was averaged to give the mean properties.&nbsp; Errors were estimated by standard methods to yield the 95% confidence intervals.&nbsp; That is, the error was take as T(n)*STD/sqrt(n), where n is the number of independent samples, T is the inverse student's t PDF at 95% level for n samples, and STD is the sample standard deviation of the independent samples.</p>
<p>&nbsp;</p>
<p><strong>Bulk properties:</strong></p>
<table>
<tbody>
<tr>
<td>sigma</td>
<td>particle diameter</td>
</tr>
<tr>
<td>m</td>
<td>particle mass</td>
</tr>
<tr>
<td>beta</td>
<td>inverse temperature</td>
</tr>
<tr>
<td>dens</td>
<td>density (reduced by sigma^3)</td>
</tr>
<tr>
<td>mu</td>
<td>reduced chemical potential</td>
</tr>
<tr>
<td>sx</td>
<td>reduced excess entropy (relative to ideal gas at same temperature and density)</td>
</tr>
<tr>
<td>P_MC</td>
<td>reduced pressure from TMMC simulations</td>
</tr>
<tr>
<td>P_MD</td>
<td>reduced pressure from MD simulations</td>
</tr>
<tr>
<td>D</td>
<td>reduced self-diffusion from MD simulations</td>
</tr>
<tr>
<td>+/-</td>
<td>95% confidence intervals for data in preceding column</td>
</tr>
</tbody>
</table>
<p>&nbsp;</p>
<p><strong>Data:</strong></p>
<p>&nbsp;</p>
<table>
<tbody>
<tr>
<td>dens</td>
<td>mu</td>
<td>sx</td>
<td>P_MC</td>
<td>P_MD</td>
<td>+/-</td>
<td>D</td>
<td>+/-</td>
</tr>
<tr>
<td>0.025</td>
<td>-3.581518</td>
<td>-0.051239</td>
<td>0.026352</td>
<td>0.026346</td>
<td>0.000000</td>
<td>8.338323</td>
<td>0.013053</td>
</tr>
<tr>
<td>0.050</td>
<td>-2.775580</td>
<td>-0.106267</td>
<td>0.055593</td>
<td>0.055582</td>
<td>0.000000</td>
<td>4.064806</td>
<td>0.006030</td>
</tr>
<tr>
<td>0.075</td>
<td>-2.251420</td>
<td>-0.163217</td>
<td>0.088023</td>
<td>0.088005</td>
<td>0.000002</td>
<td>2.640503</td>
<td>0.002924</td>
</tr>
<tr>
<td>0.100</td>
<td>-1.838804</td>
<td>-0.222135</td>
<td>0.123969</td>
<td>0.123942</td>
<td>0.000001</td>
<td>1.934599</td>
<td>0.003292</td>
</tr>
<tr>
<td>0.125</td>
<td>-1.483998</td>
<td>-0.283146</td>
<td>0.163795</td>
<td>0.163756</td>
<td>0.000002</td>
<td>1.513458</td>
<td>0.003706</td>
</tr>
<tr>
<td>0.150</td>
<td>-1.163011</td>
<td>-0.346350</td>
<td>0.207877</td>
<td>0.207845</td>
<td>0.000003</td>
<td>1.232659</td>
<td>0.002354</td>
</tr>
<tr>
<td>0.175</td>
<td>-0.862397</td>
<td>-0.411857</td>
<td>0.256694</td>
<td>0.256646</td>
<td>0.000004</td>
<td>1.033016</td>
<td>0.002243</td>
</tr>
<tr>
<td>0.200</td>
<td>-0.574198</td>
<td>-0.479805</td>
<td>0.310713</td>
<td>0.310649</td>
<td>0.000006</td>
<td>0.885175</td>
<td>0.001139</td>
</tr>
<tr>
<td>0.225</td>
<td>-0.292855</td>
<td>-0.550336</td>
<td>0.370487</td>
<td>0.370398</td>
<td>0.000006</td>
<td>0.770423</td>
<td>0.000901</td>
</tr>
<tr>
<td>0.250</td>
<td>-0.014585</td>
<td>-0.623575</td>
<td>0.436574</td>
<td>0.436478</td>
<td>0.000007</td>
<td>0.679425</td>
<td>0.000883</td>
</tr>
<tr>
<td>0.275</td>
<td>0.263858</td>
<td>-0.699679</td>
<td>0.509668</td>
<td>0.509553</td>
<td>0.000010</td>
<td>0.603851</td>
<td>0.001265</td>
</tr>
<tr>
<td>0.300</td>
<td>0.544764</td>
<td>-0.778802</td>
<td>0.590437</td>
<td>0.590354</td>
<td>0.000007</td>
<td>0.541249</td>
<td>0.000667</td>
</tr>
<tr>
<td>0.325</td>
<td>0.830785</td>
<td>-0.861131</td>
<td>0.679829</td>
<td>0.679687</td>
<td>0.000013</td>
<td>0.487871</td>
<td>0.000904</td>
</tr>
<tr>
<td>0.350</td>
<td>1.123470</td>
<td>-0.946850</td>
<td>0.778627</td>
<td>0.778477</td>
<td>0.000013</td>
<td>0.441960</td>
<td>0.000725</td>
</tr>
<tr>
<td>0.375</td>
<td>1.424630</td>
<td>-1.036160</td>
<td>0.887818</td>
<td>0.887679</td>
<td>0.000020</td>
<td>0.401539</td>
<td>0.000660</td>
</tr>
<tr>
<td>0.400</td>
<td>1.736449</td>
<td>-1.129286</td>
<td>1.008671</td>
<td>1.008452</td>
<td>0.000024</td>
<td>0.365541</td>
<td>0.000291</td>
</tr>
<tr>
<td>0.425</td>
<td>2.060345</td>
<td>-1.226464</td>
<td>1.142305</td>
<td>1.142062</td>
<td>0.000021</td>
<td>0.333621</td>
<td>0.000941</td>
</tr>
<tr>
<td>0.450</td>
<td>2.398216</td>
<td>-1.327947</td>
<td>1.290155</td>
<td>1.289858</td>
<td>0.000031</td>
<td>0.304674</td>
<td>0.000569</td>
</tr>
<tr>
<td>0.475</td>
<td>2.751827</td>
<td>-1.434012</td>
<td>1.453735</td>
<td>1.453388</td>
<td>0.000022</td>
<td>0.278082</td>
<td>0.000337</td>
</tr>
<tr>
<td>0.500</td>
<td>3.122964</td>
<td>-1.544949</td>
<td>1.634702</td>
<td>1.634467</td>
<td>0.000025</td>
<td>0.253873</td>
<td>0.000257</td>
</tr>
<tr>
<td>0.525</td>
<td>3.514262</td>
<td>-1.661079</td>
<td>1.835287</td>
<td>1.834980</td>
<td>0.000039</td>
<td>0.231995</td>
<td>0.000359</td>
</tr>
<tr>
<td>0.550</td>
<td>3.927635</td>
<td>-1.782768</td>
<td>2.057522</td>
<td>2.057119</td>
<td>0.000046</td>
<td>0.211271</td>
<td>0.000357</td>
</tr>
<tr>
<td>0.575</td>
<td>4.364901</td>
<td>-1.910388</td>
<td>2.303534</td>
<td>2.303448</td>
<td>0.000018</td>
<td>0.192091</td>
<td>0.000523</td>
</tr>
<tr>
<td>0.600</td>
<td>4.829816</td>
<td>-2.044331</td>
<td>2.576735</td>
<td>2.576640</td>
<td>0.000031</td>
<td>0.174733</td>
<td>0.000458</td>
</tr>
<tr>
<td>0.625</td>
<td>5.324387</td>
<td>-2.185097</td>
<td>2.879714</td>
<td>2.879972</td>
<td>0.000043</td>
<td>0.157914</td>
<td>0.000271</td>
</tr>
<tr>
<td>0.650</td>
<td>5.853256</td>
<td>-2.333129</td>
<td>3.216951</td>
<td>3.216875</td>
<td>0.000067</td>
<td>0.142569</td>
<td>0.000238</td>
</tr>
<tr>
<td>0.675</td>
<td>6.415393</td>
<td>-2.488999</td>
<td>3.589434</td>
<td>3.591527</td>
<td>0.000046</td>
