Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field - Volume 18 Issue 2 - Emmanuel Frénod, Sever A. Hirstoaga, Mathieu Lutz, Eric Sonnendrücker

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.

Generative artificial intelligence methods are employed for the first time to construct a surrogate model for plasma turbulence that enables long-time transport simulations. The proposed GAIT (Generative Artificial Intelligence Turbulence) model is based on the coupling of a convolutional variational autoencoder that encodes precomputed turbulence data into a reduced latent space, and a recurrent neural network and decoder that generate new turbulence states 400 times faster than the direct numerical integration. The model is applied to the Hasegawa-Wakatani (HW) plasma turbulence model, which is closely related to the quasigeostrophic model used in geophysical fluid dynamics. Very good agreement is found between the GAIT and the HW models in the spatiotemporal Fourier and Proper Orthogonal Decomposition spectra, and the flow topology characterized by the Okubo-Weiss decomposition. The GAIT model also reproduces Lagrangian transport including the probability distribution function of particle displacements and the effective turbulent diffusivity.

In the framework of a Particle-In-Cell scheme for some 1D Vlasov-Poisson system depending on a small parameter, we propose a time-stepping method which is numerically uniformly accurate when the parameter goes to zero. Based on an exponential time differencing approach, the scheme is able to use large time steps with respect to the typical size of the fast oscillations of the solution.

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