Compute collision part of fluid equations. More...

Public Member Functions
subroutine	inter_ions (a_diff, Pr_diff, a_th_ions, Pr_th_ions)
	Collision for ionic and neutral diffusion and energy equation. More...

subroutine	inter_elec (Lo_qe, Pr_qe, a_th_elec, Pr_th_elec, chauffage)
	Collision for electronic energy equation. More...

Detailed Description

Compute collision part of fluid equations.

Member Function/Subroutine Documentation

subroutine echanges::inter_elec	(	real*8, dimension(2,2)	Lo_qe,
		real*8, dimension(2)	Pr_qe,
		real*8, dimension(2,2)	a_th_elec,
		real*8, dimension(2)	Pr_th_elec,
		real*8	chauffage
	)

Collision for electronic energy equation.

Author

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subroutine echanges::inter_ions	(	real*8, dimension(:,:)	a_diff,
		real*8, dimension(:)	Pr_diff,
		real*8, dimension(:,:)	a_th_ions,
		real*8, dimension(:)	Pr_th_ions
	)

Collision for ionic and neutral diffusion and energy equation.

Author: For more details about derivation of each terms, cf Collision page.

Collision terms ions → ions.

Terme $ u_j$ → $u_i$ :

$\begin{equation} \left(\nu_{ij} + \nu_{ie}compo_j\right)\frac{C_j}{C_i}\end{equation}$

Terme $ u_j$ → $u_i$ : Polarisation

Terme 1 $u_j$ → $\gamma_i^{\parallel }$ :

$\begin{equation}t_i\left(A^{c0p}_{ij}\nu_{ij} + A^{c0p}_{ie}\nu_{ie}compo_j\right)\frac{C_j}{C_i}\frac{1}{q^{p0}_i}\end{equation}$

Terme 1 $u_j$ → $\gamma_i^{\perp }$ :

$\begin{equation}t_i\left(A^{c0t}_{ij}\nu_{ij} + A^{c0t}_{ie}\nu_{ie}compo_j\right)\frac{C_j}{C_i}\frac{1}{q^{t0}_i}\end{equation}$

Terme 2 $u_j$ → $\gamma_i^{\parallel }$ :

$\begin{equation}-3t_i^{\parallel }(\nu_{ij}+\nu_{ie}compo_j)\frac{C_j}{C_i}\frac{1}{q^{p0}_i}\end{equation}$

Terme 2 $u_j$ → $\gamma_i^{\perp }$ :

$\begin{equation}- t_i^{\perp }(\nu_{ij}+\nu_{ie}compo_j)\frac{C_j}{C_i}\frac{1}{q^{t0}_i}\end{equation}$

Terme $\gamma_j^{\parallel }$ → $u_i$ :

$\begin{equation}-\frac{1}{2} z_{ij}\frac{m_i}{m_i+m_j}\nu_{ij}\frac{1}{t_{ij}}\frac{C_j}{C_i}q^{p0}_j\end{equation}$

Terme $\gamma_j^{\parallel }$ → $u_i$ :

$\begin{equation}- z_{ij}\frac{m_i}{m_i+m_j}\nu_{ij}\frac{1}{t_{ij}}\frac{C_j}{C_i}q^{t0}_j\end{equation}$

Terme $\gamma_j^{\parallel }$ → $u_i$ : Polarisation Terme $\gamma_j^{\perp }$ → $u_i$ : Polarisation

Terme $\gamma_j^{\parallel }$ → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(D^{c4pp}_{ij}\nu_{ij}+\frac{3}{2} t_i^{\parallel }z_{ij}\frac{m_i}{m_i+m_j}\nu_{ij}\frac{1}{t_{ij}}\right)\frac{C_jq^{p0}_j}{C_iq^{p0}_i}\end{equation}$

Terme $\gamma_j^{\perp }$ → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(D^{c4pt}_{ij}\nu_{ij}+3 t_i^{\parallel }z_{ij}\frac{m_i}{m_i+m_j}\nu_{ij}\frac{1}{t_{ij}}\right)\frac{C_jq^{t0}_j}{C_iq^{p0}_i}\end{equation}$

Terme $\gamma_j^{\parallel }$ → $\gamma_i^{\perp }$ :

