Difference between revisions of "User:Tohline/Appendix/Variables templates"

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(added proton mass and gas constant)
 
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=Physical Constants, Variables, and Model Parameters=
{{LSU_HBook_header}}
{{LSU_HBook_header}}


<div align="center">
''<font size="+2" color="darkblue">
Physical Variables and Constants
</font>''
</div>


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<div align="center">
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<font color="red">Unicode</font>
<font color="red">Unicode</font>
   </th>
   </th>
</tr>
<tr>
<th colspan=4 align="left">
<font color="#332200" size="-1">Physical Constants:</font>
</th>
</tr>
<tr>
  <td align="center">
{{User:Tohline/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>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_SpeedOfLight C_SpeedOfLight]
  </td>
  <td align="center">
x0063
  </td>
</tr>
</tr>


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   </td>
   </td>
   <td>
   <td>
<font color="green">Newtonian gravitational constant</font>; &nbsp;&nbsp; <math>6.67\times 10^{-11} ~\mathrm{mks~units}</math>
<font color="green">Newtonian gravitational constant</font>; &nbsp;&nbsp;
[http://en.wikipedia.org/wiki/Gravitational_constant Authoritative Value]
   </td>
   </td>
   <td>
   <td>
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</tr>
</tr>


<tr>
  <td align="center">
{{User:Tohline/Math/C_PlanckConstant}}
  </td>
  <td>
<font color="green">Planck constant</font>; &nbsp;&nbsp;
[http://en.wikipedia.org/wiki/Planck_constant Authoritative Value]
<br />
Note: <math>\hbar \equiv \frac{h}{2\pi}</math>
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_PlanckConstant C_PlanckConstant]
  </td>
  <td align="center">
x0068
  </td>
</tr>


<tr>
<tr>
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   </td>
   </td>
   <td>
   <td>
<font color="green">Boltzmann constant</font>; &nbsp;&nbsp; <math>1.38\times 10^{-23}~\mathrm{mks~units}</math>
<font color="green">Boltzmann constant</font>; &nbsp;&nbsp;  
[http://en.wikipedia.org/wiki/Boltzmann_constant Authoritative Value]
   </td>
   </td>
   <td>
   <td>
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   <td align="center">
   <td align="center">
x006B
x006B
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/Math/C_AvogadroConstant}}
  </td>
  <td>
<font color="green">Avogadro constant</font>; &nbsp;&nbsp;
[http://en.wikipedia.org/wiki/Avogadro_constant Authoritative Value]
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_AvogadroConstant C_AvogadroConstant]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/Math/C_ElectronMass}}
  </td>
  <td>
<font color="green">Electron mass</font>; &nbsp;&nbsp;
[http://en.wikipedia.org/wiki/Electron_mass Authoritative Value]
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_ElectronMass C_ElectronMass]
  </td>
  <td align="center">
&nbsp;
   </td>
   </td>
</tr>
</tr>
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   </td>
   </td>
   <td>
   <td>
<font color="green">Proton mass</font>; &nbsp;&nbsp; <math>1.67\times 10^{-24} ~\mathrm{g}</math>
<font color="green">Proton mass</font>; &nbsp;&nbsp;  
[http://en.wikipedia.org/wiki/Proton_mass Authoritative Value]
   </td>
   </td>
   <td>
   <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_ProtonMass C_ProtonMass]
[http://www.vistrails.org/index.php/User:Tohline/Math/C_ProtonMass C_ProtonMass]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/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>m_p/m_u = 1.007276</math>
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_AtomicMassUnit C_AtomicMassUnit]
   </td>
   </td>
   <td align="center">
   <td align="center">
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   </td>
   </td>
   <td>
   <td>
<font color="green">Gas constant</font> = {{User:Tohline/Math/C_BoltzmannConstant}}/{{User:Tohline/Math/C_ProtonMass}}; &nbsp;&nbsp; <math>8.31\times 10^{7} ~\mathrm{erg}~\mathrm{deg}^{-1}~\mathrm{mole}^{-1}</math>
<font color="green">Gas constant</font> = {{User:Tohline/Math/C_BoltzmannConstant}}{{User:Tohline/Math/C_AvogadroConstant}} = 1.007276 {{User:Tohline/Math/C_BoltzmannConstant}}/{{User:Tohline/Math/C_ProtonMass}}; &nbsp;&nbsp;  
[http://en.wikipedia.org/wiki/Gas_constant Authoritative Value]
 
