In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an existence and uniqueness result for the short-term and mean-term models. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the short-term model is homogenized.35K65 (Degenerate parabolic equations); 35B25 (Singular perturbations); 35B40 (Asymptotic behavior of solutions); 35B10 (Periodic solutions); 92F05 (Other natural sciences [Sedimentology]); 86A60 (Geological problems).

In this paper we consider models built in [3] for short-term, mean-term and long-term morphodynamics of dunes and megariples. We give an existence and uniqueness result for long term dynamics of dunes. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the mean-term and long-term models are homogenized. 1

The generalized oscillator strengths (GOS) of the argon transitions 3p6−3p5(3d, 4d, 5d) and 3p6−3p54f respectively for multiple strengths and are determined using the wavefunctions which have been generated from the CIV3 code of Hibbert. Calculations of these generalized oscillator strengths, as a function of momentum transfer, are also carried out respectively in the configuration interaction method and in the random phase approximation with exchange. The length and velocity forms have been used in this work. The gap between the absolute values of the generalized oscillator strength obtained in the theoretical calculations and those of the experimental results of Zhu et al have been noticeably reduced in the present work for the octupole excitations to 3p5(3d, 4d). This is due to the configuration interaction wavefunctions. The profiles and the positions of the extrema in the generalized oscillator strength have also received particular attention in the evaluation. The results of length and velocity form studies also show that the electron correlation effects are very significant for the excitations to 3p5(3d, 4d) but are found to have no great influence in the positions of the extrema.

The quadrupole, monopole and dipole generalized oscillator strengths (GOSs) as a function of momentum transfer are respectively calculated for these 3p 6 →3p 5 (4p, 5p, 6p) and 3p 6 →3p 5 (4s, 5s, 6s) transitions. Configuration interaction (CI) and random phase approximation with exchange (RPAE) methods are used in the determination of these GOS, in the length and velocity forms. The code of Hibbert has been used to generate the wavefunctions from which a partial of argon GOSs are been computed. The present work has reduced the gap between the absolute values of the theoretical calculations of GOSs and those of the experimental results of Zhu et al for the quadrupole excitations to 3p 5 (4p, 5p). The profile of our quadrupole GOS 3p 6 →3p 5 5p transition agrees well with the experimental result of Zhu. The best agreement (0.7%) is observed between the (length) first maximum position and the experimental one for the quadrupole GOS 3p 6 →3p 5 4p transition. The present velocity GOS minimum position for the dipole excitation in 3p 6 →3p 5 4s and the calculated velocity GOS maximum position of the monopole 3p 6 →3p 5 4p transition are in good agreement with the experimental observations (differences of 1.82% and 3.08%, respectively). Correlation effects decrease with increasing of the excited state principal quantum number and have no great influence on the extrema positions.

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