$\begin{equation}\left(D^{c4tp}_{ij}\nu_{ij}+\frac{1}{2} t_i^{\perp }z_{ij}\frac{m_i}{m_i+m_j}\nu_{ij}\frac{1}{t_{ij}}\right)\frac{C_jq^{p0}_j}{C_iq^{t0}_i}\end{equation}$

Terme $\gamma_j^{\perp }$ → $\gamma_i^{\perp }$ :

$\begin{equation}\left(D^{c4tt}_{ij}\nu_{ij}+ t_i^{\perp }z_{ij}\frac{m_i}{m_i+m_j}\nu_{ij}\frac{1}{t_{ij}}\right)\frac{C_jq^{t0}_j}{C_iq^{t0}_i}\end{equation}$

Terme $\gamma_e$ → $u_i$ :

$\begin{equation}-z_{ie}\frac{m_i}{m_i+m_e}\nu_{ie}\frac{1}{t_{ie}}\frac{C_e}{C_i}\frac{q_e}{n_e}\end{equation}$

Terme $\gamma_e^{\parallel }$ → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(D^{c4pp}_{ie}\nu_{ie}-\frac{3}{2} t_i^{\parallel }z_{ie}\frac{m_i}{m_i+m_e}\nu_{ie}\frac{1}{t_{ie}}\right)\frac{C_e}{C_i}\frac{1}{q^{p0}_i}\frac{q_e^{\parallel }}{n_e}\end{equation}$

Terme $\gamma_e^{\perp }$ → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(D^{c4pt}_{ie}\nu_{ie}-3 t_i^{\parallel }z_{ie}\frac{m_i}{m_i+m_e}\nu_{ie}\frac{1}{t_{ie}}\right)\frac{C_e}{C_i}\frac{1}{q^{p0}_i}\frac{q_e^{\perp }}{n_e}\end{equation}$

Terme $\gamma_e^{\parallel }$ → $\gamma_i^{\perp }$ :

$\begin{equation}\left(D^{c4tp}_{ie}\nu_{ie}-\frac{1}{2} t_i^{\perp }z_{ie}\frac{m_i}{m_i+m_e}\nu_{ie}\frac{1}{t_{ie}}\right)\frac{C_e}{C_i}\frac{1}{q^{t0}_i}\frac{q_e^{\parallel }}{n_e}\end{equation}$

Terme $\gamma_e^{\perp }$ → $\gamma_i^{\perp }$ :

$\begin{equation}\left(D^{c4tt}_{ie}\nu_{ie}- t_i^{\perp }z_{ie}\frac{m_i}{m_i+m_e}\nu_{ie}\frac{1}{t_{ie}}\right)\frac{C_e}{C_i}\frac{1}{q^{t0}_i}\frac{q_e^{\perp }}{n_e}\end{equation}$

Terme $u_i$ → $u_i$ :

$\begin{equation} -\sum_n \nu_{in} -\sum_{j \neq i} \nu_{ij} -\nu_{ie} + \nu_{ie} compo_i\end{equation}$

Terme $u_i$ → $u_i$ : Polarisation

Terme 1 $u_i$ → $\gamma_i^{\parallel }$ :

$\begin{equation}-t_i\left(\sum_{j \neq i} A^{c0p}_{ij}\nu_{ij} + \sum_{n}A^{m0p}_{in}\nu_{in} + A^{c0p}_{ie}\nu_{ie} - A^{c0p}_{ie}\nu_{ie}compo_i\right)\frac{1}{q^{p0}_i}\end{equation}$

Terme 1 $u_i$ → $\gamma_i^{\perp }$ :

$\begin{equation}-t_i\left(\sum_{j \neq i} A^{c0t}_{ij}\nu_{ij} + \sum_{n}A^{m0t}_{in}\nu_{in} + A^{c0t}_{ie}\nu_{ie} - A^{c0t}_{ie}\nu_{ie}compo_i\right)\frac{1}{q^{t0}_i}\end{equation}$

Terme 2 $u_i$ → $\gamma_i^{\parallel }$ :

$\begin{equation}3t^{\parallel }_i\left(\sum_n\nu_{in} + \sum_{j\neq i}\nu_{ij} + \nu_{ie} - \nu_{ie}compo_i\right)\frac{1}{q^{p0}_i}\end{equation}$

