Comoving frame

We consider the non-LTE spectral formation in a spherically expanding atmosphere. The velocity field v(r) is specified in its supersonic part by the usual analytical law with the parameters y, (final velocity) and the exponent 8=1, The temperature structure is derived from the assumption of radiative equilibrium, but only approximately evaluated for the grey LTE case. The atmosphere is assumed to consist of pure helium. The model atom has a total of 28 energy levels, among these 17 levels of He I. The line radiation transfer is treated in the "comoving frame". 

The equations for the moments (frequency integrated) are, in the comoving frame (Castor 1972) ... 

Keywords Planck system of units, L-regions (local regions), O-regions (observable regions), comoving frame, Second Law of Thermodynamics, heat death, Planck power versus heat death, low-entropy boundary conditions versus heat death, kinetic versus thermodynamic control, kinetic control versus heat death, minimal Boltzmann brains, extraordinary observers. 

In the case of localized losses we treat them as discontinuities of the energy, momentum and particle number fluxes at the shock front, which are characterized by three parameters e, 5, r/ equal to the fractions of corresponding fluxes lost at the shock front in the front comoving frame. We obtain the following expressions for the pressure p2, number density n2 and the Lorentz factor 72 immediately behind the shock front ... 

Reducing the solution of the convection-diffusion equation for the concentration field to a ID problem in the comoving frame-of-reference clearly reaches its limits if the fluid lamellae get deformed and are no longer arranged in parallel. Such a situation may occur if the channel depth is not small compared to its width and the design comprises a sudden expansion or contraction of the flow... 

On the infinite axis, this equation (with = const) has a solution steadily propagating with a speed dependent on /x, and satisfying the stationary equation in the comoving frame... 

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