View source for Appendix/VariablesTemplates

=Variables Templates=

==Physical Constants==

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  <td colspan=4>
To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...<br /><center>
&#123;&#123; Math/<i><font color="red">Template_Name</font></i> &#125;&#125;</center>
  </td>
</tr>
<tr>
  <th width="8%">
<font color="red">Symbol</font>
  </th>
  <th>
<font color="red">Definition</font>
  </th>
  <th width="25%">
<font color="red">Template_Name</font>
  </th>
  <th width="10%">
<font color="red">Unicode</font>
  </th>
</tr>

<tr>
  <td align="center">
{{ Math/C_SpeedOfLight}}
  </td>
  <td>
<font color="green">Speed of light</font>; &nbsp;&nbsp;
[http://en.wikipedia.org/wiki/Speed_of_light Authoritative Value]
  </td>
  <td>
[[Template:Math/C_SpeedOfLight|C_SpeedOfLight]]
  </td>
  <td align="center">
x0063
  </td>
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  <td align="center">
{{ Math/C_GravitationalConstant}}
  </td>
  <td>
<font color="green">Newtonian gravitational constant</font>; &nbsp;&nbsp;
[http://en.wikipedia.org/wiki/Gravitational_constant Authoritative Value]
  </td>
  <td>
[[Template:Math/C_GravitationalConstant|C_GravitationalConstant]]
  </td>
  <td align="center">
x0047
  </td>
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  <td align="center">
{{ Math/C PlanckConstant}}
  </td>
  <td>
<font color="green">Planck constant</font>; &nbsp;&nbsp;
[http://en.wikipedia.org/wiki/Planck_constant Authoritative Value];  &nbsp;&nbsp;
NOTE: <span title="h-bar"><math>\hbar</math></span> <math>\equiv</math> {{ Math/C_PlanckConstant }}/(2<math>\pi</math>)
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[[Template:Math/C_PlanckConstant|C_PlanckConstant]]
  </td>
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x0068
  </td>
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{{ Math/C_BoltzmannConstant}}
  </td>
  <td>
<font color="green">Boltzmann constant</font>; &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Boltzmann_constant Authoritative Value]
  </td>
  <td>
[[Template:Math/C_BoltzmannConstant|C_BoltzmannConstant]]
  </td>
  <td align="center">
x006B
  </td>
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{{ Math/C_AvogadroConstant}}
  </td>
  <td>
<font color="green">Avogadro constant</font>; &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Avogadro_constant Authoritative Value]
  </td>
  <td>
[[Template:Math/C_AvogadroConstant|C_AvogadroConstant]]
  </td>
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&nbsp;
  </td>
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{{ Math/C_ElectronMass}}
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  <td>
<font color="green">Electron mass</font>; &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Electron_mass Authoritative Value]
  </td>
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[[Template:Math/C_ElectronMass|C_ElectronMass]]
  </td>
  <td align="center">
&nbsp;
  </td>
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{{ Math/C_ProtonMass}}
  </td>
  <td>
<font color="green">Proton mass</font>; &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Proton_mass Authoritative Value]
  </td>
  <td>
[[Template:Math/C_ProtonMass|C_ProtonMass]]
  </td>
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&nbsp;
  </td>
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{{ Math/C_AtomicMassUnit}}
  </td>
  <td>
<font color="green">Atomic mass unit</font>; &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Atomic_mass_unit Authoritative Value]; &nbsp;&nbsp; 
NOTE: {{ Math/C_ProtonMass }}/{{ Math/C_AtomicMassUnit }} = 1.007276
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[[Template:Math/C_AtomicMassUnit|C_AtomicMassUnit]]
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&nbsp;
  </td>
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{{ Math/C_GasConstant}}
  </td>
  <td>
<font color="green">Gas constant</font> = {{ Math/C_BoltzmannConstant }}{{ Math/C_AvogadroConstant }} = 1.007276 {{ Math/C_BoltzmannConstant }}/{{ Math/C_ProtonMass }}; &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Gas_constant Authoritative Value]