Terme 2 $u_i$ → $\gamma_i^{\perp }$ :

$\begin{equation} t^{\perp }_i\left(\sum_n\nu_{in} + \sum_{j\neq i}\nu_{ij} + \nu_{ie} - \nu_{ie}compo_i\right)\frac{1}{q^{t0}_i}\end{equation}$

Terme $\gamma_i^{\parallel }$ → $u_i$ :

$\begin{equation} \frac{1}{2} \left( \sum_n z_{in}\nu_{in}\frac{m_n}{m_i+m_n}\frac{1}{t_{in}} + \sum_{j \neq i}z_{ij}\nu_{ij}\frac{m_j}{m_i+m_j}\frac{1}{t_{ij}} + z_{ie}\nu_{ie}\frac{m_e}{m_i+m_e}\frac{1}{t_{ie}}\right)q^{p0}_i\end{equation}$

Terme $\gamma_i^{\perp }$ → $u_i$ :

$\begin{equation} \left( \sum_n z_{in}\nu_{in}\frac{m_n}{m_i+m_n}\frac{1}{t_{in}} + \sum_{j \neq i}z_{ij}\nu_{ij}\frac{m_j}{m_i+m_j}\frac{1}{t_{ij}} + z_{ie}\nu_{ie}\frac{m_e}{m_i+m_e}\frac{1}{t_{ie}}\right)q^{t0}_i\end{equation}$

Terme $\gamma_i^{\parallel }$ → $u_i$ : Polarisation Terme $\gamma_i^{\perp }$ → $u_i$ : Polarisation

Terme $\gamma_i^{\parallel }$ → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(\sum_j D^{c1pp}_{ij}\nu_{ij} + \sum_n D^{m1pp}_{in}\nu_{in} + D^{c4pp}\nu_{ii} - \frac{3}{2} t_i^{\parallel }\left(\sum_n z_{in}\frac{m_n}{m_i+m_n}\nu_{in}\frac{1}{t_{in}} + \sum_{j \neq i}z_{ij}\nu_{ij}\frac{m_j}{m_i+m_j}\frac{1}{t_{ij}}\right)\right)\end{equation}$

Terme $\gamma_i^{\perp }$ → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(\sum_j D^{c1pt}_{ij}\nu_{ij} + \sum_n D^{m1pt}_{in}\nu_{in} + D^{c4pt}\nu_{ii} - 3 t_i^{\parallel }\left(\sum_n z_{in}\frac{m_n}{m_i+m_n}\nu_{in}\frac{1}{t_{in}} + \sum_{j \neq i}z_{ij}\nu_{ij}\frac{m_j}{m_i+m_j}\frac{1}{t_{ij}}\right)\right)\frac{q^{t0}_i}{q^{p0}_i}\end{equation}$

Terme $\gamma_i^{\parallel }$ → $\gamma_i^{\perp }$ :

$\begin{equation}\left(\sum_j D^{c1tp}_{ij}\nu_{ij} + \sum_n D^{m1tp}_{in}\nu_{in} + D^{c4tp}\nu_{ii} - \frac{1}{2} t_i^{\perp }\left(\sum_n z_{in}\frac{m_n}{m_i+m_n}\nu_{in}\frac{1}{t_{in}} + \sum_{j \neq i}z_{ij}\nu_{ij}\frac{m_j}{m_i+m_j}\frac{1}{t_{ij}}\right)\right)\frac{q^{p0}_i}{q^{t0}_i}\end{equation}$

Terme $\gamma_i^{\perp }$ → $\gamma_i^{\perp }$ :

$\begin{equation}\left(\sum_j D^{c1tt}_{ij}\nu_{ij} + \sum_n D^{m1tt}_{in}\nu_{in} + D^{c4tt}\nu_{ii} - t_i^{\perp }\left(\sum_n z_{in}\frac{m_n}{m_i+m_n}\nu_{in}\frac{1}{t_{in}} + \sum_{j \neq i}z_{ij}\nu_{ij}\frac{m_j}{m_i+m_j}\frac{1}{t_{ij}}\right)\right)\end{equation}$

Collision terms neutrals → ions.

