Cauchy problem and quasi-stationary limit for the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations

In this paper we continue the investigation of the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations. In particular we extend some previous results about the Cauchy problem and the quasi-stationary limit to the case where the magnetic permeability and the electric permittivity are variable

On the weak solutions to the Maxwell-Landau-Lifshitz equations and to the Hall-Magneto-Hydrodynamic equations

In this paper we deal with weak solutions to the Maxwell-Landau-Lifshitz equations and to the Hall-Magneto-Hydrodynamic equations. First we prove that these solutions satisfy some weak-strong uniqueness property. Then we investigate the validity of energy identities. In particular we give a sufficient condition on the regularity of weak solutions to rule out anomalous dissipation. In the case of the Hall-Magneto-Hydrodynamic equations we also give a sufficient condition to guarantee the magneto-helicity identity. Our conditions correspond to the same heuristic scaling as the one introduced by Onsager in hydrodynamic theory. Finally we examine the sign, locally, of the anomalous dissipations of weak solutions obtained by some natural approximation processes.Comment: 45 page

On the coupling of wave and three-dimensional circulation models : Choice of theoretical framework, practical implementation and adiabatic tests

Many theoretical approaches and implementations have been proposed for the coupling of the three-dimensional ocean circulation with waves. The theoretical models are reviewed and it is shown that the formulation in terms of the quasi-Eulerian velocity circumvents the essential difficulty of alternative formulations for the Lagrangian mean velocity. Namely, models based on this Lagrangian velocity require an estimation of wave-induced motions to first order in the horizontal gradients of the wave field in order to estimate the vertical flux of wave pseudo-momentum. So far, only three-dimensional wave models have been able to provide these estimates, and all published theories based on the simpler Airy theory are not consistent at the leading order, because they ignore or incorrectly estimate the vertical momentum flux. With an adiabatic example on a sloping bottom it is shown that this inconsistency produces very large spurious velocities. These errors are independent of the slope for the inviscid case, and are still significant when a realistic vertical mixing is applied. A quick diagnostic of the potential accuracy of a theoretical model is the vertical profile of the wave-induced forcing terms: if it is not uniform over depth in adiabatic conditions then it will produce spurious artificial flow patterns in conditions with shoaling waves. Although conceptually more challenging, the quasi-Eulerian velocity theories only introduce minor modifications of the solution procedure for the standard primitive equations: a modification of the surface boundary condition for the mass conservation, the addition of the Stokes drift in the tracer advection equations, and sources of momentum and turbulent kinetic energy with associated surface and bottom fluxes. All the necessary modifications of primitive equation models are given in detail. This implementation is illustrated with the MARS3D model, which passes the test of the adiabatic shoaling waves

Optimal control models and elicitation of attitudes towards climate damages

This paper examines the consequences of various attitudes towards climate damages through a family of stochastic optimal control models (RESPONSE): cost-efficiency for a given temperature ceiling; cost-benefit analysis with a "pure preference for current climate regime" and full cost-benefit analysis. The choice of a given proxy of climate change risks is actually more than a technical option. It is essentially motivated by the degree of distrust regarding the legitimacy of an assessment of climate damages and the possibility of providing in due time reliable and non controversial estimates. Our results demonstrate that a) for early decades abatement, the difference between various decision-making frameworks appears to matter less than the difference between stochastic and non stochastic approach given the cascade of uncertainty from emissions to damages; b) in a stochastic approach, the possibility of non-catastrophic singularities in the damage function is sufficient to significantly increase earlier optimal abatements; c) a window of opportunity for action exists up to 2040: abatements further delayed may induce significant regret in case of bad news about climate response or singularities in damages.Cost-efficiency; Cost-benefit; Climate sensitivity; Climate change damages; Uncertainty; Optimal climate policy; Decision making frameworks

Revisiting the Sample Adaptive Offset post-filter of VVC with Neural-Networks

The Sample Adaptive Offset (SAO) filter has been introduced in HEVC to reduce general coding and banding artefacts in the reconstructed pictures, in complement to the De-Blocking Filter (DBF) which reduces artifacts at block boundaries specifically. The new video compression standard Versatile Video Coding (VVC) reduces the BD-rate by about 36% at the same reconstruction quality compared to HEVC. It implements an additional new in-loop Adaptive Loop Filter (ALF) on top of the DBF and the SAO filter, the latter remaining unchanged compared to HEVC. However, the relative performance of SAO in VVC has been lowered significantly. In this paper, it is proposed to revisit the SAO filter using Neural Networks (NN). The general principles of the SAO are kept, but the a-priori classification of SAO is replaced with a set of neural networks that determine which reconstructed samples should be corrected and in which proportion. Similarly to the original SAO, some parameters are determined at the encoder side and encoded per CTU. The average BD-rate gain of the proposed SAO improves VVC by at least 2.3% in Random Access while the overall complexity is kept relatively small compared to other NN-based methods

Comparative analysis of classical models (MARS3D, AZOV3D) and lattice Boltzmann models for shallow water hydrodynamics computations

Different numerical approaches of hydrodynamics of shallow water basins are considered and compared. Two approaches are developped in TIT-Russia: one of them is classical and based on numerical solution of the Navier-Stokes equations by Pressure-Correction method, another (developed several years ago) is  based on the solution of the Lattice Boltzmann kinetic equation. The comparative analysis of these two approaches with MARS3D is performed for a shallow water basin example: «Etang de Berre»