<td>0.128386</td>
<td>0.000154</td>
</tr>
<tr>
<td>0.700</td>
<td>7.021445</td>
<td>-2.653314</td>
<td>4.006137</td>
<td>4.008462</td>
<td>0.000054</td>
<td>0.114739</td>
<td>0.000185</td>
</tr>
<tr>
<td>0.725</td>
<td>7.676348</td>
<td>-2.826629</td>
<td>4.472914</td>
<td>4.472877</td>
<td>0.000055</td>
<td>0.102400</td>
<td>0.000191</td>
</tr>
<tr>
<td>0.750</td>
<td>8.387102</td>
<td>-3.010079</td>
<td>4.997208</td>
<td>4.990787</td>
<td>0.000025</td>
<td>0.090396</td>
<td>0.000136</td>
</tr>
<tr>
<td>0.775</td>
<td>9.139130</td>
<td>-3.204061</td>
<td>5.570849</td>
<td>5.569115</td>
<td>0.000090</td>
<td>0.079376</td>
<td>0.000099</td>
</tr>
<tr>
<td>0.800</td>
<td>9.951519</td>
<td>-3.409416</td>
<td>6.210771</td>
<td>6.215551</td>
<td>0.000097</td>
<td>0.068904</td>
<td>0.000098</td>
</tr>
<tr>
<td>0.825</td>
<td>10.849336</td>
<td>-3.627195</td>
<td>6.940487</td>
<td>6.939064</td>
<td>0.000099</td>
<td>0.059316</td>
<td>0.000062</td>
</tr>
<tr>
<td>0.850</td>
<td>11.822939</td>
<td>-3.859202</td>
<td>7.755800</td>
<td>7.750263</td>
<td>0.000096</td>
<td>0.050306</td>
<td>0.000035</td>
</tr>
<tr>
<td>0.875</td>
<td>12.868237</td>
<td>-4.105596</td>
<td>8.657578</td>
<td>8.661019</td>
<td>0.000063</td>
<td>0.041938</td>
<td>0.000062</td>
</tr>
<tr>
<td>0.900</td>
<td>14.019667</td>
<td>-4.367802</td>
<td>9.679868</td>
<td>9.685615</td>
<td>0.000120</td>
<td>0.034327</td>
<td>0.000087</td>
</tr>
</tbody>
</table>
<p>&nbsp;</p>
<p><strong>Slit Pore Properties</strong></p>
<p class="text-align-center">&nbsp;</p>
<figure class=" align-left nist-image--lightbox nist-image" role="group">
<div data-lightbox="https://www.nist.gov/sites/default/files/styles/2800_x_2800_limit/public/images/mml/csd/informatics_research/img19_1.gif?itok=gTnYcM00" data-media-id="162806">
<img alt="img19" height="193" loading="lazy" src="/sites/default/files/styles/480_x_480_limit/public/images/mml/csd/informatics_research/img19_1.gif?itok=naMoYTF-" typeof="foaf:Image" width="224">
</div>
<figcaption class="nist-image__caption"></figcaption>
</figure>
<p class="text-align-center">&nbsp;</p>
<p class="text-align-center">&nbsp;</p>
<p class="text-align-center">&nbsp;</p>
<p>&nbsp;</p>
<p>Figure 1: Schematic of slit-pore geometry. Wall separation is given by H, and center accessible separation given by h=H-sigma, where sigma is the particle diameter.</p>
<h2>Data:</h2>
<table>
<tbody>
<tr>
<td>H</td>
<td>Wall separation</td>
</tr>
<tr>
<td>sx_1</td>
<td>Excess entropy relative to an ideal gas with a&nbsp; density profile equivalent to the actual fluid</td>
</tr>
<tr>
<td>sx_2</td>
<td>Excess entropy relative to an ideal gas with a&nbsp; uniform density profile</td>
</tr>
<tr>
<td>P_MC_T</td>
<td>Pore averaged transverse pressure calculated from TMMC&nbsp; simulations [3]</td>
</tr>
<tr>
<td>P_MD_T</td>
<td>Pore averaged transverse pressure calculated&nbsp; from molecular dynamics simulations (see&nbsp; [4])</td>
</tr>
<tr>
<td>P_MD_N</td>
<td>Normal pressure calculated from MD simulations</td>
</tr>
<tr>
<td>P_bulk_mu</td>
<td>Equilibrium pressure of the bulk fluid (that&nbsp; is, the pressure of the bulk fluid at the same value of chemical potential)</td>
</tr>
</tbody>
</table>
<p><br>
Note: NaN implies no data available at that state point.</p>
<p>&nbsp;</p>
<p>&nbsp;</p>
<p>&nbsp;</p>
<table>
<tbody>
<tr>
<td>Gap</td>
<td>dens</td>
<td>mu</td>
<td>sx_1</td>
<td>sx_2</td>
<td>P_MC_T</td>
<td>P_MD_T</td>
<td>+/-</td>
<td>P_MD_N</td>
<td>+/-</td>
<td>D</td>
<td>+/-</td>
</tr>
<tr>
<td>5.0</td>
<td>0.05</td>
<td>-2.523062</td>
<td>-0.119700</td>
<td>-0.120403</td>
<td>0.070428</td>
<td>0.070431</td>
<td>0.000001</td>
<td>0.069591</td>
<td>0.000001</td>
<td>3.610898</td>
<td>0.007756</td>
</tr>
<tr>
<td>5.0</td>
<td>0.10</td>
<td>-1.553323</td>
<td>-0.248980</td>
<td>-0.251914</td>
<td>0.159004</td>
<td>0.159009</td>
<td>0.000002</td>
<td>0.155314</td>
<td>0.000003</td>
<td>1.753338</td>
<td>0.004868</td>
</tr>
<tr>
<td>5.0</td>
<td>0.15</td>
<td>-0.840555</td>
<td>-0.386410</td>
<td>-0.392980</td>
<td>0.269691</td>
<td>0.269691</td>
<td>0.000004</td>
<td>0.260541</td>
<td>0.000008</td>
<td>1.141261</td>
<td>0.002083</td>
</tr>
<tr>
<td>5.0</td>
<td>0.20</td>
<td>-0.210475</td>
<td>-0.532890</td>
<td>-0.544659</td>
<td>0.407286</td>
<td>0.407305</td>
<td>0.000013</td>
<td>0.389342</td>
<td>0.000011</td>
<td>0.834870</td>
<td>0.001844</td>
</tr>
<tr>
<td>5.0</td>
<td>0.25</td>
<td>0.395759</td>
<td>-0.689490</td>
<td>-0.708058</td>
<td>0.577755</td>
<td>0.577737</td>
<td>0.000012</td>
<td>0.546707</td>
<td>0.000011</td>
<td>0.647695</td>
<td>0.001386</td>
</tr>
<tr>
<td>5.0</td>
<td>0.30</td>
<td>1.007739</td>
<td>-0.857400</td>
<td>-0.884671</td>
<td>0.788214</td>
<td>0.788213</td>
<td>0.000017</td>
<td>0.738646</td>
<td>0.000019</td>
<td>0.521783</td>
<td>0.002015</td>
</tr>
<tr>
<td>5.0</td>
<td>0.35</td>
<td>1.645818</td>
<td>-1.037980</td>
<td>-1.075913</td>
<td>1.047615</td>
<td>1.047615</td>
<td>0.000018</td>
<td>0.972547</td>
<td>0.000013</td>
<td>0.427086</td>
<td>0.001786</td>
</tr>
<tr>
<td>5.0</td>
<td>0.40</td>
<td>2.326486</td>
<td>-1.232900</td>
<td>-1.283756</td>
<td>1.366941</td>
<td>1.367078</td>
<td>0.000031</td>
<td>1.257604</td>
<td>0.000045</td>
<td>0.353118</td>
<td>0.000642</td>
</tr>
<tr>
<td>5.0</td>
<td>0.45</td>
<td>3.066765</td>
<td>-1.443920</td>
<td>-1.510175</td>
<td>1.760569</td>
<td>1.760472</td>
<td>0.000041</td>
