User:Tohline/Appendix/Variables templates

Physical Constants, Variables, and Model Parameters

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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): Chandraskehar, S. (1967) An Introduction to the Study of Stellar Structure (New York: Dover)	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): Chandraskehar, S. (1967) An Introduction to the Study of Stellar Structure (New York: Dover)	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

 

© 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