Voter model

2013-10-02T14:55:02Z

150.140.255.82: /* A special linear voter model */

{{Documentation subpage}}

This template is used to include the oriented integrals around closed surfaces (or hypersurfaces in higher dimensions), usually in a mathematical formula. They are additional symbols to [[Help:Displaying a formula#\oiint and \oiiint|\oiint and \oiiint]] which are not yet rendered on wikipedia.

==Arguments==

* '''mode:''' choose either "svg" (large, 45px width) or "[[mathjax]]" (small, 35px width), depending on which rendering is used. The default is the average of 40px width.
* '''preintegral''' the text or formula immediately before the integral
* '''symbol''' the integral symbol,

:{| class="wikitable"
|-
!rowspan="2"| Select one of...
!colspan="3"| Arrow up, integrals over a closed
!colspan="3"| Arrow down, integrals over a closed
|-
!1-surface
!2-surface
!3-surface
!1-surface
!2-surface
!3-surface
|-
!Clockwise<br />orientation
|oint=[[File:OintclockwiseLaTeX.svg|x45px|alt=\oiint]]
|oiint=[[File:OiintclockwiseLaTeX.svg|x45px|alt=\oiint]]
|oiiint=[[File:OiiintclockwiseLaTeX.svg|x45px|alt=\oiint]]
|varoint=[[File:VarointclockwiseLaTeX.svg|x45px|alt=\oiint]]
|varoiint=[[File:VaroiintclockwiseLaTeX.svg|x45px|alt=\oiint]]
|varoiiint=[[File:VaroiiintclockwiseLaTeX.svg|x45px|alt=\oiint]]
|-
!Counterclockwise<br />orientation
|ointctr=[[File:OintctrclockwiseLaTeX.svg|x45px|alt=\oiint]]
|oiintctr=[[File:OiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]]
|oiiintctr=[[File:OiiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]]
|varointctr=[[File:VarointctrclockwiseLaTeX.svg|x45px|alt=\oiint]]
|varoiintctr=[[File:VaroiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]]
|varoiiintctr=[[File:VaroiiintctrclockwiseLaTeX.svg|x45px|alt=\oiint]]
|-
|}

:The default is [[File:OintclockwiseLaTeX.svg|x45px|alt=\oiint]]

* '''intsubscpt''' the subscript below the integral
* '''integrand''' the text or formula immediately after the formula

All parameters are optional.

==Examples==

*The work done in a [[thermodynamic cycle]] on an [[indicator diagram]]: {{intorient
| preintegral=<math>W=</math>
| symbol = varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>p{\rm d}V</math>
}}

<pre><nowiki>{{intorient
| preintegral=<math>W=</math>
| symbol = varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>p{\rm d}V</math>
}}</nowiki></pre>

*In [[complex analysis]] for [[contour integral]]s: {{intorient|
| preintegral =
| symbol=varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>\frac{{\rm d}z}{(z+a)^3z^{1/2}}</math>
}}

<pre><nowiki>{{intorient|
| preintegral =
|symbol=varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>\frac{{\rm d}z}{(z+a)^3z^{1/2}}</math>
}}</nowiki></pre>

*Line integrals of vector fields: {{intorient|
| preintegral = {{intorient|
| preintegral =
|symbol=oint
| intsubscpt = <math>{\scriptstyle \partial S}</math>
| integrand = <math>\mathbf{F}\cdot{\rm d}\mathbf{r}=-</math>
}}
|symbol=ointctr
| intsubscpt = <math>{\scriptstyle \partial S}</math>
| integrand = <math>\mathbf{F}\cdot{\rm d}\mathbf{r}</math>
}}

<pre><nowiki>{{intorient|
| preintegral = {{intorient|
| preintegral =
|symbol=oint
| intsubscpt = <math>{\scriptstyle \partial S}</math>
| integrand = <math>\mathbf{F}\cdot{\rm d}\mathbf{r}=-</math>
}}
|symbol=ointctr
| intsubscpt = <math>{\scriptstyle \partial S}</math>
| integrand = <math>\mathbf{F}\cdot{\rm d}\mathbf{r}</math>
}}</nowiki></pre>

*Other examples: {{Intorient|
| preintegral =
|symbol=oiint
| intsubscpt = <math>{\scriptstyle \Sigma}</math>
| integrand = <math>(E+H\wedge T) {\rm d}^2 \Sigma</math>
}}

<pre><nowiki>{{Intorient|
| preintegral =
|symbol=oiiintctr
| intsubscpt = <math>{\scriptstyle \Sigma}</math>
| integrand = <math>(E+H\wedge T) {\rm d}^2 \Sigma</math>
}}</nowiki></pre>

:{{Intorient|
| preintegral =
|symbol=varoiiintctr
| intsubscpt = <math>{\scriptstyle \Omega}</math>
| integrand = <math>(E+H\wedge T) {\rm d}^4\Omega</math>
}}

<pre><nowiki>{{Intorient|
| preintegral =
|symbol=varoiiintctr
| intsubscpt = <math>{\scriptstyle \Omega}</math>
| integrand = <math>(E+H\wedge T) {\rm d}^4 \Omega</math>
}}</nowiki></pre>

==See also==

* [[User:Nageh/mathJax]]

Non-oriented boundary integrals over a 2-surface and 3-surface can be implemented respectively by:

* {{tl|Oiint}}
* {{tl|Oiiint}}

<includeonly>

[[Category:Wikipedia formatting and function templates]]
[[Category:Mathematical formatting templates]]

</includeonly>

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Voter model