<td>1.605749</td>
<td>0.000037</td>
<td>0.292893</td>
<td>0.000731</td>
</tr>
<tr>
<td>5.0</td>
<td>0.50</td>
<td>3.880649</td>
<td>-1.673040</td>
<td>-1.757686</td>
<td>2.244242</td>
<td>2.244863</td>
<td>0.000031</td>
<td>2.032641</td>
<td>0.000047</td>
<td>0.242393</td>
<td>0.000643</td>
</tr>
<tr>
<td>5.0</td>
<td>0.55</td>
<td>4.787536</td>
<td>-1.921920</td>
<td>-2.029168</td>
<td>2.839891</td>
<td>2.840505</td>
<td>0.000025</td>
<td>2.558410</td>
<td>0.000044</td>
<td>0.198315</td>
<td>0.000530</td>
</tr>
<tr>
<td>5.0</td>
<td>0.60</td>
<td>5.803869</td>
<td>-2.191380</td>
<td>-2.327745</td>
<td>3.571009</td>
<td>3.570998</td>
<td>0.000087</td>
<td>3.206249</td>
<td>0.000090</td>
<td>0.161360</td>
<td>0.000294</td>
</tr>
<tr>
<td>5.0</td>
<td>0.65</td>
<td>6.946580</td>
<td>-2.482570</td>
<td>-2.656698</td>
<td>4.464488</td>
<td>4.464864</td>
<td>0.000084</td>
<td>3.997596</td>
<td>0.000074</td>
<td>0.128925</td>
<td>0.000389</td>
</tr>
<tr>
<td>5.0</td>
<td>0.70</td>
<td>8.248008</td>
<td>-2.797450</td>
<td>-3.019913</td>
<td>5.563606</td>
<td>5.562612</td>
<td>0.000069</td>
<td>4.945632</td>
<td>0.000111</td>
<td>0.100538</td>
<td>0.000249</td>
</tr>
<tr>
<td>5.0</td>
<td>0.75</td>
<td>9.762154</td>
<td>-3.140440</td>
<td>-3.423620</td>
<td>6.937112</td>
<td>6.929774</td>
<td>0.000086</td>
<td>6.054381</td>
<td>0.000110</td>
<td>0.075243</td>
<td>0.000242</td>
</tr>
<tr>
<td>5.0</td>
<td>0.80</td>
<td>11.549069</td>
<td>-3.523940</td>
<td>-3.875160</td>
<td>8.670022</td>
<td>8.677227</td>
<td>0.000050</td>
<td>7.328106</td>
<td>0.000186</td>
<td>0.053136</td>
<td>0.000215</td>
</tr>
<tr>
<td>5.0</td>
<td>0.85</td>
<td>13.741602</td>
<td>-3.963690</td>
<td>-4.386488</td>
<td>10.932307</td>
<td>10.980952</td>
<td>0.000126</td>
<td>8.796609</td>
<td>0.000246</td>
<td>0.034185</td>
<td>0.000193</td>
</tr>
<tr>
<td>5.0</td>
<td>0.90</td>
<td>14.389045</td>
<td>NaN</td>
<td>NaN</td>
<td>11.632706</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
</tr>
<tr>
<td>6.0</td>
<td>0.05</td>
<td>-2.568841</td>
<td>-0.117344</td>
<td>-0.117599</td>
<td>0.067465</td>
<td>0.067459</td>
<td>0.000001</td>
<td>0.066836</td>
<td>0.000002</td>
<td>3.682524</td>
<td>0.007993</td>
</tr>
<tr>
<td>6.0</td>
<td>0.10</td>
<td>-1.604890</td>
<td>-0.244385</td>
<td>-0.246502</td>
<td>0.151978</td>
<td>0.151978</td>
<td>0.000004</td>
<td>0.149227</td>
<td>0.000003</td>
<td>1.778212</td>
<td>0.003673</td>
</tr>
<tr>
<td>6.0</td>
<td>0.15</td>
<td>-0.898488</td>
<td>-0.379640</td>
<td>-0.384710</td>
<td>0.257277</td>
<td>0.257272</td>
<td>0.000005</td>
<td>0.250429</td>
<td>0.000005</td>
<td>1.151070</td>
<td>0.002664</td>
</tr>
<tr>
<td>6.0</td>
<td>0.20</td>
<td>-0.275511</td>
<td>-0.523986</td>
<td>-0.533262</td>
<td>0.387872</td>
<td>0.387877</td>
<td>0.000008</td>
<td>0.374401</td>
<td>0.000005</td>
<td>0.838072</td>
<td>0.002677</td>
</tr>
<tr>
<td>6.0</td>
<td>0.25</td>
<td>0.322632</td>
<td>-0.678540</td>
<td>-0.693338</td>
<td>0.549337</td>
<td>0.549312</td>
<td>0.000014</td>
<td>0.525959</td>
<td>0.000013</td>
<td>0.649536</td>
<td>0.001188</td>
</tr>
<tr>
<td>6.0</td>
<td>0.30</td>
<td>0.925286</td>
<td>-0.844455</td>
<td>-0.866247</td>
<td>0.748289</td>
<td>0.748349</td>
<td>0.000012</td>
<td>0.710990</td>
<td>0.000012</td>
<td>0.522184</td>
<td>0.000409</td>
</tr>
<tr>
<td>6.0</td>
<td>0.35</td>
<td>1.553131</td>
<td>-1.023098</td>
<td>-1.053504</td>
<td>0.993313</td>
<td>0.993324</td>
<td>0.000015</td>
<td>0.936694</td>
<td>0.000016</td>
<td>0.427201</td>
<td>0.000716</td>
</tr>
<tr>
<td>6.0</td>
<td>0.40</td>
<td>2.222081</td>
<td>-1.216020</td>
<td>-1.256905</td>
<td>1.294582</td>
<td>1.294602</td>
<td>0.000031</td>
<td>1.211977</td>
<td>0.000027</td>
<td>0.352609</td>
<td>0.000968</td>
</tr>
<tr>
<td>6.0</td>
<td>0.45</td>
<td>2.947651</td>
<td>-1.424940</td>
<td>-1.478443</td>
<td>1.664952</td>
<td>1.665002</td>
<td>0.000026</td>
<td>1.547889</td>
<td>0.000060</td>
<td>0.293025</td>
<td>0.000418</td>
</tr>
<tr>
<td>6.0</td>
<td>0.50</td>
<td>3.746670</td>
<td>-1.651940</td>
<td>-1.720599</td>
<td>2.120819</td>
<td>2.120647</td>
<td>0.000066</td>
<td>1.958587</td>
<td>0.000050</td>
<td>0.242476</td>
<td>0.000884</td>
</tr>
<tr>
<td>6.0</td>
<td>0.55</td>
<td>4.635354</td>
<td>-1.899227</td>
<td>-1.986161</td>
<td>2.681191</td>
<td>2.681461</td>
<td>0.000057</td>
<td>2.462137</td>
<td>0.000028</td>
<td>0.199669</td>
<td>0.000649</td>
</tr>
<tr>
<td>6.0</td>
<td>0.60</td>
<td>5.633863</td>
<td>-2.168980</td>
<td>-2.278240</td>
<td>3.370760</td>
<td>3.371777</td>
<td>0.000097</td>
<td>3.081307</td>
<td>0.000071</td>
<td>0.162678</td>
<td>0.000824</td>
</tr>
<tr>
<td>6.0</td>
<td>0.65</td>
<td>6.767947</td>
<td>-2.463380</td>
<td>-2.600943</td>
<td>4.222075</td>
<td>4.221458</td>
<td>0.000048</td>
<td>3.841814</td>
<td>0.000077</td>
<td>0.130251</td>
<td>0.000312</td>
</tr>
<tr>
<td>6.0</td>
<td>0.70</td>
<td>8.059413</td>
<td>-2.784407</td>
<td>-2.958180</td>
<td>5.269135</td>
<td>5.269621</td>
<td>0.000077</td>
<td>4.768928</td>
<td>0.000091</td>
<td>0.101980</td>
<td>0.000262</td>
</tr>
<tr>
<td>6.0</td>
<td>0.75</td>
<td>9.559559</td>
<td>-3.136967</td>
<td>-3.355418</td>
<td>6.575715</td>
<td>6.574329</td>
<td>0.000096</td>
<td>5.886106</td>
<td>0.000108</td>
<td>0.077113</td>
<td>0.000336</td>
</tr>
<tr>
<td>6.0</td>
<td>0.80</td>
<td>11.330729</td>
<td>-3.530512</td>
<td>-3.800528</td>
<td>8.224443</td>
<td>8.227210</td>
<td>0.000123</td>
<td>7.226547</td>
<td>0.000163</td>
<td>0.055667</td>
<td>0.000154</td>
</tr>
<tr>
<td>6.0</td>
<td>0.85</td>
<td>13.500937</td>
<td>-3.981122</td>
<td>-4.304579</td>
<td>10.375289</td>
<td>10.365951</td>
<td>0.000130</td>
<td>8.876845</td>
<td>0.000432</td>
<td>0.037010</td>
<td>0.000108</td>
</tr>
<tr>
<td>6.0</td>
<td>0.90</td>
<td>16.505228</td>
<td>-4.504592</td>
<td>NaN</td>
<td>13.642548</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
</tr>
<tr>
<td>7.0</td>
<td>0.05</td>
<td>-2.600641</td>
<td>-0.115640</td>
<td>-0.115939</td>
<td>0.065478</td>
<td>0.065479</td>
<td>0.000001</td>
<td>0.064986</td>
<td>0.000001</td>
<td>3.729969</td>
<td>0.011858</td>
</tr>
<tr>
<td>7.0</td>
<td>0.10</td>
<td>-1.640697</td>
<td>-0.241170</td>
<td>-0.242925</td>
<td>0.147292</td>
<td>0.147295</td>
<td>0.000001</td>
<td>0.145114</td>
<td>0.000004</td>
<td>1.796364</td>
<td>0.003717</td>
</tr>
<tr>
<td>7.0</td>
<td>0.15</td>
<td>-0.938752</td>
<td>-0.374691</td>
<td>-0.379067</td>
<td>0.249013</td>
<td>0.249004</td>
<td>0.000004</td>
<td>0.243568</td>
<td>0.000005</td>
<td>1.160307</td>
<td>0.001509</td>
</tr>
<tr>
<td>7.0</td>
<td>0.20</td>
<td>-0.320857</td>
<td>-0.517648</td>
<td>-0.525380</td>
<td>0.374943</td>
<td>0.374942</td>
<td>0.000006</td>
<td>0.364213</td>
<td>0.000010</td>
<td>0.842751</td>
<td>0.001596</td>
</tr>
<tr>
<td>7.0</td>
<td>0.25</td>
<td>0.271487</td>
<td>-0.670559</td>
<td>-0.683001</td>
<td>0.530397</td>
<td>0.530389</td>
<td>0.000018</td>
<td>0.511760</td>
<td>0.000018</td>
<td>0.650426</td>
<td>0.001899</td>
</tr>
<tr>
<td>7.0</td>
<td>0.30</td>
<td>0.868022</td>
<td>-0.835136</td>
<td>-0.853305</td>
<td>0.721861</td>
<td>0.721848</td>
<td>0.000013</td>
<td>0.691981</td>
<td>0.000026</td>
<td>0.520877</td>
<td>0.001007</td>
</tr>
<tr>
<td>7.0</td>
<td>0.35</td>
<td>1.488327</td>
<td>-1.012263</td>
<td>-1.037794</td>
<td>0.957212</td>
<td>0.957270</td>
<td>0.000013</td>
<td>0.911912</td>
<td>0.000025</td>
<td>0.427374</td>
<td>0.000729</td>
</tr>
<tr>
<td>7.0</td>
<td>0.40</td>
<td>2.149188</td>
<td>-1.203859</td>
<td>-1.238073</td>
<td>1.246569</td>
<td>1.246517</td>
<td>0.000043</td>
<td>1.180310</td>
<td>0.000042</td>
<td>0.352527</td>
<td>0.001370</td>
</tr>
<tr>
<td>7.0</td>
<td>0.45</td>
<td>2.864824</td>
<td>-1.411375</td>
<td>-1.456240</td>
<td>1.601708</td>
<td>1.601907</td>
<td>0.000029</td>
<td>1.507977</td>
<td>0.000034</td>
<td>0.292858</td>
<td>0.000549</td>
</tr>
<tr>
<td>7.0</td>
<td>0.50</td>
<td>3.652093</td>
<td>-1.637099</td>
<td>-1.694615</td>
<td>2.038370</td>
<td>2.038643</td>
<td>0.000032</td>
<td>1.908438</td>
<td>0.000043</td>
<td>0.243090</td>
<td>0.000211</td>
</tr>
<tr>
<td>7.0</td>
<td>0.55</td>
<td>4.529029</td>
<td>-1.883148</td>
<td>-1.956063</td>
<td>2.575975</td>
<td>2.576109</td>
<td>0.000057</td>
<td>2.398874</td>
<td>0.000052</td>
<td>0.200323</td>
<td>0.000245</td>
</tr>
<tr>
<td>7.0</td>
<td>0.60</td>
<td>5.513861</td>
<td>-2.152178</td>
<td>-2.243575</td>
<td>3.237230</td>
<td>3.238169</td>
<td>0.000096</td>
<td>3.000984</td>
<td>0.000073</td>
<td>0.163185</td>
<td>0.000391</td>
</tr>
<tr>
<td>7.0</td>
<td>0.65</td>
<td>6.632302</td>
<td>-2.446995</td>
<td>-2.561300</td>
<td>4.053477</td>
<td>4.054812</td>
<td>0.000048</td>
<td>3.741582</td>
<td>0.000063</td>
<td>0.131379</td>
<td>0.000405</td>
</tr>
<tr>
<td>7.0</td>
<td>0.70</td>
<td>7.912163</td>
<td>-2.769997</td>
<td>-2.913233</td>
<td>5.062123</td>
<td>5.064299</td>
<td>0.000067</td>
<td>4.651018</td>
<td>0.000099</td>
<td>0.103401</td>
<td>0.000315</td>
</tr>
<tr>
<td>7.0</td>
<td>0.75</td>
<td>9.391189</td>
<td>-3.127170</td>
<td>-3.305240</td>
<td>6.314396</td>
<td>6.319617</td>
<td>0.000074</td>
<td>5.763342</td>
<td>0.000131</td>
<td>0.078844</td>
<td>0.000277</td>
</tr>
<tr>
<td>7.0</td>
<td>0.80</td>
<td>11.149337</td>
<td>-3.523552</td>
<td>-3.744325</td>
<td>7.905501</td>
<td>7.897676</td>
<td>0.000121</td>
<td>7.126259</td>
<td>0.000161</td>
<td>0.057480</td>
<td>0.000170</td>
</tr>
<tr>
<td>7.0</td>
<td>0.85</td>
<td>13.224048</td>
<td>-3.972839</td>
<td>-4.240474</td>
<td>9.904432</td>
<td>9.901127</td>
<td>0.000192</td>
<td>8.840516</td>
<td>0.000239</td>
<td>0.039114</td>
<td>0.000097</td>
</tr>
<tr>
<td>7.0</td>
<td>0.90</td>
<td>15.630033</td>
<td>-4.476738</td>
<td>NaN</td>
<td>12.361201</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
</tr>
<tr>
<td>7.5</td>
<td>0.05</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>0.064716</td>
<td>0.000001</td>
<td>0.064272</td>
<td>0.000001</td>
<td>3.749998</td>
<td>0.007295</td>
</tr>
<tr>
<td>7.5</td>
<td>0.10</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>0.145493</td>
<td>0.000004</td>
<td>0.143522</td>
<td>0.000004</td>
<td>1.804281</td>
<td>0.004415</td>
</tr>
<tr>
<td>7.5</td>
<td>0.15</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>0.245823</td>
<td>0.000006</td>
<td>0.240898</td>
<td>0.000005</td>
<td>1.161573</td>
<td>0.001582</td>
</tr>
<tr>
<td>7.5</td>
<td>0.20</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>0.369979</td>
<td>0.000006</td>
<td>0.360250</td>
<td>0.000006</td>
<td>0.844042</td>
<td>0.001627</td>
</tr>
<tr>
<td>7.5</td>
<td>0.25</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>0.523128</td>
<td>0.000013</td>
<td>0.506226</td>
<td>0.000010</td>
<td>0.652081</td>
<td>0.001642</td>
</tr>
<tr>
<td>7.5</td>
<td>0.30</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>0.711673</td>