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[[Template:Math/C_GasConstant|C_GasConstant]]
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x211C
  </td>
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{{ Math/C_FermiPressure}}
  </td>
  <td>
<font color="green">Characteristic Fermi pressure</font>; <br />
<math>A_\mathrm{F} \equiv \frac{\pi m_e^4 c^5}{3h^3} = 6.00228\times 10^{22}~\mathrm{erg}~\mathrm{cm}^{-3}</math><br />
<br />
<font size="-1">
Reference (original): [http://adsabs.harvard.edu/abs/1935MNRAS..95..207C Chandraskehar, S. (1935)]<br />
Reference (recent): See Appendix of [http://adsabs.harvard.edu/abs/2009ApJS..184..248E Even &amp; Tohline (2009)]<br />
Reference (authoritative book): [<b>[[Appendix/References#C67|<font color="red">C67</font>]]</b>] 
</font>
  </td>
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[[Template:Math/C_FermiPressure|C_FermiPressure]]
  </td>
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&nbsp;
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{{ Math/C_FermiDensity }}
  </td>
  <td>
<font color="green">Characteristic Fermi density</font>; 
<math>\frac{B_\mathrm{F}}{\mu_e} \equiv \frac{8\pi m_p}{3} \biggl( \frac{m_e c}{h} \biggr)^3 = 9.81011\times 10^{5}~\mathrm{g}~\mathrm{cm}^{-3}</math><br />
<br />
<font size="-1">
Reference (original): [http://adsabs.harvard.edu/abs/1935MNRAS..95..207C Chandraskehar, S. (1935)]<br />
Reference (recent): See Appendix of [http://adsabs.harvard.edu/abs/2009ApJS..184..248E Even &amp; Tohline (2009)]<br />
Reference (authoritative book): [<b>[[Appendix/References#C67|<font color="red">C67</font>]]</b>] 
</font>
  </td>
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[[Template:Math/C_FermiDensity|C_FermiDensity]]
  </td>
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&nbsp;
  </td>
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  <td align="center">
{{ Math/C_RadiationConstant}}
  </td>
  <td>
<font color="green">Radiation [density] constant</font>; &nbsp;&nbsp; 
[http://scienceworld.wolfram.com/physics/RadiationConstant.html Authoritative Value] <br />
<math>a_\mathrm{rad} \equiv \frac{8\pi^5}{15}\frac{k^4}{(hc)^3} = 7.56576\times 10^{-15}~\mathrm{erg}~\mathrm{cm}^{-3}~\mathrm{K}^{-4}</math><br />
NOTE: <math>a_\mathrm{rad} = 4\sigma_\mathrm{SB}/c</math>, where <math>\sigma_\mathrm{SB}</math> is the [https://en.wikipedia.org/wiki/Stefan–Boltzmann_constant Stefan-Boltzmann constant]; see, for example, p. 428 of [[Appendix/References#HK94|[<b><font color="red">HK94</font></b>]]].
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[[Template:Math/C_RadiationConstant|C_RadiationConstant]]
  </td>
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&nbsp;
  </td>
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  <td align="center">
{{ Math/C_ElectronTemperature}}
  </td>
  <td>
<font color="green">Temperature associated with the rest-mass energy of the electron</font>; &nbsp;&nbsp; 
[[SR/PressureCombinations#Normalized_Ideal-Gas_Pressure|Context of Definition]] <br />
<math>T_e \equiv \frac{m_e c^2}{k} = 5.9381\times 10^{9}~\mathrm{K}</math><br />
  </td>
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[[Template:Math/C_ElectronTemperature|C_ElectronTemperature]]
  </td>
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&nbsp;
  </td>
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  <td align="center">
{{ Math/C_ElectronCharge }}
  </td>
  <td>
<font color="green">Charge on an electron</font>; &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Charge_of_electron Authoritative Value]
<br />
The cgs units (statcoulombs) are equivalent to <math>(\mathrm{g}~\mathrm{cm}^3~\mathrm{s}^{-2})^{1/2}</math>
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[[Template:Math/C_ElectronCharge|C_ElectronCharge]]
  </td>
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&nbsp;
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{{ Math/C_FineStructureConstant}}
  </td>
  <td>
<font color="green">Fine structure constant</font> (dimensionless); &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Fine-structure_constant Authoritative Value] <br />
<math>\alpha_\mathrm{fs} \equiv \frac{e^2}{\hbar c} = \frac{1}{137.0359997}</math><br />
  </td>
  <td>
[[Template:Math/C_FineStructureConstant|C_FineStructureConstant]]
  </td>
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&nbsp;
  </td>
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{{ Math/C_ThompsonCrossSection}}
  </td>
  <td>
<font color="green">Thompson cross-section</font>; &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Thompson_scattering Authoritative Value]
<br />
<math>\sigma_T \equiv \frac{8\pi}{3} \biggl(\frac{\alpha_\mathrm{fs} \hbar}{m_e c} \biggr)^2 = 0.6652458\times 10^{-24}~\mathrm{cm}^2</math><br />
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  <td>
[[Template:Math/C_ThompsonCrossSection|C_ThompsonCrossSection]]
  </td>
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&nbsp;
  </td>
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</table>
</div>

