Adjoint variational principles for regularised conservative systems

Adjoint variational principles for regularised conservative systems

Adjoint variational principles for regularised conservative systems 150 150 Mathew

Adjoint variational principles for regularised conservative systems

Variational principles are powerful tools in many branches of theoretical physics. Certain conservative systems which do not admit of a traditional Euler-Lagrange variational formulation are given a novel generalization. Illustrative examples, including the recently discovered scale-invariant analogue of the Korteweg-de Vries equation are presented. The new "adjoint variational method" is applied to regularized, incompressible, conservative hydrodynamics expressed in Eulerian variables, as opposed to the usual Lagrangian variables. The regularized, two-fluid, non-dissipative, quasi-neutral, incompressible plasma equations [known as "Hall MHD" ] and the electromagnetic field equations are derived from the new formulation. It turns out that the associated adjoint equations are precisely the two-fluid "cross-helicity/frozen-field" theorems pertaining to these regularized systems which have no standard variational formulation). The adjoint equations also provide a direct route to the integral invariants of the system and suggest new analytical and numerical approaches to the dynamics.

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01/01/2014