<td>0.000020</td>
<td>0.684551</td>
<td>0.000017</td>
<td>0.522322</td>
<td>0.001894</td>
</tr>
<tr>
<td>7.5</td>
<td>0.35</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>0.943429</td>
<td>0.000028</td>
<td>0.902224</td>
<td>0.000035</td>
<td>0.427207</td>
<td>0.001074</td>
</tr>
<tr>
<td>7.5</td>
<td>0.40</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>1.228091</td>
<td>0.000032</td>
<td>1.167894</td>
<td>0.000048</td>
<td>0.353778</td>
<td>0.001053</td>
</tr>
<tr>
<td>7.5</td>
<td>0.45</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>1.577673</td>
<td>0.000038</td>
<td>1.492294</td>
<td>0.000029</td>
<td>0.293238</td>
<td>0.000931</td>
</tr>
<tr>
<td>7.5</td>
<td>0.50</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>2.007224</td>
<td>0.000022</td>
<td>1.888848</td>
<td>0.000059</td>
<td>0.243392</td>
<td>0.000585</td>
</tr>
<tr>
<td>7.5</td>
<td>0.55</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>2.535604</td>
<td>0.000075</td>
<td>2.374142</td>
<td>0.000063</td>
<td>0.200860</td>
<td>0.000535</td>
</tr>
<tr>
<td>7.5</td>
<td>0.60</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>3.186788</td>
<td>0.000093</td>
<td>2.969176</td>
<td>0.000075</td>
<td>0.164173</td>
<td>0.000511</td>
</tr>
<tr>
<td>7.5</td>
<td>0.65</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>3.991370</td>
<td>0.000096</td>
<td>3.700630</td>
<td>0.000094</td>
<td>0.131882</td>
<td>0.000266</td>
</tr>
<tr>
<td>7.5</td>
<td>0.70</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>4.988454</td>
<td>0.000075</td>
<td>4.605141</td>
<td>0.000119</td>
<td>0.104081</td>
<td>0.000171</td>
</tr>
<tr>
<td>7.5</td>
<td>0.75</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>6.224015</td>
<td>0.000092</td>
<td>5.731521</td>
<td>0.000089</td>
<td>0.079456</td>
<td>0.000155</td>
</tr>
<tr>
<td>7.5</td>
<td>0.80</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>7.749119</td>
<td>0.000062</td>
<td>7.135838</td>
<td>0.000124</td>
<td>0.058210</td>
<td>0.000159</td>
</tr>
<tr>
<td>7.5</td>
<td>0.85</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>9.622471</td>
<td>0.000150</td>
<td>8.848316</td>
<td>0.000234</td>
<td>0.039923</td>
<td>0.000186</td>
</tr>
<tr>
<td>8.0</td>
<td>0.05</td>
<td>-2.624020</td>
<td>-0.114500</td>
<td>-0.114905</td>
<td>0.064061</td>
<td>0.064064</td>
<td>0.000001</td>
<td>0.063658</td>
<td>0.000000</td>
<td>3.770250</td>
<td>0.006176</td>
</tr>
<tr>
<td>8.0</td>
<td>0.10</td>
<td>-1.666879</td>
<td>-0.238670</td>
<td>-0.240384</td>
<td>0.143965</td>
<td>0.143952</td>
<td>0.000002</td>
<td>0.142151</td>
<td>0.000002</td>
<td>1.812298</td>
<td>0.002364</td>
</tr>
<tr>
<td>8.0</td>
<td>0.15</td>
<td>-0.968441</td>
<td>-0.371160</td>
<td>-0.374984</td>
<td>0.243109</td>
<td>0.243107</td>
<td>0.000002</td>
<td>0.238610</td>
<td>0.000008</td>
<td>1.166124</td>
<td>0.002646</td>
</tr>
<tr>
<td>8.0</td>
<td>0.20</td>
<td>-0.354264</td>
<td>-0.512830</td>
<td>-0.519630</td>
<td>0.365721</td>
<td>0.365719</td>
<td>0.000007</td>
<td>0.356830</td>
<td>0.000008</td>
<td>0.845826</td>
<td>0.001143</td>
</tr>
<tr>
<td>8.0</td>
<td>0.25</td>
<td>0.233732</td>
<td>-0.664730</td>
<td>-0.675495</td>
<td>0.516880</td>
<td>0.516907</td>
<td>0.000008</td>
<td>0.501450</td>
<td>0.000016</td>
<td>0.651550</td>
<td>0.001909</td>
</tr>
<tr>
<td>8.0</td>
<td>0.30</td>
<td>0.825575</td>
<td>-0.828070</td>
<td>-0.843801</td>
<td>0.702955</td>
<td>0.702954</td>
<td>0.000012</td>
<td>0.678140</td>
<td>0.000023</td>
<td>0.523422</td>
<td>0.001404</td>
</tr>
<tr>
<td>8.0</td>
<td>0.35</td>
<td>1.440646</td>
<td>-1.004180</td>
<td>-1.026054</td>
<td>0.931564</td>
<td>0.931554</td>
<td>0.000023</td>
<td>0.893824</td>
<td>0.000031</td>
<td>0.427972</td>
<td>0.000715</td>
</tr>
<tr>
<td>8.0</td>
<td>0.40</td>
<td>2.095303</td>
<td>-1.194660</td>
<td>-1.224117</td>
<td>1.212357</td>
<td>1.212268</td>
<td>0.000017</td>
<td>1.157127</td>
<td>0.000029</td>
<td>0.353869</td>
<td>0.000868</td>
</tr>
<tr>
<td>8.0</td>
<td>0.45</td>
<td>2.804028</td>
<td>-1.401210</td>
<td>-1.439753</td>
<td>1.556898</td>
<td>1.556956</td>
<td>0.000036</td>
<td>1.478688</td>
<td>0.000024</td>
<td>0.293908</td>
<td>0.000649</td>
</tr>
<tr>
<td>8.0</td>
<td>0.50</td>
<td>3.583470</td>
<td>-1.625860</td>
<td>-1.675363</td>
<td>1.980404</td>
<td>1.980399</td>
<td>0.000051</td>
<td>1.871762</td>
<td>0.000048</td>
<td>0.243357</td>
<td>0.000803</td>
</tr>
<tr>
<td>8.0</td>
<td>0.55</td>
<td>4.450287</td>
<td>-1.871010</td>
<td>-1.933741</td>
<td>2.500947</td>
<td>2.501251</td>
<td>0.000047</td>
<td>2.353129</td>
<td>0.000059</td>
<td>0.201529</td>
<td>0.000339</td>
</tr>
<tr>
<td>8.0</td>
<td>0.60</td>
<td>5.425181</td>
<td>-2.139340</td>
<td>-2.217999</td>
<td>3.142140</td>
<td>3.142835</td>
<td>0.000070</td>
<td>2.943826</td>
<td>0.000111</td>
<td>0.164520</td>
<td>0.000314</td>
</tr>
<tr>
<td>8.0</td>
<td>0.65</td>
<td>6.531029</td>
<td>-2.433780</td>
<td>-2.531823</td>
<td>3.932751</td>
<td>3.934696</td>
<td>0.000044</td>
<td>3.670595</td>
<td>0.000108</td>
<td>0.132660</td>
<td>0.000258</td>
</tr>
<tr>
<td>8.0</td>
<td>0.70</td>
<td>7.804626</td>
<td>-2.758190</td>
<td>-2.880261</td>
<td>4.916097</td>
<td>4.914320</td>
<td>0.000062</td>
<td>4.565729</td>
<td>0.000112</td>
<td>0.104754</td>
<td>0.000187</td>
</tr>
<tr>
<td>8.0</td>
<td>0.75</td>
<td>9.269163</td>
<td>-3.116060</td>
<td>-3.268262</td>
<td>6.130574</td>
<td>6.131574</td>
<td>0.000106</td>