   </td>
   </td>
   <td>
   <td>
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   </td>
   </td>
   <td align="center">
   <td align="center">
&#x211C;
x211C
  </td>
</tr>
 
<tr>
  <td align="center">
{{User:Tohline/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>[[User:Tohline/Appendix/References#C67|<font color="red">C67</font>]]</b>]
</font>
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_FermiPressure C_FermiPressure]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
 
<tr>
  <td align="center">
{{User:Tohline/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>[[User:Tohline/Appendix/References#C67|<font color="red">C67</font>]]</b>]
</font>
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_FermiDensity C_FermiDensity]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
 
<tr>
  <td align="center">
{{User:Tohline/Math/C_RadiationConstant}}
  </td>
  <td>
<font color="green">Radiation 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 />
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_RadiationConstant C_RadiationConstant]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
 
<tr>
  <td align="center">
{{User:Tohline/Math/C_ElectronTemperature}}
  </td>
  <td>
<font color="green">Temperature associated with the rest-mass energy of the electron</font>; &nbsp;&nbsp;
[http://www.vistrails.org/index.php/User:Tohline/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>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_ElectronTemperature C_ElectronTemperature]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
 
 
<tr>
  <td align="center">
{{User:Tohline/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>
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_ElectronCharge C_ElectronCharge]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
 
<tr>
  <td align="center">
{{User:Tohline/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>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_FineStructureConstant C_FineStructureConstant]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
 
<tr>
  <td align="center">
{{User:Tohline/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 />
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/C_ThompsonCrossSection C_ThompsonCrossSection]
  </td>
  <td align="center">
&nbsp;
   </td>
   </td>
</tr>
</tr>
<tr>
<th colspan=4 align="left">
<font color="#332200" size="-1">Variables:</font>
</th>
</tr>


