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	<id>https://en.formulasearchengine.com/index.php?action=history&amp;feed=atom&amp;title=Regular_semigroup</id>
	<title>Regular semigroup - Revision history</title>
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	<updated>2026-05-22T10:52:20Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Regular_semigroup&amp;diff=250389&amp;oldid=prev</id>
		<title>en&gt;JMP EAX: /* Generalizations */ since both names seems to have almost equal traction...</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Regular_semigroup&amp;diff=250389&amp;oldid=prev"/>
		<updated>2014-09-02T19:45:03Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Generalizations: &lt;/span&gt; since both names seems to have almost equal traction...&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&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 21:45, 2 September 2014&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Multiple issues|unreferenced = December 2009|orphan = October 2008|&lt;/del&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;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The writer&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s name is Christy. My day job is an invoicing officer but I&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ve already utilized for an additional one. My wife and I live &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Kentucky&lt;/ins&gt;. The &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;favorite pastime for him and his kids &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;to play lacross &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;he would never give it up.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Look into my web site&lt;/ins&gt;; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;free psychic reading ([http:&lt;/ins&gt;//&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cartoonkorea&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ce002&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1093612 click through &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;next website page&lt;/ins&gt;]&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;)&lt;/ins&gt;&lt;/div&gt;&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{underlinked|date=December 2012}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;Preferential concentration&#039;&#039;&#039; is the tendency of dense particles &lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a turbulent fluid to cluster in regions of high strain (low vorticity) due to their inertia&lt;/del&gt;. The &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;extent by which particles cluster &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;determined by the [[Stokes number]], defined as &amp;lt;math&amp;gt;St = tau_p / tau_f = (rho_p * d^2 * epsilon^{1/2}) / (18 * rho_f * nu^{3/2})&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;tau_p&amp;lt;/math&amp;gt; &lt;/del&gt;and &amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tau_f&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;are the timescales for the particle and fluid respectively&lt;/del&gt;; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;note that &amp;lt;math&amp;gt;rho_p&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;rho_f&amp;lt;&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; are the mass densities of the fluid and the particle, respectively, &amp;lt;math&amp;gt;nu&amp;lt;&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; is the kinematic viscosity of the fluid, and &amp;lt;math&amp;gt;epsilon&amp;lt;/math&amp;gt; is the kinetic energy dissipation rate of the turbulence&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Maximum preferential concentration occurs at Stokes ~ 1. Particles with &amp;lt;math&amp;gt;St &amp;lt;&amp;lt; 1&amp;lt;&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; follow fluid streamlines and particles with &amp;lt;math&amp;gt;St &amp;gt;&amp;gt; 1&amp;lt;&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; do not respond significantly to &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fluid within the times the fluid motions are coherent.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Systems that can be strongly influenced by the dynamics of preferential concentration are aerosol production of fine powders, spray, emulsifier, and crystallization reactors, pneumatic devices, cloud droplet formation, aerosol transport in the upper atmosphere, and even planet formation from [[protoplanetary nebula&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;].&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Turbulence]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Physics-stub}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;JMP EAX</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Regular_semigroup&amp;diff=14912&amp;oldid=prev</id>
		<title>en&gt;Illia Connell: /* References */standardize journal name using AWB</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Regular_semigroup&amp;diff=14912&amp;oldid=prev"/>
		<updated>2013-05-10T00:37:34Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;References: &lt;/span&gt;standardize journal name using &lt;a href=&quot;/index.php?title=Testwiki:AWB&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Testwiki:AWB (page does not exist)&quot;&gt;AWB&lt;/a&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&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 02:37, 10 May 2013&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The title of &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;writer is Jayson. I am really fond &lt;/del&gt;of to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;go to karaoke but I&#039;ve been using on new issues recently. For a while I&#039;ve been &lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Alaska but I will have &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;transfer in a year or two&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Credit authorising &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;how he makes cash.&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Also visit my site&lt;/del&gt;; are &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;psychics real ([http:&lt;/del&gt;//&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;www&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;khuplaza&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;dent&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;14869889 www&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;khuplaza&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;)&lt;/del&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;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Multiple issues|unreferenced = December 2009|orphan = October 2008|&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;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{underlinked|date=December 2012}}&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;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&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;&#039;&#039;&#039;Preferential concentration&#039;&#039;&#039; is &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tendency &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;dense particles in a turbulent fluid &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cluster &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;regions of high strain (low vorticity) due &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;their inertia&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The extent by which particles cluster &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;determined by the [[Stokes number]], defined as &amp;lt;math&amp;gt;St = tau_p / tau_f = (rho_p * d^2 * epsilon^{1/2}) / (18 * rho_f * nu^{3/2})&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;tau_p&amp;lt;/math&amp;gt; and &lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tau_f&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/ins&gt;&amp;gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;are the timescales for the particle and fluid respectively&lt;/ins&gt;; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;note that &amp;lt;math&amp;gt;rho_p&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;rho_f&amp;lt;/math&amp;gt; &lt;/ins&gt;are &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the mass densities of the fluid and the particle, respectively, &amp;lt;math&amp;gt;nu&amp;lt;&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; is the kinematic viscosity of the fluid, and &amp;lt;math&amp;gt;epsilon&amp;lt;&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; is the kinetic energy dissipation rate of the turbulence&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Maximum preferential concentration occurs at Stokes ~ 1&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Particles with &amp;lt;math&amp;gt;St &amp;lt;&amp;lt; 1&amp;lt;&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; follow fluid streamlines and particles with &amp;lt;math&amp;gt;St &amp;gt;&amp;gt; 1&amp;lt;&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&amp;gt; do not respond significantly to the fluid within the times the fluid motions are coherent&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;Systems that can be strongly influenced by the dynamics of preferential concentration are aerosol production of fine powders, spray, emulsifier, and crystallization reactors, pneumatic devices, cloud droplet formation, aerosol transport in the upper atmosphere, and even planet formation from [[protoplanetary nebula]]&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;[[Category:Turbulence&lt;/ins&gt;]&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&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;/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;{{Physics-stub}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Illia Connell</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Regular_semigroup&amp;diff=250388&amp;oldid=prev</id>
		<title>en&gt;ZéroBot: r2.7.1) (Robot: Adding fr:Demi-groupe régulier</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Regular_semigroup&amp;diff=250388&amp;oldid=prev"/>
		<updated>2012-08-14T06:21:48Z</updated>

		<summary type="html">&lt;p&gt;r2.7.1) (Robot: Adding &lt;a href=&quot;/index.php?title=Fr:Demi-groupe_r%C3%A9gulier&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Fr:Demi-groupe régulier (page does not exist)&quot;&gt;fr:Demi-groupe régulier&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;The title of the writer is Jayson. I am really fond of to go to karaoke but I&amp;#039;ve been using on new issues recently. For a while I&amp;#039;ve been in Alaska but I will have to transfer in a year or two. Credit authorising is how he makes cash.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Also visit my site; are psychics real ([http://www.khuplaza.com/dent/14869889 www.khuplaza.com])&lt;/div&gt;</summary>
		<author><name>en&gt;ZéroBot</name></author>
	</entry>
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