<td>5.667944</td>
<td>0.000109</td>
<td>0.080081</td>
<td>0.000204</td>
</tr>
<tr>
<td>8.0</td>
<td>0.80</td>
<td>10.987243</td>
<td>-3.513730</td>
<td>-3.702052</td>
<td>7.653868</td>
<td>7.654425</td>
<td>0.000155</td>
<td>7.030824</td>
<td>0.000082</td>
<td>0.058794</td>
<td>0.000219</td>
</tr>
<tr>
<td>8.0</td>
<td>0.85</td>
<td>13.000985</td>
<td>-3.959060</td>
<td>-4.191299</td>
<td>9.553840</td>
<td>9.565989</td>
<td>0.000169</td>
<td>8.748016</td>
<td>0.000313</td>
<td>0.040538</td>
<td>0.000121</td>
</tr>
<tr>
<td>8.0</td>
<td>0.90</td>
<td>15.385838</td>
<td>-4.447830</td>
<td>NaN</td>
<td>11.940553</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
</tr>
<tr>
<td>9.0</td>
<td>0.05</td>
<td>-2.641729</td>
<td>-0.113442</td>
<td>-0.113423</td>
<td>0.063006</td>
<td>0.063003</td>
<td>0.000001</td>
<td>0.062658</td>
<td>0.000001</td>
<td>3.800816</td>
<td>0.006367</td>
</tr>
<tr>
<td>9.0</td>
<td>0.10</td>
<td>-1.687112</td>
<td>-0.236785</td>
<td>-0.237875</td>
<td>0.141449</td>
<td>0.141444</td>
<td>0.000004</td>
<td>0.139914</td>
<td>0.000003</td>
<td>1.823410</td>
<td>0.003640</td>
</tr>
<tr>
<td>9.0</td>
<td>0.15</td>
<td>-0.991100</td>
<td>-0.368236</td>
<td>-0.371362</td>
<td>0.238700</td>
<td>0.238684</td>
<td>0.000003</td>
<td>0.234857</td>
<td>0.000007</td>
<td>1.172099</td>
<td>0.002518</td>
</tr>
<tr>
<td>9.0</td>
<td>0.20</td>
<td>-0.379936</td>
<td>-0.509107</td>
<td>-0.514776</td>
<td>0.358804</td>
<td>0.358804</td>
<td>0.000008</td>
<td>0.351236</td>
<td>0.000009</td>
<td>0.848748</td>
<td>0.002412</td>
</tr>
<tr>
<td>9.0</td>
<td>0.25</td>
<td>0.205031</td>
<td>-0.660059</td>
<td>-0.669248</td>
<td>0.506834</td>
<td>0.506806</td>
<td>0.000007</td>
<td>0.493621</td>
<td>0.000015</td>
<td>0.654682</td>
<td>0.002184</td>
</tr>
<tr>
<td>9.0</td>
<td>0.30</td>
<td>0.793081</td>
<td>-0.822592</td>
<td>-0.836132</td>
<td>0.688830</td>
<td>0.688800</td>
<td>0.000010</td>
<td>0.667606</td>
<td>0.000029</td>
<td>0.524030</td>
<td>0.000874</td>
</tr>
<tr>
<td>9.0</td>
<td>0.35</td>
<td>1.403831</td>
<td>-0.997799</td>
<td>-1.016817</td>
<td>0.912281</td>
<td>0.912319</td>
<td>0.000023</td>
<td>0.880052</td>
<td>0.000033</td>
<td>0.428553</td>
<td>0.000666</td>
</tr>
<tr>
<td>9.0</td>
<td>0.40</td>
<td>2.053439</td>
<td>-1.187455</td>
<td>-1.213037</td>
<td>1.186552</td>
<td>1.186646</td>
<td>0.000013</td>
<td>1.139461</td>
<td>0.000038</td>
<td>0.354097</td>
<td>0.000679</td>
</tr>
<tr>
<td>9.0</td>
<td>0.45</td>
<td>2.757311</td>
<td>-1.393174</td>
<td>-1.426736</td>
<td>1.523381</td>
<td>1.523347</td>
<td>0.000021</td>
<td>1.456305</td>
<td>0.000035</td>
<td>0.294409</td>
<td>0.000642</td>
</tr>
<tr>
<td>9.0</td>
<td>0.50</td>
<td>3.530144</td>
<td>-1.617063</td>
<td>-1.660279</td>
<td>1.936732</td>
<td>1.936880</td>
<td>0.000028</td>
<td>1.843732</td>
<td>0.000028</td>
<td>0.244614</td>
<td>0.000428</td>
</tr>
<tr>
<td>9.0</td>
<td>0.55</td>
<td>4.390853</td>
<td>-1.861504</td>
<td>-1.916330</td>
<td>2.445541</td>
<td>2.445263</td>
<td>0.000046</td>
<td>2.318197</td>
<td>0.000064</td>
<td>0.202047</td>
<td>0.000255</td>
</tr>
<tr>
<td>9.0</td>
<td>0.60</td>
<td>5.358016</td>
<td>-2.129296</td>
<td>-2.198093</td>
<td>3.071731</td>
<td>3.071491</td>
<td>0.000060</td>
<td>2.900525</td>
<td>0.000064</td>
<td>0.165315</td>
<td>0.000403</td>
</tr>
<tr>
<td>9.0</td>
<td>0.65</td>
<td>6.454986</td>
<td>-2.423515</td>
<td>-2.509107</td>
<td>3.843736</td>
<td>3.844430</td>
<td>0.000070</td>
<td>3.616991</td>
<td>0.000057</td>
<td>0.133591</td>
<td>0.000196</td>
</tr>
<tr>
<td>9.0</td>
<td>0.70</td>
<td>7.712832</td>
<td>-2.747473</td>
<td>-2.854180</td>
<td>4.799765</td>
<td>4.800968</td>
<td>0.000112</td>
<td>4.500636</td>
<td>0.000043</td>
<td>0.105709</td>
<td>0.000255</td>
</tr>
<tr>
<td>9.0</td>
<td>0.75</td>
<td>9.168933</td>
<td>-3.106304</td>
<td>-3.238723</td>
<td>5.988516</td>
<td>5.988933</td>
<td>0.000111</td>
<td>5.592164</td>
<td>0.000123</td>
<td>0.081220</td>
<td>0.000180</td>
</tr>
<tr>
<td>9.0</td>
<td>0.80</td>
<td>10.874549</td>
<td>-3.503939</td>
<td>-3.668175</td>
<td>7.477441</td>
<td>7.471133</td>
<td>0.000067</td>
<td>6.946346</td>
<td>0.000108</td>
<td>0.060102</td>
<td>0.000165</td>
</tr>
<tr>
<td>9.0</td>
<td>0.85</td>
<td>12.862319</td>
<td>-3.946623</td>
<td>-4.151619</td>
<td>9.324232</td>
<td>9.323168</td>
<td>0.000057</td>
<td>8.647043</td>
<td>0.000262</td>
<td>0.041693</td>
<td>0.000096</td>
</tr>
<tr>
<td>9.0</td>
<td>0.90</td>
<td>15.158590</td>
<td>-4.429011</td>
<td>NaN</td>
<td>11.585506</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
</tr>
<tr>
<td>10.0</td>
<td>0.05</td>
<td>-2.655929</td>
<td>-0.112760</td>
<td>-0.113116</td>
<td>0.062175</td>
<td>0.062179</td>
<td>0.000001</td>
<td>0.061880</td>
<td>0.000001</td>
<td>3.828065</td>
<td>0.008916</td>
</tr>
<tr>
<td>10.0</td>
<td>0.10</td>
<td>-1.702996</td>
<td>-0.235300</td>
<td>-0.236657</td>
<td>0.139501</td>
<td>0.139498</td>
<td>0.000003</td>
<td>0.138168</td>
<td>0.000003</td>
<td>1.834671</td>
<td>0.004733</td>
</tr>
<tr>
<td>10.0</td>
<td>0.15</td>
<td>-1.009155</td>
<td>-0.366100</td>
<td>-0.369087</td>
<td>0.235254</td>
<td>0.235248</td>
<td>0.000004</td>
<td>0.231917</td>
<td>0.000008</td>
<td>1.177262</td>
<td>0.003609</td>
</tr>
<tr>
<td>10.0</td>
<td>0.20</td>
<td>-0.400188</td>
<td>-0.506140</td>
<td>-0.511435</td>
<td>0.353445</td>
<td>0.353438</td>
<td>0.000005</td>
<td>0.346848</td>
<td>0.000005</td>
