While developing a new semi-Lagrangian solver, the gap between a linear Landau run in 1D×1D and a 5D gyrokinetic simulation in toroidal geometry is quite huge. Intermediate test cases are welcome for testing the code. A new fully two-dimensional conservative semi-Lagrangian (CSL) method is presented here and is validated on 2D polar geometries. We consider here as building block, a 2D guiding-c...

In this work, we deal with the 1D compressible fluid coupled with elastic solid in an Eulerian-Lagrangian system. To facilitate the analysis, the Naviers equation for elastic solid is cast into a 2×2 system similar to the Euler equation but in Lagrangian coordinate. The modified Ghost Fluid Method is employed to treat the fluid-elastic solid coupling, where an Eulerian-Lagrangian Riemann proble...

An effective action is obtained for the area and mass aspect of a thin shell of radiating selfgravitating matter. On following a mini-superspace approach, the geometry of the embedding space-time is not dynamical but fixed to be either Minkowski or Schwarzschild inside the shell and Vaidya in the external space filled with radiation. The Euler-Lagrange equations of motion are discussed and show...

We show that the extended cosmological equation-of-state developed starting from a Chaplygin equation-of-state, recently applied to stellar modeling, is viable dark energy model consistent with standard scalar potentials. Moreover we find Lagrangian formulation based on canonical field appropriate self-interaction potential. Finally, fit potential obtained numerically concrete functions well st...

Abstract We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such are real analytic in domain.