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	<title>Timothy Gowers - Revision history</title>
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	<updated>2026-04-20T01:36:17Z</updated>
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		<title>en&gt;Papageno92: /* Family relations and personal life */</title>
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		<updated>2015-01-02T14:42:32Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Family relations and personal life&lt;/span&gt;&lt;/p&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 16:42, 2 January 2015&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-l1008&quot;&gt;Line 1,008:&lt;/td&gt;
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&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;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;   &amp;lt;li&amp;gt;[http://www.nwcommunities.org/author-diana-leafe-christian-to-present-talk-at-east-west-bookshop-tea-garden-august-21-2013/comment-page-/#comment- http://www.nwcommunities.org/author-diana-leafe-christian-to-present-talk-at-east-west-bookshop-tea-garden-august-21-2013/comment-page-/#comment-]&amp;lt;/li&amp;gt;&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;    &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;    &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;  &amp;lt;/ul&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;/ul&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Papageno92</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Timothy_Gowers&amp;diff=288449&amp;oldid=prev</id>
		<title>en&gt;Bobfish 341 at 15:03, 27 February 2014</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Timothy_Gowers&amp;diff=288449&amp;oldid=prev"/>
		<updated>2014-02-27T15:03:03Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;a href=&quot;https://en.formulasearchengine.com/index.php?title=Timothy_Gowers&amp;amp;diff=288449&amp;amp;oldid=4326&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>en&gt;Bobfish 341</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Timothy_Gowers&amp;diff=4326&amp;oldid=prev</id>
		<title>en&gt;Monkbot: /* Popularization Work */Fix CS1 deprecated date parameter errors</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Timothy_Gowers&amp;diff=4326&amp;oldid=prev"/>
		<updated>2014-01-30T23:19:45Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Popularization Work: &lt;/span&gt;Fix &lt;a href=&quot;/index.php?title=Help:CS1_errors&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Help:CS1 errors (page does not exist)&quot;&gt;CS1 deprecated date parameter errors&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Unreferenced|date=December 2009}}&lt;br /&gt;
:&amp;#039;&amp;#039;This article describes the &amp;#039;&amp;#039;distribution function&amp;#039;&amp;#039; as used in physics. You may be looking for the related mathematical concepts of [[cumulative distribution function]] or [[probability density function]].&amp;#039;&amp;#039;&lt;br /&gt;
&lt;br /&gt;
In molecular [[kinetic theory]] in [[physics]], a particle&amp;#039;s &amp;#039;&amp;#039;&amp;#039;distribution function&amp;#039;&amp;#039;&amp;#039; is a function of seven variables, &amp;lt;math&amp;gt;f(x,y,z,t;v_x,v_y,v_z)&amp;lt;/math&amp;gt;, which gives the number of particles per unit volume in single-particle [[phase space]].  It is the number of particles per unit volume having approximately the [[velocity]] &amp;lt;math&amp;gt;(v_x,v_y,v_z)&amp;lt;/math&amp;gt; near the place &amp;lt;math&amp;gt;(x,y,z)&amp;lt;/math&amp;gt; and time &amp;lt;math&amp;gt;(t)&amp;lt;/math&amp;gt;.  The usual normalization of the distribution function is&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;n(x,y,z,t) = \int f \,dv_x \,dv_y \,dv_z&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;N(t) = \int n \,dx \,dy \,dz. &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Here, N is the total number of particles and &amp;#039;&amp;#039;n&amp;#039;&amp;#039; is the number density of particles - the number of particles per unit volume, or the [[density]] divided by the mass of individual particles.&lt;br /&gt;
&lt;br /&gt;
A distribution function may be specialised with respect to a particular set of dimensions. E.g. take the quantum mechanical six dimensional phase space, &amp;lt;math&amp;gt;f(x,y,z;p_x,p_y,p_z)&amp;lt;/math&amp;gt; and multiply by the total space volume, to give the momentum distribution i.e. the number of particles in the momentum phase space having approximately the [[momentum]] &amp;lt;math&amp;gt;(p_x,p_y,p_z)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Particle distribution functions are often used in [[plasma physics]] to describe wave-particle interactions and velocity-space instabilities.  Distribution functions are also used in [[fluid mechanics]], [[statistical mechanics]] and [[nuclear physics]].&lt;br /&gt;
&lt;br /&gt;
The [[Maxwell-Boltzmann distribution|basic distribution function]] uses the [[Boltzmann constant]] &amp;lt;math&amp;gt;k&amp;lt;/math&amp;gt; and temperature &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt; with the number density to modify the [[normal distribution]]:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt; f = n\left(\frac{m}{2 \pi  kT}\right)^{3/2} \exp\left({-\frac{m(v_x^2 + v_y^2 + v_z^2)}{2kT}}\right). &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Related distribution functions may allow bulk fluid flow, in which case the velocity origin is shifted, so that the [[exponent]]&amp;#039;s [[numerator]] is &amp;lt;math&amp;gt;m((v_x - u_x)^2 + (v_y - u_y)^2 + (v_z - u_z)^2)&amp;lt;/math&amp;gt;;  &amp;lt;math&amp;gt;(u_x, u_y, u_z)&amp;lt;/math&amp;gt; is the bulk velocity of the fluid.  Distribution functions may also feature non-isotropic temperatures, in which each term in the exponent is divided by a different temperature.&lt;br /&gt;
&lt;br /&gt;
Plasma theories such as [[magnetohydrodynamics]] may assume the particles to be in [[thermodynamic equilibrium]].  In this case, the distribution function is &amp;#039;&amp;#039;[[Maxwellian]]{{dn|date=July 2012}}&amp;#039;&amp;#039;.  This distribution function allows fluid flow and different temperatures in the directions parallel to, and perpendicular to, the local magnetic field.  More complex distribution functions may also be used since [[Plasma (physics)|plasmas]] are rarely in thermal equilibrium.&lt;br /&gt;
&lt;br /&gt;
The mathematical analog of a distribution is a [[measure (mathematics)|measure]]; the time evolution of a measure on a phase space is the topic of study in [[dynamical systems]].&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Distribution Function}}&lt;br /&gt;
[[Category:Statistical mechanics]]&lt;br /&gt;
[[Category:Dynamical systems]]&lt;br /&gt;
&lt;br /&gt;
[[nl:Verdelingsfunctie]]&lt;/div&gt;</summary>
		<author><name>en&gt;Monkbot</name></author>
	</entry>
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