<td>0.850134</td>
<td>0.002086</td>
</tr>
<tr>
<td>10.0</td>
<td>0.25</td>
<td>0.182100</td>
<td>-0.656430</td>
<td>-0.664817</td>
<td>0.498973</td>
<td>0.498963</td>
<td>0.000018</td>
<td>0.487474</td>
<td>0.000013</td>
<td>0.655563</td>
<td>0.001497</td>
</tr>
<tr>
<td>10.0</td>
<td>0.30</td>
<td>0.767246</td>
<td>-0.818180</td>
<td>-0.830457</td>
<td>0.677832</td>
<td>0.677806</td>
<td>0.000018</td>
<td>0.659342</td>
<td>0.000012</td>
<td>0.525334</td>
<td>0.000744</td>
</tr>
<tr>
<td>10.0</td>
<td>0.35</td>
<td>1.374626</td>
<td>-0.992750</td>
<td>-1.009819</td>
<td>0.897308</td>
<td>0.897357</td>
<td>0.000017</td>
<td>0.869223</td>
<td>0.000017</td>
<td>0.429175</td>
<td>0.000592</td>
</tr>
<tr>
<td>10.0</td>
<td>0.40</td>
<td>2.020643</td>
<td>-1.181660</td>
<td>-1.204601</td>
<td>1.166692</td>
<td>1.166719</td>
<td>0.000023</td>
<td>1.125537</td>
<td>0.000027</td>
<td>0.354984</td>
<td>0.000341</td>
</tr>
<tr>
<td>10.0</td>
<td>0.45</td>
<td>2.720036</td>
<td>-1.386730</td>
<td>-1.416804</td>
<td>1.497243</td>
<td>1.497264</td>
<td>0.000022</td>
<td>1.438690</td>
<td>0.000048</td>
<td>0.295404</td>
<td>0.000475</td>
</tr>
<tr>
<td>10.0</td>
<td>0.50</td>
<td>3.488151</td>
<td>-1.609940</td>
<td>-1.648616</td>
<td>1.903006</td>
<td>1.903022</td>
<td>0.000038</td>
<td>1.821591</td>
<td>0.000059</td>
<td>0.245625</td>
<td>0.000558</td>
</tr>
<tr>
<td>10.0</td>
<td>0.55</td>
<td>4.342587</td>
<td>-1.853810</td>
<td>-1.902708</td>
<td>2.401861</td>
<td>2.401853</td>
<td>0.000031</td>
<td>2.290708</td>
<td>0.000056</td>
<td>0.203296</td>
<td>0.000567</td>
</tr>
<tr>
<td>10.0</td>
<td>0.60</td>
<td>5.302675</td>
<td>-2.120990</td>
<td>-2.182286</td>
<td>3.015806</td>
<td>3.016096</td>
<td>0.000075</td>
<td>2.866433</td>
<td>0.000077</td>
<td>0.166396</td>
<td>0.000239</td>
</tr>
<tr>
<td>10.0</td>
<td>0.65</td>
<td>6.392146</td>
<td>-2.414780</td>
<td>-2.491118</td>
<td>3.773039</td>
<td>3.774290</td>
<td>0.000033</td>
<td>3.574953</td>
<td>0.000038</td>
<td>0.134562</td>
<td>0.000186</td>
</tr>
<tr>
<td>10.0</td>
<td>0.70</td>
<td>7.641344</td>
<td>-2.738850</td>
<td>-2.833660</td>
<td>4.710694</td>
<td>4.712470</td>
<td>0.000111</td>
<td>4.449126</td>
<td>0.000082</td>
<td>0.106676</td>
<td>0.000187</td>
</tr>
<tr>
<td>10.0</td>
<td>0.75</td>
<td>9.079698</td>
<td>-3.097300</td>
<td>-3.214587</td>
<td>5.870472</td>
<td>5.877442</td>
<td>0.000077</td>
<td>5.530702</td>
<td>0.000063</td>
<td>0.082347</td>
<td>0.000143</td>
</tr>
<tr>
<td>10.0</td>
<td>0.80</td>
<td>10.760901</td>
<td>-3.495590</td>
<td>-3.641881</td>
<td>7.318974</td>
<td>7.329399</td>
<td>0.000067</td>
<td>6.874078</td>
<td>0.000147</td>
<td>0.060909</td>
<td>0.000141</td>
</tr>
<tr>
<td>10.0</td>
<td>0.85</td>
<td>12.736051</td>
<td>-3.938110</td>
<td>-4.122407</td>
<td>9.130506</td>
<td>9.141104</td>
<td>0.000117</td>
<td>8.556013</td>
<td>0.000213</td>
<td>0.042495</td>
<td>0.000074</td>
</tr>
<tr>
<td>10.0</td>
<td>0.90</td>
<td>15.013105</td>
<td>-4.421070</td>
<td>NaN</td>
<td>11.344811</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
</tr>
<tr>
<td>15.0</td>
<td>0.05</td>
<td>-2.697185</td>
<td>-0.110414</td>
<td>-0.110458</td>
<td>0.059822</td>
<td>0.059824</td>
<td>0.000001</td>
<td>0.059645</td>
<td>0.000001</td>
<td>3.899576</td>
<td>0.005454</td>
</tr>
<tr>
<td>15.0</td>
<td>0.10</td>
<td>-1.749725</td>
<td>-0.230747</td>
<td>-0.231439</td>
<td>0.133945</td>
<td>0.133940</td>
<td>0.000002</td>
<td>0.133141</td>
<td>0.000004</td>
<td>1.864668</td>
<td>0.003974</td>
</tr>
<tr>
<td>15.0</td>
<td>0.15</td>
<td>-1.061974</td>
<td>-0.359472</td>
<td>-0.361170</td>
<td>0.225453</td>
<td>0.225452</td>
<td>0.000003</td>
<td>0.223446</td>
<td>0.000003</td>
<td>1.192309</td>
<td>0.002397</td>
</tr>
<tr>
<td>15.0</td>
<td>0.20</td>
<td>-0.459774</td>
<td>-0.497250</td>
<td>-0.500528</td>
<td>0.338152</td>
<td>0.338132</td>
<td>0.000006</td>
<td>0.334154</td>
<td>0.000006</td>
<td>0.861787</td>
<td>0.001197</td>
</tr>
<tr>
<td>15.0</td>
<td>0.25</td>
<td>0.114696</td>
<td>-0.645286</td>
<td>-0.650663</td>
<td>0.476595</td>
<td>0.476597</td>
<td>0.000010</td>
<td>0.469637</td>
<td>0.000013</td>
<td>0.663227</td>
<td>0.000896</td>
</tr>
<tr>
<td>15.0</td>
<td>0.30</td>
<td>0.691041</td>
<td>-0.804982</td>
<td>-0.812776</td>
<td>0.646467</td>
<td>0.646493</td>
<td>0.000006</td>
<td>0.635275</td>
<td>0.000014</td>
<td>0.530581</td>
<td>0.000762</td>
</tr>
<tr>
<td>15.0</td>
<td>0.35</td>
<td>1.288918</td>
<td>-0.977541</td>
<td>-0.988319</td>
<td>0.854786</td>
<td>0.854773</td>
<td>0.000015</td>
<td>0.837655</td>
<td>0.000026</td>
<td>0.433637</td>
<td>0.000593</td>
</tr>
<tr>
<td>15.0</td>
<td>0.40</td>
<td>1.923592</td>
<td>-1.164250</td>
<td>-1.178963</td>
<td>1.109986</td>
<td>1.110019</td>
<td>0.000026</td>
<td>1.084896</td>
<td>0.000029</td>
<td>0.359106</td>
<td>0.000945</td>
</tr>
<tr>
<td>15.0</td>
<td>0.45</td>
<td>2.609898</td>
<td>-1.367111</td>
<td>-1.386525</td>
<td>1.422756</td>
<td>1.422911</td>
<td>0.000035</td>
<td>1.387178</td>
<td>0.000026</td>
<td>0.299288</td>
<td>0.000430</td>
</tr>
<tr>
<td>15.0</td>
<td>0.50</td>
<td>3.363557</td>
<td>-1.588511</td>
<td>-1.613317</td>
<td>1.806653</td>
<td>1.806744</td>
<td>0.000046</td>
<td>1.756972</td>
<td>0.000040</td>
<td>0.249353</td>
<td>0.000550</td>
</tr>
<tr>
<td>15.0</td>
<td>0.55</td>
<td>4.200814</td>
<td>-1.830632</td>
<td>-1.861848</td>
<td>2.278025</td>
<td>2.278204</td>
<td>0.000030</td>