Terme $u_p$ not solved → $u_i$ :

$\begin{equation}\sum_p \nu_{ip}u_p\frac{C_p}{C_i}\end{equation}$

Terme $u_p$ not solved → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(t_i\sum_p A^{m0p}_{ip}\nu_{ip}u_p - 3t^{\parallel }_i\sum_p \nu_{ip}u_p\right)\frac{C_p}{C_i}\frac{1}{q^{p0}_i}\end{equation}$

Terme $u_p$ not solved → $\gamma_i^{\perp }$ :

$\begin{equation}\left(t_i\sum_p A^{m0t}_{ip}\nu_{ip}u_p - t^{\perp }_i\sum_p \nu_{ip}u_p\right)\frac{C_p}{C_i}\frac{1}{q^{t0}_i}\end{equation}$

Terme $u_n$ → $u_i$ :

$\begin{equation} \nu_{in}\frac{C_n}{C_i}\end{equation}$

Terme $u_n$ → $u_i$ : Polarisation

Terme $u_n$ → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(t_iA^{m0p}_{in}\nu_{in}-3t^{\parallel }_i\nu_{in}\right)\frac{C_n}{C_i}\frac{1}{q^{p0}_i}\end{equation}$

Terme $u_n$ → $\gamma_i^{\perp }$ :

$\begin{equation}\left(t_iA^{m0t}_{in}\nu_{in}- t^{\perp }_i\nu_{in}\right)\frac{C_n}{C_i}\frac{1}{q^{t0}_i}\end{equation}$

Terme $\gamma_n^{\parallel }$ → $u_i$ :

$\begin{equation} -\frac{1}{2} z_{in}\frac{m_i}{m_i+m_n}\nu_{in}\frac{1}{t_{in}}\frac{C_n}{C_i}q^{p0}_n\end{equation}$

Terme $\gamma_n^{\perp }$ → $u_i$ :

$\begin{equation} - z_{in}\frac{m_i}{m_i+m_n}\nu_{in}\frac{1}{t_{in}}\frac{C_n}{C_i}q^{t0}_n\end{equation}$

Terme $\gamma_n^{\parallel }$ → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(D^{m4pp}_{in}\nu_{in} + \frac{3}{2} t_i^{\parallel }z_{in}\frac{m_i}{m_i+m_n}\nu_{in}\frac{1}{t_{in}}\right)\frac{C_nq^{p0}_n}{C_iq^{p0}_i}\end{equation}$

Terme $\gamma_n^{\perp }$ → $\gamma_i^{\parallel }$ :

$\begin{equation}\left(D^{m4pt}_{in}\nu_{in} + 3 t_i^{\parallel }z_{in}\frac{m_i}{m_i+m_n}\nu_{in}\frac{1}{t_{in}}\right)\frac{C_nq^{t0}_n}{C_iq^{p0}_i}\end{equation}$

Terme $\gamma_n^{\parallel }$ → $\gamma_i^{\perp }$ :

$\begin{equation}\left(D^{m4tp}_{in}\nu_{in} + \frac{1}{2} t_i^{\perp }z_{in}\frac{m_i}{m_i+m_n}\nu_{in}\frac{1}{t_{in}}\right)\frac{C_nq^{p0}_n}{C_iq^{t0}_i}\end{equation}$

Terme $\gamma_n^{\perp }$ → $\gamma_i^{\perp }$ :

$\begin{equation}\left(D^{m4tt}_{in}\nu_{in} + t_i^{\perp }z_{in}\frac{m_i}{m_i+m_n}\nu_{in}\frac{1}{t_{in}}\right)\frac{C_nq^{t0}_n}{C_iq^{t0}_i}\end{equation}$

Collision terms ions → neutrals.

