The atmospheric ion rate ionization is explicitly obtained for 40°N, 60°N and 80°N latitudes.
Since the gas-kinetic scheme uses a continuous gas distribution function at a cell interface for the fluxes evaluation, the moments of a gas distribution function can be explicitly obtained for the multiple temperature model.
The strong and mean-square convergence rates are explicitly obtained.
For four physical cases, closed-form coupled magneto-electro-elastic field variables in the space are explicitly obtained.
The curve is explicitly obtained from Eq. (8), with (b=cos alpha).
(57) Furthermore, the approximation of the time derivative can be computed as Du_{r}(t) =sum _{j=0}^{K}a_{r,j}Dbigl(P^{(alpha_{3},beta_{3})}_{T,j}(t) bigr),quad r=1,ldots, R, (58) where the time derivative, (D(P^{(alpha_{3},beta_{3})}_{T,j}(t))), can be explicitly obtained by using (3) for (q=1), with a direct calculation at the points (t^{(alpha_{3},beta_{3})}_{T,K,i}).
Such energy allocation can be explicitly obtained as follows [1].
These expressions have been explicitly obtained [14, 15] to give (17).
The direct ionization by various primary cosmic ray nuclei is explicitly obtained.
The contribution of different cascade components, namely electromagnetic, hadron and muon is explicitly obtained.