<td>2.210155</td>
<td>0.000048</td>
<td>0.206959</td>
<td>0.000337</td>
</tr>
<tr>
<td>15.0</td>
<td>0.60</td>
<td>5.141221</td>
<td>-2.095960</td>
<td>-2.135357</td>
<td>2.857884</td>
<td>2.858447</td>
<td>0.000022</td>
<td>2.766619</td>
<td>0.000073</td>
<td>0.170705</td>
<td>0.000615</td>
</tr>
<tr>
<td>15.0</td>
<td>0.65</td>
<td>6.209108</td>
<td>-2.388056</td>
<td>-2.437320</td>
<td>3.573661</td>
<td>3.574262</td>
<td>0.000062</td>
<td>3.451758</td>
<td>0.000077</td>
<td>0.138541</td>
<td>0.000317</td>
</tr>
<tr>
<td>15.0</td>
<td>0.70</td>
<td>7.431799</td>
<td>-2.711255</td>
<td>-2.772134</td>
<td>4.458694</td>
<td>4.460000</td>
<td>0.000035</td>
<td>4.297887</td>
<td>0.000097</td>
<td>0.110500</td>
<td>0.000360</td>
</tr>
<tr>
<td>15.0</td>
<td>0.75</td>
<td>8.839178</td>
<td>-3.070076</td>
<td>-3.145232</td>
<td>5.552641</td>
<td>5.559524</td>
<td>0.000062</td>
<td>5.346428</td>
<td>0.000098</td>
<td>0.086070</td>
<td>0.000297</td>
</tr>
<tr>
<td>15.0</td>
<td>0.80</td>
<td>10.484866</td>
<td>-3.469050</td>
<td>-3.563044</td>
<td>6.920035</td>
<td>6.929339</td>
<td>0.000096</td>
<td>6.650362</td>
<td>0.000156</td>
<td>0.064573</td>
<td>0.000276</td>
</tr>
<tr>
<td>15.0</td>
<td>0.85</td>
<td>12.432600</td>
<td>-3.912918</td>
<td>-4.032293</td>
<td>8.643062</td>
<td>8.641765</td>
<td>0.000102</td>
<td>8.278002</td>
<td>0.000083</td>
<td>0.045855</td>
<td>0.000036</td>
</tr>
<tr>
<td>15.0</td>
<td>0.90</td>
<td>14.681943</td>
<td>-4.408871</td>
<td>NaN</td>
<td>10.752998</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
<td>NaN</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td>Self-diffusion versus density</td>
<td>Self-diffusion vs excess entropy type 1</td>
</tr>
<tr>
<td>
<figure class=" align-left nist-image--lightbox nist-image" role="group">
<div data-lightbox="https://www.nist.gov/sites/default/files/styles/2800_x_2800_limit/public/images/mml/csd/informatics_research/fig2_2.gif?itok=z3KUzXR5" data-media-id="162781">
<img alt="fig2" height="294" loading="lazy" src="/sites/default/files/styles/480_x_480_limit/public/images/mml/csd/informatics_research/fig2_2.gif?itok=L0n8Tp75" typeof="foaf:Image" width="341">
</div>
<figcaption class="nist-image__caption"></figcaption>
</figure>
</td>
<td>&nbsp;
<figure class=" align-left nist-image--lightbox nist-image" role="group">
<div data-lightbox="https://www.nist.gov/sites/default/files/styles/2800_x_2800_limit/public/images/mml/csd/informatics_research/fig3_2.gif?itok=aPSfIP4i" data-media-id="162776">
<img alt="self-diffusion vs excess entropy 1" height="305" loading="lazy" src="/sites/default/files/styles/480_x_480_limit/public/images/mml/csd/informatics_research/fig3_2.gif?itok=mzLbCo_B" typeof="foaf:Image" width="349">
</div>
<figcaption class="nist-image__caption"></figcaption>
</figure>
</td>
</tr>
<tr>
<td>Self-diffusion vs excess entropy type 2</td>
<td>&nbsp;</td>
</tr>
<tr>
<td>
<figure class=" align-left nist-image--lightbox nist-image" role="group">
<div data-lightbox="https://www.nist.gov/sites/default/files/styles/2800_x_2800_limit/public/images/mml/csd/informatics_research/fig4_1.gif?itok=P_9nJ5ma" data-media-id="162771">
<img alt="diffusion vs excess entropy 2" height="305" loading="lazy" src="/sites/default/files/styles/480_x_480_limit/public/images/mml/csd/informatics_research/fig4_1.gif?itok=3l3hOr6d" typeof="foaf:Image" width="349">
</div>
<figcaption class="nist-image__caption"></figcaption>
</figure>
</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
<blockquote>&nbsp;</blockquote>
<p><strong>References</strong></p>
<p>1. Rapaport, D. C. The Art of Molecular Dynamic Simulation; Cambridge University Press, Cambridge, 2nd ed., 2004.</p>
<p>2. <a href="http://dx.doi.org/10.1063/1.1572463">J.R. Errington, J. Chem. Phys. <strong>118</strong>, 9915-9925 (2003).</a></p>
<p>3. <a href="http://dx.doi.org/10.1063/1.2748045">J. Mittal, J. R. Errington, T. M. Truskett, Chem. Phys. <strong>126</strong>, 244708 (2007).</a></p>
<p>4. <a href="http://www.tandfonline.com/doi/abs/10.1080/00268978400100651#preview">J. R. Henderson, F. van Swol, Mol. Phys. <strong>51</strong>, 991 (1984)</a>.</p>
<p>5. <a href="http://link.aps.org/abstract/PRL/v96/e177804">J. Mittal, J. R. Errington, T. M. Truskett, Phys. Rev. Lett. <strong>96</strong>, 177804 (2006).</a></p>
<p>6.&nbsp;<a href="http://link.aps.org/abstract/PRL/v100/e106001">G. Goel, W. P. Krekelberg, M. J. Pond, J. Mittal, V. K. Shen, J. R. Errington, T. M. Truskett, J. Stat. Mech. 2009, P04006 (2009).</a></p>
<p>7.&nbsp;<a href="http://dx.doi.org/10.1063/1.4884124">V. K. Shen and D. W. Siderius, J. Chem. Phys., <strong>140</strong>, 244106, 2014.</a></p>
<p>8.&nbsp;<a href="http://dx.doi.org/10.1063/1.4884124">V. K. Shen and D. W. Siderius, J. Chem. Phys., <strong>140</strong>, 244106, 2014.</a></p>
<p>9.&nbsp;<a href="https://doi.org/10.1021/jp040218y">V. K. Shen and J. R. Errington, JPC B <strong>108</strong>, 19595, 2004.</a></p>
<p>10.&nbsp;<a href="https://doi.org/10.1063/1.1844372">V. K. Shen and J. R. Errington, JCP <strong>122</strong>, 064508, 2005</a>.</p>
<p>11.&nbsp;<a href="https://doi.org/10.1021/jp070374f">V. K. Shen, R. D. Mountain, and J. R. Errington, JPC B <strong>111</strong>, 6198, 2007.</a></p>
<p>12.&nbsp;<a href="https://doi.org/10.1021/jp400480q">D. W. Siderius and V. K. Shen, JPC C <strong>117</strong>, 5681, 2013.</a></p>
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