Terme $ u_i$ → $u_n$ :

$\begin{equation} \left(\nu_{ni} + \nu_{ne}compo_i\right)\frac{C_i}{C_n}\end{equation}$

Terme $\gamma_i^{\parallel }$ → $u_n$ :

$\begin{equation} -\frac{1}{2} z_{ni}\frac{m_n}{m_i+m_n}\nu_{ni}\frac{1}{t_{in}}\frac{C_i}{C_n}q^{p0}_i\end{equation}$

Terme $\gamma_i^{\perp }$ → $u_n$ :

$\begin{equation} - z_{ni}\frac{m_n}{m_i+m_n}\nu_{ni}\frac{1}{t_{in}}\frac{C_i}{C_n}q^{t0}_i\end{equation}$

Terme 1 $u_i$ → $\gamma_n^{\parallel }$ :

$\begin{equation}t_n\left(A^{m0p}_{in}\nu_{ni} + A^{m0p}_{en}\nu_{ne}compo_i\right)\frac{C_i}{C_n}\frac{1}{q^{p0}_n}\end{equation}$

Terme 1 $u_i$ → $\gamma_n^{\perp }$ :

$\begin{equation}t_n\left(A^{m0t}_{in}\nu_{ni} + A^{m0t}_{en}\nu_{ne}compo_i\right)\frac{C_i}{C_n}\frac{1}{q^{t0}_n}\end{equation}$

Terme 2 $u_i$ → $\gamma_n^{\parallel }$ :

$\begin{equation}-3t_n^{\parallel }(\nu_{ni}+\nu_{ne}compo_i)\frac{C_i}{C_n}\frac{1}{q^{p0}_n}\end{equation}$

Terme 2 $u_i$ → $\gamma_n^{\perp }$ :

$\begin{equation}-3t_n^{\perp }(\nu_{ni}+\nu_{ne}compo_i)\frac{C_i}{C_n}\frac{1}{q^{t0}_n}\end{equation}$

Terme $\gamma_i^{\parallel }$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(D^{m4pp}_{in}\nu_{ni} + \frac{3}{2} t_n^{\parallel }z_{in}\frac{m_i}{m_i+m_n}\nu_{ni}\frac{1}{t_{in}}\right)\frac{C_iq^{p0}_i}{C_nq^{p0}_n}\end{equation}$

Terme $\gamma_i^{\perp }$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(D^{m4pt}_{in}\nu_{ni} + 3 t_n^{\parallel }z_{in}\frac{m_i}{m_i+m_n}\nu_{ni}\frac{1}{t_{in}}\right)\frac{C_iq^{t0}_i}{C_nq^{p0}_n}\end{equation}$

Terme $\gamma_i^{\parallel }$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(D^{m4tp}_{in}\nu_{ni} + \frac{1}{2} t_n^{\perp }z_{in}\frac{m_i}{m_i+m_n}\nu_{ni}\frac{1}{t_{in}}\right)\frac{C_iq^{p0}_i}{C_nq^{t0}_n}\end{equation}$

Terme $\gamma_i^{\perp }$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(D^{m4tt}_{in}\nu_{ni} + t_n^{\perp }z_{in}\frac{m_i}{m_i+m_n}\nu_{ni}\frac{1}{t_{in}}\right)\frac{C_iq^{t0}_i}{C_nq^{t0}_n}\end{equation}$

Terme $\gamma_e$ → $u_n$ :

$\begin{equation}-z_{ne}\frac{m_n}{m_n+m_e}\nu_{ne}\frac{1}{t_{ne}}\frac{C_e}{C_n}\frac{q_e}{n_e}\end{equation}$

Terme $\gamma_e^{\parallel }$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(D^{m4pp}_{ne}\nu_{ne} + \frac{3}{2} t_n^{\parallel }z_{ne}\frac{m_n}{m_n+m_e}\nu_{ne}\frac{1}{t_{ne}}\right)\frac{C_e}{C_n}\frac{1}{q^{p0}_n}\frac{q_e^{\parallel }}{n_e}\end{equation}$

Terme $\gamma_e^{\perp }$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(D^{m4pt}_{ne}\nu_{ne} + 3 t_n^{\parallel }z_{ne}\frac{m_n}{m_n+m_e}\nu_{ne}\frac{1}{t_{ne}}\right)\frac{C_e}{C_n}\frac{1}{q^{p0}_n}\frac{q_e^{\perp }}{n_e}\end{equation}$

Terme $\gamma_e^{\parallel }$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(D^{m4tp}_{ne}\nu_{ne} + \frac{1}{2} t_n^{\perp }z_{ne}\frac{m_n}{m_n+m_e}\nu_{ne}\frac{1}{t_{ne}}\right)\frac{C_e}{C_n}\frac{1}{q^{t0}_n}\frac{q_e^{\parallel }}{n_e}\end{equation}$

Terme $\gamma_e^{\perp }$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(D^{m4tt}_{ne}\nu_{ne} + t_n^{\perp }z_{ne}\frac{m_n}{m_n+m_e}\nu_{ne}\frac{1}{t_{ne}}\right)\frac{C_e}{C_n}\frac{1}{q^{t0}_n}\frac{q_e^{\perp }}{n_e}\end{equation}$

Collision terms neutrals → neutrals.

