Editing Equation of state (section)

=== Jones–Wilkins–Lee equation of state for explosives (JWL equation) ===

The equation of state from Jones–Wilkins–Lee is used to describe the detonation products of explosives.
<math display="block">p = A \left( 1 - \frac{\omega}{R_1 V} \right) \exp(-R_1 V) + B \left( 1 - \frac{\omega}{R_2 V} \right) \exp\left(-R_2 V\right) + \frac{\omega e_0}{V}</math>

The ratio <math> V = \rho_e / \rho </math> is defined by using <math> \rho_e </math>, which is the density of the explosive (solid part) and <math> \rho </math>, which is the density of the detonation products. The parameters <math> A </math>, <math> B </math>, <math> R_1 </math>, <math> R_2 </math> and <math> \omega </math> are given by several references.<ref name="Dobratz">{{Cite journal |author1=B. M. Dobratz |author2=P. C. Crawford | year=1985 | title=LLNL Explosives Handbook: Properties of Chemical Explosives and Explosive Simulants|journal=Ucrl-52997 |url=https://ci.nii.ac.jp/naid/10012469501/|access-date = 31 August 2018}}</ref> In addition, the initial density (solid part) <math> \rho_0 </math>, speed of detonation <math> V_D </math>, Chapman–Jouguet pressure <math> P_{CJ} </math> and the chemical energy per unit volume of the explosive <math> e_0 </math> are given in such references. These parameters are obtained by fitting the JWL-EOS to experimental results.  Typical parameters for some explosives are listed in the table below.
{| class="wikitable centre"
!  Material !! <math>\rho_e\,</math> (g/cm<sup>3</sup>) !! <math>v_D\,</math> (m/s) !! <math>p_{CJ}\,</math> (GPa) !! <math>A\,</math> (GPa) !! <math>B\,</math> (GPa) !! <math>R_1</math> !! <math>R_2</math> !! <math>\omega</math> !! <math>e_0\,</math> (GPa)
|- 
|[[Trinitrotoluene|TNT]] || 1.630 || 6930 || 21.0 || 373.8 || 3.747 || 4.15 || 0.90 || 0.35 || 6.00 
|-
|[[Composition B]] || 1.717 || 7980 || 29.5 || 524.2 || 7.678 || 4.20 || 1.10 || 0.35 || 8.50
|-
| [[Polymer-bonded explosive|PBX 9501]]<ref name="Wilkins">{{Citation|last=Wilkins|first=Mark L.|title=Computer Simulation of Dynamic Phenomena| publisher=Springer|year=1999|page=80|url=https://books.google.com/books?id=b3npCAAAQBAJ&pg=PA1|access-date = 31 August 2018 |isbn=9783662038857}}</ref> || 1.844 || || 36.3 || 852.4 || 18.02 || 4.55 || 1.3 || 0.38 || 10.2
|}