==Variables==

<div align="center">
<table border=3 cellpadding=5 cellspacing=1 width="95%" bordercolor="darkblue">
<tr>
  <td colspan=4>
To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...<br /><center>
&#123;&#123; Math/<i><font color="red">Template_Name</font></i> &#125;&#125;</center>
  </td>
</tr>
<tr>
  <th width="8%">
<font color="red">Symbol</font>
  </th>
  <th>
<font color="red">Definition</font>
  </th>
  <th width="25%">
<font color="red">Template_Name</font>
  </th>
  <th width="10%">
<font color="red">Unicode</font>
  </th>
</tr>


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  <td align="center">
{{ Math/VAR_NumberDensity01 }}
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  <td>
<font color="green">Number density of gas particles</font>; &nbsp;&nbsp; units of "1/volume"
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  <td>
[[Template:Math/VAR_NumberDensity01|VAR_NumberDensity01]]
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x004E
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{{ Math/VAR_Density01}}
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<font color="green">Mass density</font>; &nbsp;&nbsp; units of "mass/volume"
  </td>
  <td>
[[Template:Math/VAR_Density01|VAR_Density01]]
  </td>
  <td align="center">
x03C1
  </td>
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{{ Math/VAR_SpecificVolume01}}
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  <td>
<font color="green">Specific Volume</font> = 1/{{ Math/VAR_Density01 }}; &nbsp;&nbsp; units of "volume/mass"
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[[Template:Math/VAR_SpecificVolume01|VAR_SpecificVolume01]]
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x0056
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{{ Math/VAR_NewtonianPotential01}}
  </td>
  <td>
<font color="green">Newtonian gravitational potential</font>; &nbsp;&nbsp; units of "energy/mass" or "velocity-squared"
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[[Template:Math/VAR_NewtonianPotential01|VAR_NewtonianPotential01]]
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x03A6
  </td>
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{{ Math/VAR_Enthalpy01}}
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  <td>
<font color="green">Enthalpy</font>; &nbsp;&nbsp; units of "energy/mass" or "velocity-squared"
  </td>
  <td>
[[Template:Math/VAR_Enthalpy01|VAR_Enthalpy01]]
  </td>
  <td align="center">
x0048
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{{ Math/VAR_Pressure01}}
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  <td>
<font color="green">Pressure</font>; &nbsp;&nbsp; units of "force/area" or "energy/volume"
  </td>
  <td>
[[Template:Math/VAR_Pressure01|VAR_Pressure01]]
  </td>
  <td align="center">
x0050
  </td>
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  <td align="center">
{{ Math/VAR_SpecificInternalEnergy01}}
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  <td>
<font color="green">Specific internal energy</font>; &nbsp;&nbsp; units of "energy/mass" or "velocity-squared"
  </td>
  <td>
[[Template:Math/VAR_SpecificInternalEnergy01|VAR_SpecificInternalEnergy01]]
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x03B5
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{{ Math/VAR_SpecificEntropy01}}
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  <td>
<font color="green">Specific entropy</font>; 
  </td>
  <td>
[[Template:Math/VAR_SpecificEntropy01|VAR_SpecificEntropy01]]
  </td>
  <td align="center">
x0073
  </td>
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{{ Math/VAR_Time01}}
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  <td>
<font color="green">Time</font>
  </td>
  <td>
[[Template:Math/VAR_Time01|VAR_Time01]]
  </td>
  <td align="center">
x0074
  </td>
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{{ Math/VAR_Temperature01}}
  </td>
  <td>
<font color="green">Temperature</font>; &nbsp;&nbsp; units of "Kelvin"
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  <td>
[[Template:Math/VAR_Temperature01|VAR_Temperature01]]
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x0054
  </td>
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  <td align="center">
{{ Math/VAR_VelocityVector01}}
  </td>
  <td>
<font color="green">Euclidean 3-space velocity vector</font>; &nbsp;&nbsp; units of "length/time"
  </td>
  <td>
[[Template:Math/VAR_VelocityVector01|VAR_VelocityVector01]]
  </td>
  <td align="center">
&nbsp;
  </td>
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{{ Math/VAR_PositionVector01}}
  </td>
  <td>
<font color="green">Euclidean 3-space position vector</font>
  </td>
  <td>
[[Template:Math/VAR_PositionVector01|VAR_PositionVector01]]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
</table>
</div>

==Model Parameters==

<div align="center">
<table border=3 cellpadding=5 cellspacing=1 width="95%" bordercolor="darkblue">
<tr>
  <td colspan=4>
To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...<br /><center>
&#123;&#123; Math/<i><font color="red">Template_Name</font></i> &#125;&#125;</center>
  </td>
</tr>
<tr>
  <th width="8%">
<font color="red">Symbol</font>
  </th>
  <th>
<font color="red">Definition</font>
  </th>
  <th width="25%">
<font color="red">Template_Name</font>
  </th>
  <th width="10%">
<font color="red">Unicode</font>
  </th>
</tr>


<tr>
  <td align="center">
{{ Math/MP_AdiabaticIndex }}
  </td>
  <td>
<font color="green">Adiabatic Index (or Ratio of Specific Heats)</font>; dimensionless &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Heat_capacity_ratio Wikipedia Discussion]
  </td>
  <td>
[[Template:Math/MP_AdiabaticIndex|MP_AdiabaticIndex]]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>

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  <td align="center">
{{ Math/MP_MeanMolecularWeight }}
  </td>
  <td>
<font color="green">Mean molecular weight</font>; dimensionless; &nbsp;&nbsp;
defined such that {{ Math/MP_MeanMolecularWeight }} = {{ Math/VAR_Density01 }} / ({{ Math/C_AtomicMassUnit }}{{Template:Math/VAR_NumberDensity01}}).
  </td>
  <td>
[[Template:Math/MP_MeanMolecularWeight | MP_MeanMolecularWeight]]
  </td>
  <td align="center">
x03BC
  </td>
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<tr>
  <td align="center">
{{ Math/MP_ElectronMolecularWeight }}
  </td>
  <td>
<font color="green">Molecular weight of electrons</font>; dimensionless; <br />
defined such that {{ Math/MP_ElectronMolecularWeight }} = {{ Math/VAR_Density01 }} / ({{ Math/C_AtomicMassUnit }} <math>N_e</math>), where <math>N_e</math> is the number density of electrons.
  </td>
  <td>
[[Template:Math/MP_ElectronMolecularWeight | MP_ElectronMolecularWeight]]
  </td>
  <td align="center">
x03BC
  </td>
</tr>

<tr>
  <td align="center">
{{ Math/MP_PolytropicIndex }}
  </td>
  <td>
<font color="green">Polytropic Index</font>; dimensionless &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Polytrope Wikipedia Discussion]
  </td>
  <td>
[[Template:Math/MP_PolytropicIndex | MP_PolytropicIndex]]
  </td>
  <td align="center">
x006E
  </td>
</tr>

<tr>
  <td align="center">
{{ Math/MP_PolytropicConstant }}
  </td>
  <td>
<font color="green">Polytropic Constant</font>; dimensions depend on choice of {{ Math/MP_PolytropicIndex }}  &nbsp;&nbsp; 
[http://en.wikipedia.org/wiki/Polytrope Wikipedia Discussion]
  </td>
  <td>
[[Template:Math/MP_PolytropicConstant | MP_PolytropicConstant]]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>


</table>
</div>

&nbsp;<br />
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