Terme $u_m$ → $u_n$ :

$\begin{equation} \nu_{nm}\frac{C_m}{C_n}\end{equation}$

Terme $\gamma_m^{\parallel }$ → $u_n$ :

$\begin{equation} -\frac{1}{2} z_{nm}\frac{m_n}{m_n+m_m}\nu_{nm}\frac{1}{t_{nm}}\frac{C_m}{C_n}q^{p0}_m\end{equation}$

Terme $\gamma_m^{\perp }$ → $u_n$ :

$\begin{equation} - z_{nm}\frac{m_n}{m_n+m_m}\nu_{nm}\frac{1}{t_{nm}}\frac{C_m}{C_n}q^{p0}_m\end{equation}$

Terme $u_m$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(t_nA^{n0p}_{nm}\nu_{nm} - 3t_n^{\parallel }\nu_{nm}\right)\frac{C_m}{C_n}\frac{1}{q^{p0}_n}\end{equation}$

Terme $u_m$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(t_nA^{n0t}_{nm}\nu_{nm} - t_n^{\perp }\nu_{nm}\right)\frac{C_m}{C_n}\frac{1}{q^{p0}_n}\end{equation}$

Terme $\gamma_m^{\parallel }$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(D^{n4pp}_{nm}\nu_{nm} + \frac{3}{2} t_n^{\parallel }z_{nm}\frac{m_n}{m_n+m_m}\nu_{nm}\frac{1}{t_{nm}}\right)\frac{C_mq^{p0}_m}{C_nq^{p0}_n}\end{equation}$

Terme $\gamma_m^{\perp }$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(D^{n4pt}_{nm}\nu_{nm} + 3 t_n^{\parallel }z_{nm}\frac{m_n}{m_n+m_m}\nu_{nm}\frac{1}{t_{nm}}\right)\frac{C_mq^{t0}_m}{C_nq^{p0}_n}\end{equation}$

Terme $\gamma_m^{\parallel }$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(D^{n4tp}_{nm}\nu_{nm} + \frac{1}{2} t_n^{\perp }z_{nm}\frac{m_n}{m_n+m_m}\nu_{nm}\frac{1}{t_{nm}}\right)\frac{C_mq^{p0}_m}{C_nq^{t0}_n}\end{equation}$

Terme $\gamma_m^{\perp }$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(D^{n4tt}_{nm}\nu_{nm} + t_n^{\perp }z_{nm}\frac{m_n}{m_n+m_m}\nu_{nm}\frac{1}{t_{nm}}\right)\frac{C_mq^{t0}_m}{C_nq^{t0}_n}\end{equation}$

Terme $u_n$ → $u_n$ :

$\begin{equation} -\sum_i \nu_{ni} -\sum_{m \neq n} \nu_{nm}\end{equation}$

Terme $u_n$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(t_n\left(-\sum_{m \neq n} A^{n0p}_{nm}\nu_{nm} - \sum_jA^{m0p}_{in}\nu_{ni}\right) - 3t^{\parallel }_n\left(-\sum_j(\nu_{ni} + \nu_{ne}compo_i) - \sum_{m\neq n}\nu_{nm}\right)\right)\frac{1}{q^{p0}_n}\end{equation}$

Terme $u_n$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(t_n\left(-\sum_{m \neq n} A^{n0p}_{nm}\nu_{nm} - \sum_jA^{m0t}_{in}\nu_{ni}\right) - t^{\perp }_n\left(-\sum_j(\nu_{ni} + \nu_{ne}compo_i) - \sum_{m\neq n}\nu_{nm}\right)\right)\frac{1}{q^{t0}_n}\end{equation}$

Terme $\gamma_n^{\parallel }$ → $u_n$ :

