The nonlinear properties of electromagnetic waves traveling through a magnetized vacuum is of particular interest in the study of neutron stars. Heisenberg and Euler [1] and Weisskopf [2] first derived nonlinear corrections to the Maxwell equations of the electromagnetic field. Lutzky and Toll [3] and Zheleznyakov and Fabrikant [4] applied the weak-field expansion to show that shock waves can d...

We provide necessary and sufficient conditions for Lyapunov stabilizability and exponential stabilizability by the energy shaping method for the class of all linear controlled Lagrangian systems of an arbitrary degree of under-actuation, and for the class of all controlled Lagrangian systems of one degree of under-actuation. We give a sufficient condition for asymptotic stabilizability for the ...

A numerical method for passive scalar and self-advection dynamics, Lagrangian rearrangement, is proposed. This fully Lagrangian advection algorithm introduces no artificial numerical dissipation or interpolation of parcel values. In the zero-viscosity limit, it preserves all of the Casimir invariants associated with parcel rearrangement. In the twodimensional case presented here, these invarian...

Arbitrary Lagrangian Eulerian methods are well suited to modelling high speed compressible multimaterial flow problems in complex geometry. In this talk three stage ALE schemes will be considered, which are typically used for practical calculations of multimaterial flows. These three stages are: a Lagrangian stage, in which the solution and the computational mesh are updated; a rezoning stage, ...

A. In general, Lagrangian Floer homology HF∗(L, φH(L)) – if well-defined – is not isomorphic to the singular homology of the Lagrangian submanifold L. For arbitrary closed Lagrangian submanifolds a local version of Floer homology HF ∗ (L, φH(L)) is defined in [Flo89, Oh96] which is isomorphic to singular homology. This construction assumes that the Hamiltonian function H is sufficiently ...