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Joël Wagner
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Prof. Dr.
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Wagner
First name
Joël
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@ProfDrJWagner
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Item type:Publication, On a class of implicit solutions of the continuity and Euler's equations for 1D systems with long range interactions, IIResults of theoretical and numerical investigations concerning the space-time evolution in 1D of Coulombian and Newtonian systems with densities departing from a uniform and homogeneous background are reported here. In the Coulombian case, the model is called a One Component Plasma. In the Newtonian case, we have the cosmological models of Cold Dark Matter in expanding universes with expansion parameters depending or not upon the cosmological constant. A canonical Hamiltonian formulation is given for studying single-speed solutions of their Coulomb- or Jeans-Vlasov-Poisson descriptions. It is shown that using the Gel'fand mass coordinate the equations of motion are exactly integrable and that the corresponding equations of their characteristics are inhomogeneous, linear and second order ODE's with variable coefficients for the cosmological models. It is furthermore shown that, using correlated initial conditions, Burgers' type of implicit equations for the velocity fields are obtained. Comparison is made between this way to generate exact solutions for the characteristics of the models and that put forward by Zel'dovich. Two examples illustrate the resulting regular and singular mean-field dynamics of the models: a periodic initial excess density for the One Component Plasma and a local departure from homogeneity for the cosmological models.Type:journal articleJournal:Physica D: Nonlinear PhenomenaVolume:226Issue:2Scopus© Citations 2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, On a class of implicit solutions of the continuity and Euler's equations for 1D systems with long range interactionsResults of computer simulations and of theoretical analysis done to investigate and interpret the space-time evolution of the mass density and the velocity field of the inviscid self-gravitating (attractive) and (repulsive) Coulomb liquids in 1D with correlated initial conditions, namely proportionality between the mass density and the divergence of the velocity field are reported here. Numerical data gathered for both models in a collisionless regime reveal an evolution with a time-dependent proportionality factor. Feeding this result in the continuity and div-Euler equations leads to the introduction of another field which is shown to satisfy a Burgers type of implicit equation. A thorough description of regular implosion followed by singular collapses in the attractive case, and of regular explosion in the repulsive case is obtained. Time-inversion symmetry is investigated, energy conservation and stability properties are shown to apply in the regular regions of smooth solutions. The velocity potential satisfies a new local and inhomogeneous PDE.Type:journal articleJournal:Physica D: Nonlinear PhenomenaVolume:201Issue:3Scopus© Citations 5