$\begin{equation} \frac{1}{2} \left( \sum_{m \neq n} z_{nm}\nu_{nm}\frac{m_m}{m_n+m_m}\frac{1}{t_{nm}} + \sum_i z_{ni}\nu_{ni}\frac{m_i}{m_i+m_n}\frac{1}{t_{in}}\right)q^{p0}_n\end{equation}$

Terme $\gamma_n^{\perp }$ → $u_n$ :

$\begin{equation} \left( \sum_{m \neq n} z_{nm}\nu_{nm}\frac{m_m}{m_n+m_m}\frac{1}{t_{nm}} + \sum_i z_{ni}\nu_{ni}\frac{m_i}{m_n+m_i}\frac{1}{t_{in}}\right)q^{t0}_n\end{equation}$

Terme $\gamma_n^{\parallel }$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(\sum_j D^{m1pp}_{jn}\nu_{nj} + \sum_m D^{n1pp}_{nm}\nu_{nm} + D^{n4pp}_{nn}\nu_{nn} - \frac{3}{2} t_n^{\parallel }\left(\sum_j z_{nj}\frac{m_j}{m_n+m_j}\nu_{nj}\frac{1}{T_{nj}} + \sum_{m \neq n}z_{nm}\nu_{nm}\frac{m_m}{m_n+m_m}\frac{1}{t_{nm}}\right)\right)\end{equation}$

Terme $\gamma_n^{\perp }$ → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(\sum_j D^{m1pt}_{jn}\nu_{nj} + \sum_m D^{n1pt}_{nm}\nu_{nm} + D^{n4pt}_{nn}\nu_{nn} - \frac{3}{2} t_n^{\parallel }\left(\sum_j z_{nj}\frac{m_j}{m_n+m_j}\nu_{nj}\frac{1}{T_{nj}} + \sum_{m \neq n}z_{nm}\nu_{nm}\frac{m_m}{m_n+m_m}\frac{1}{t_{nm}}\right)\right)\frac{q^{t0}_n}{q^{p0}_n}\end{equation}$

Terme $\gamma_n^{\parallel }$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(\sum_j D^{m1tp}_{jn}\nu_{nj} + \sum_m D^{n1tp}_{nm}\nu_{nm} + D^{n4tp}_{nn}\nu_{nn} - \frac{3}{2} t_n^{\perp }\left(\sum_j z_{nj}\frac{m_j}{m_n+m_j}\nu_{nj}\frac{1}{T_{nj}} + \sum_{m \neq n}z_{nm}\nu_{nm}\frac{m_m}{m_n+m_m}\frac{1}{t_{nm}}\right)\right)\frac{q^{p0}_n}{q^{t0}_n}\end{equation}$

Terme $\gamma_n^{\perp }$ → $\gamma_n^{\perp }$ :

$\begin{equation}\left(\sum_j D^{m1tt}_{jn}\nu_{nj} + \sum_m D^{n1tt}_{nm}\nu_{nm} + D^{n4tt}_{nn}\nu_{nn} - \frac{3}{2} t_n^{\perp }\left(\sum_j z_{nj}\frac{m_j}{m_n+m_j}\nu_{nj}\frac{1}{T_{nj}} + \sum_{m \neq n}z_{nm}\nu_{nm}\frac{m_m}{m_n+m_m}\frac{1}{t_{nm}}\right)\right)\end{equation}$

Terme $u_p$ not solved → $u_n$ :

$\begin{equation}\sum_p \nu_{np}u_p\frac{C_p}{C_n}\end{equation}$

Terme $u_p$ not solved → $\gamma_n^{\parallel }$ :

$\begin{equation}\left(\sum_p A^{n0p}_{ip}\nu_{np}u_p - 3t^{\parallel }_n\sum_p \nu_{np}u_p\right)\frac{C_p}{C_n}\end{equation}$

Terme $u_p$ not solved → $\gamma_n^{\perp }$ :

$\begin{equation}\left(\sum_p A^{n0t}_{ip}\nu_{np}u_p - t^{\perp }_n\sum_p \nu_{np}u_p\right)\frac{C_p}{C_n}\end{equation}$

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The documentation for this module was generated from the following file:

dir.module/echanges.f90

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