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	<id>http://www.sklogwiki.org/SklogWiki/index.php?action=history&amp;feed=atom&amp;title=Pair_stress_approximation</id>
	<title>Pair stress approximation - Revision history</title>
	<link rel="self" type="application/atom+xml" href="http://www.sklogwiki.org/SklogWiki/index.php?action=history&amp;feed=atom&amp;title=Pair_stress_approximation"/>
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	<updated>2026-04-05T16:29:56Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.41.0</generator>
	<entry>
		<id>http://www.sklogwiki.org/SklogWiki/index.php?title=Pair_stress_approximation&amp;diff=11881&amp;oldid=prev</id>
		<title>Carl McBride at 14:35, 19 October 2011</title>
		<link rel="alternate" type="text/html" href="http://www.sklogwiki.org/SklogWiki/index.php?title=Pair_stress_approximation&amp;diff=11881&amp;oldid=prev"/>
		<updated>2011-10-19T14:35:50Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 16:35, 19 October 2011&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Pair stress approximation&#039;&#039;&#039; &amp;lt;ref&amp;gt;[http://dx.doi.org/10.1063/1.1669587 Emmanuel Meeron and Arnold J. F. Siegert &quot;Statistical Mechanics of Hard‐Particle Systems&quot;, Journal of Chemical Physics &#039;&#039;&#039;48&#039;&#039;&#039; pp. 3139-3155 (1968)]&amp;lt;/ref&amp;gt; (Eq. 3.18)&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Pair stress approximation&#039;&#039;&#039; &amp;lt;ref&amp;gt;[http://dx.doi.org/10.1063/1.1669587 Emmanuel Meeron and Arnold J. F. Siegert &quot;Statistical Mechanics of Hard‐Particle Systems&quot;, Journal of Chemical Physics &#039;&#039;&#039;48&#039;&#039;&#039; pp. 3139-3155 (1968)]&amp;lt;/ref&amp;gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;for [[Idealised models#&#039;Hard&#039; models | hard particles]] is given by &lt;/ins&gt;(Eq. 3.18)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;lt;math&amp;gt;\rho B_2  = \frac{q}{(1+q)^{B_3}}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;lt;math&amp;gt;\rho B_2  = \frac{q}{(1+q)^{B_3}}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Carl McBride</name></author>
	</entry>
	<entry>
		<id>http://www.sklogwiki.org/SklogWiki/index.php?title=Pair_stress_approximation&amp;diff=11880&amp;oldid=prev</id>
		<title>Carl McBride: Added equation of state</title>
		<link rel="alternate" type="text/html" href="http://www.sklogwiki.org/SklogWiki/index.php?title=Pair_stress_approximation&amp;diff=11880&amp;oldid=prev"/>
		<updated>2011-10-19T14:25:00Z</updated>

		<summary type="html">&lt;p&gt;Added equation of state&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 16:25, 19 October 2011&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Pair stress approximation&#039;&#039;&#039; &amp;lt;ref&amp;gt;[http://dx.doi.org/10.1063/1.1669587 Emmanuel Meeron and Arnold J. F. Siegert &quot;Statistical Mechanics of Hard‐Particle Systems&quot;, Journal of Chemical Physics &#039;&#039;&#039;48&#039;&#039;&#039; pp. 3139-3155 (1968)]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Pair stress approximation&#039;&#039;&#039; &amp;lt;ref&amp;gt;[http://dx.doi.org/10.1063/1.1669587 Emmanuel Meeron and Arnold J. F. Siegert &quot;Statistical Mechanics of Hard‐Particle Systems&quot;, Journal of Chemical Physics &#039;&#039;&#039;48&#039;&#039;&#039; pp. 3139-3155 (1968)]&amp;lt;/ref&amp;gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(Eq. 3.18)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&amp;lt;math&amp;gt;\rho B_2  = \frac{q}{(1+q)^{B_3}}&amp;lt;/math&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;where &amp;lt;math&amp;gt;q= P/k_BT\rho -1&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;B_2&amp;lt;/math&amp;gt; is the  [[second virial coefficient]] and &amp;lt;math&amp;gt;B_3&amp;lt;/math&amp;gt; is the third [[Virial equation of state#Virial coefficients | virial coefficient]].&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==See also==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==See also==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*[[Scaled-particle theory]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*[[Scaled-particle theory]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot;&gt;Line 6:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 10:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: statistical mechanics]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: statistical mechanics]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[category: equations of state]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Carl McBride</name></author>
	</entry>
	<entry>
		<id>http://www.sklogwiki.org/SklogWiki/index.php?title=Pair_stress_approximation&amp;diff=11863&amp;oldid=prev</id>
		<title>Carl McBride: Created page with &quot;&#039;&#039;&#039;Pair stress approximation&#039;&#039;&#039; &lt;ref&gt;[http://dx.doi.org/10.1063/1.1669587 Emmanuel Meeron and Arnold J. F. Siegert &quot;Statistical Mechanics of Hard‐Particle Systems&quot;, Journal of ...&quot;</title>
		<link rel="alternate" type="text/html" href="http://www.sklogwiki.org/SklogWiki/index.php?title=Pair_stress_approximation&amp;diff=11863&amp;oldid=prev"/>
		<updated>2011-10-18T13:14:52Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;&amp;#039;&amp;#039;&amp;#039;Pair stress approximation&amp;#039;&amp;#039;&amp;#039; &amp;lt;ref&amp;gt;[http://dx.doi.org/10.1063/1.1669587 Emmanuel Meeron and Arnold J. F. Siegert &amp;quot;Statistical Mechanics of Hard‐Particle Systems&amp;quot;, Journal of ...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Pair stress approximation&amp;#039;&amp;#039;&amp;#039; &amp;lt;ref&amp;gt;[http://dx.doi.org/10.1063/1.1669587 Emmanuel Meeron and Arnold J. F. Siegert &amp;quot;Statistical Mechanics of Hard‐Particle Systems&amp;quot;, Journal of Chemical Physics &amp;#039;&amp;#039;&amp;#039;48&amp;#039;&amp;#039;&amp;#039; pp. 3139-3155 (1968)]&amp;lt;/ref&amp;gt;&lt;br /&gt;
==See also==&lt;br /&gt;
*[[Scaled-particle theory]]&lt;br /&gt;
*[[BBGKY hierarchy]]&lt;br /&gt;
==References==&lt;br /&gt;
&amp;lt;references/&amp;gt;&lt;br /&gt;
[[category: statistical mechanics]]&lt;/div&gt;</summary>
		<author><name>Carl McBride</name></author>
	</entry>
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