<tr>
<tr>
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   </td>
   </td>
   <td>
   <td>
<font color="green">Number density</font>; &nbsp;&nbsp; units of "1/volume"
<font color="green">Number density of gas particles</font>; &nbsp;&nbsp; units of "1/volume"
   </td>
   </td>
   <td>
   <td>
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   <td align="center">
   <td align="center">
x03A6
x03A6
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/Math/VAR_Enthalpy01}}
  </td>
  <td>
<font color="green">Enthalpy</font>; &nbsp;&nbsp; units of "energy/mass" or "velocity-squared"
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/VAR_Enthalpy01 VAR_Enthalpy01]
  </td>
  <td align="center">
x0048
   </td>
   </td>
</tr>
</tr>
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   <td align="center">
   <td align="center">
x03B5
x03B5
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/Math/VAR_SpecificEntropy01}}
  </td>
  <td>
<font color="green">Specific entropy</font>;
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/VAR_SpecificEntropy01 VAR_SpecificEntropy01]
  </td>
  <td align="center">
x0073
   </td>
   </td>
</tr>
</tr>
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   <td align="center">
   <td align="center">
x0074
x0074
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/Math/VAR_Temperature01}}
  </td>
  <td>
<font color="green">Temperature</font>; &nbsp;&nbsp; units of "Kelvin"
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/VAR_Temperature01 VAR_Temperature01]
  </td>
  <td align="center">
x0054
   </td>
   </td>
</tr>
</tr>
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   </td>
   </td>
</tr>
</tr>
<tr>
<th colspan=4 align="left">
<font color="#332200" size="-1">Model Parameters:</font>
</th>
</tr>
<tr>
  <td align="center">
{{User:Tohline/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>
[http://www.vistrails.org/index.php/User:Tohline/Math/MP_AdiabaticIndex MP_AdiabaticIndex]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/Math/MP_MeanMolecularWeight}}
  </td>
  <td>
<font color="green">Mean molecular weight</font>; dimensionless; &nbsp;&nbsp;
defined such that {{User:Tohline/Math/MP_MeanMolecularWeight}} = {{User:Tohline/Math/VAR_Density01}}/({{User:Tohline/Math/C_AtomicMassUnit}}{{User:Tohline/Math/VAR_NumberDensity01}} ).
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/MP_MeanMolecularWeight MP_MeanMolecularWeight]
  </td>
  <td align="center">
x03BC
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/Math/MP_ElectronMolecularWeight}}
  </td>
  <td>
<font color="green">Molecular weight of electrons</font>; dimensionless; <br />
defined such that {{User:Tohline/Math/MP_ElectronMolecularWeight}} = {{User:Tohline/Math/VAR_Density01}}/({{User:Tohline/Math/C_AtomicMassUnit}} <math>N_e</math>), where <math>N_e</math> is the number density of electrons.
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/MP_ElectronMolecularWeight MP_ElectronMolecularWeight]
  </td>
  <td align="center">
x03BC
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/Math/MP_PolytropicIndex}}
  </td>
  <td>
<font color="green">Polytropic Index</font>; dimensionless &nbsp;&nbsp;
[http://en.wikipedia.org/wiki/Polytrope Wikipedia Discussion]
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/MP_PolytropicIndex MP_PolytropicIndex]
  </td>
  <td align="center">
x006E
  </td>
</tr>
<tr>
  <td align="center">
{{User:Tohline/Math/MP_PolytropicConstant}}
  </td>
  <td>
<font color="green">Polytropic Constant</font>; dimensions depend on choice of {{User:Tohline/Math/MP_PolytropicIndex}}  &nbsp;&nbsp;
[http://en.wikipedia.org/wiki/Polytrope Wikipedia Discussion]
  </td>
  <td>
[http://www.vistrails.org/index.php/User:Tohline/Math/MP_PolytropicConstant MP_PolytropicConstant]
  </td>
  <td align="center">
&nbsp;
  </td>
</tr>


</table>
</table>

Latest revision as of 21:51, 26 October 2018

Physical Constants, Variables, and Model Parameters

Whitworth's (1981) Isothermal Free-Energy Surface
|   Tiled Menu   |   Tables of Content   |  Banner Video   |  Tohline Home Page   |


To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...
{{ User:Tohline/Math/Template_Name }}

Symbol

Definition

Template_Name

Unicode

Physical Constants:

<math>~c</math>

Speed of light;    Authoritative Value

C_SpeedOfLight

x0063

<math>~G</math>

Newtonian gravitational constant;    Authoritative Value

C_GravitationalConstant

x0047

<math>~h</math>

Planck constant;    Authoritative Value
Note: <math>\hbar \equiv \frac{h}{2\pi}</math>

C_PlanckConstant

x0068

<math>~k</math>

Boltzmann constant;    Authoritative Value

C_BoltzmannConstant

x006B

<math>~N_A</math>

Avogadro constant;    Authoritative Value

C_AvogadroConstant

 

<math>~m_e</math>

Electron mass;    Authoritative Value

C_ElectronMass

 

<math>~m_p</math>

Proton mass;    Authoritative Value

C_ProtonMass

 

<math>~m_u</math>

Atomic mass unit;    Authoritative Value;    NOTE: <math>m_p/m_u = 1.007276</math>

C_AtomicMassUnit

 

<math>~\Re</math>

Gas constant = <math>~k</math><math>~N_A</math> = 1.007276 <math>~k</math>/<math>~m_p</math>;    Authoritative Value

C_GasConstant

x211C

<math>~A_\mathrm{F}</math>

Characteristic Fermi pressure;
<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>

Reference (original): Chandraskehar, S. (1935)
Reference (recent): See Appendix of Even & Tohline (2009)
Reference (authoritative book): [C67]

C_FermiPressure

 

<math>~B_\mathrm{F}</math>

Characteristic Fermi density; <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>

Reference (original): Chandraskehar, S. (1935)
Reference (recent): See Appendix of Even & Tohline (2009)
Reference (authoritative book): [C67]

C_FermiDensity

 

<math>~a_\mathrm{rad}</math>

Radiation constant;    Authoritative Value
<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>

C_RadiationConstant

 

<math>~T_e</math>

Temperature associated with the rest-mass energy of the electron;    Context of Definition
<math>T_e \equiv \frac{m_e c^2}{k} = 5.9381\times 10^{9}~\mathrm{K}</math>

C_ElectronTemperature

 

<math>~e</math>

Charge on an electron;    Authoritative Value
The cgs units (statcoulombs) are equivalent to <math>(\mathrm{g}~\mathrm{cm}^3~\mathrm{s}^{-2})^{1/2}</math>

C_ElectronCharge

 

<math>~\alpha_\mathrm{fs}</math>

Fine structure constant (dimensionless);    Authoritative Value
<math>\alpha_\mathrm{fs} \equiv \frac{e^2}{\hbar c} = \frac{1}{137.0359997}</math>

C_FineStructureConstant

 

<math>~\sigma_T</math>

Thompson cross-section;    Authoritative Value
<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>

C_ThompsonCrossSection

 

Variables:

<math>~n_g</math>

Number density of gas particles;    units of "1/volume"

VAR_NumberDensity01

x004E

<math>~\rho</math>

Mass density;    units of "mass/volume"

VAR_Density01

x03C1

<math>~V</math>

Specific Volume = 1/<math>~\rho</math>;    units of "volume/mass"

VAR_SpecificVolume01

x0056

<math>~\Phi</math>

Newtonian gravitational potential;    units of "energy/mass" or "velocity-squared"

VAR_NewtonianPotential01

x03A6

<math>~H</math>

Enthalpy;    units of "energy/mass" or "velocity-squared"

VAR_Enthalpy01

x0048

<math>~P</math>

Pressure;    units of "force/area" or "energy/volume"

VAR_Pressure01

x0050

<math>~\epsilon</math>

Specific internal energy;    units of "energy/mass" or "velocity-squared"

VAR_SpecificInternalEnergy01

x03B5

<math>~s</math>

Specific entropy;

VAR_SpecificEntropy01

x0073

<math>~t</math>

Time

VAR_Time01

x0074

<math>~T</math>

Temperature;    units of "Kelvin"

VAR_Temperature01

x0054

<math>~\vec{v}</math>

Euclidean 3-space velocity vector;    units of "length/time"

VAR_VelocityVector01

 

<math>~\vec{x}</math>

Euclidean 3-space position vector

VAR_PositionVector01

 

Model Parameters:

<math>~\gamma_\mathrm{g}</math>

Adiabatic Index (or Ratio of Specific Heats); dimensionless    Wikipedia Discussion

MP_AdiabaticIndex

 

<math>~\bar{\mu}</math>

Mean molecular weight; dimensionless;    defined such that <math>~\bar{\mu}</math> = <math>~\rho</math>/(<math>~m_u</math><math>~n_g</math> ).

MP_MeanMolecularWeight

x03BC

<math>~\mu_e</math>

Molecular weight of electrons; dimensionless;
defined such that <math>~\mu_e</math> = <math>~\rho</math>/(<math>~m_u</math> <math>N_e</math>), where <math>N_e</math> is the number density of electrons.

MP_ElectronMolecularWeight

x03BC

<math>~n</math>

Polytropic Index; dimensionless    Wikipedia Discussion

MP_PolytropicIndex

x006E

<math>~K_\mathrm{n}</math>

Polytropic Constant; dimensions depend on choice of <math>~n</math>    Wikipedia Discussion

MP_PolytropicConstant

 

 

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
|   H_Book Home   |   YouTube   |
Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS |
Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation