Related papers: Toroidal regularization of the guiding center Lagr…
The evolution of a Taylor-Green forced magnetohydrodynamic (MHD) system showing dynamo activity is analyzed via direct numerical simulations. The statistical properties of the velocity and magnetic field in Eulerian coordinates and along…
In the guiding center theory, smooth unit vectors perpendicular to the magnetic field are required to define the gyrophase. The question of global existence of these vectors is addressed using a general result from the theory of…
For a separable Hamiltonian, there are two fundamental, time-symmetric, second-order velocity-Verlet (VV) and position-Verlet (PV) symplectic integrators. Similarly, there are two VV and PV version of exact energy conserving algorithms for…
Effective Lagrangian of itinerant electron system of finite density at finite magnetic field is found to include Chern-Simons term of electromagnetic potentials of lower scale dimension than those studied before. This term has an origin in…
A numerical integration method for guiding-center orbits of charged particles in toroidal fusion devices with three-dimensional field geometry is described. Here, high order interpolation of electromagnetic fields in space is replaced by a…
The problems that are connected with Lagrangians which depend on higher order derivatives (namely additional degrees of freedom, unbound energy from below, etc.) are absent if effective Lagrangians are considered because the equations of…
We present a novel scheme of carrying out the Lie-transform perturbation for the guiding-center motion, with an aim at addressing directly the problem of singularity which exists intrinsically in the determining equation for the generating…
The motion of a charged particle in a nonuniform straight magnetic field with a uniform magnetic-field gradient is solved exactly in terms of elliptic functions. The connection between this problem and the guiding-center approximation is…
The equations of motion for a Lagrangian ${\cal L}(k_1)$, depending on the curvature $k_1$ of the particle worldline, embedded in a space--time of constant curvature, are considered and reformulated in terms of the principal curvatures. It…
The effective Lagrangian of electromagnetic fields at the cubic order in field strength has been considered. This generalized Lagrangian is motivated by electrodynamics on non-commutative spaces. We find the canonical and symmetrical…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along…
The connection is established between two different action principles for perfect fluids in the context of general relativity. For one of these actions, $S$, the fluid four--velocity is expressed as a sum of products of scalar fields and…
The influence of an externally applied magnetic field upon classic cubic quintic dissipative solitons is investigated using both exact simulations and a Lagrangian technique. The basic approach is to use a spatially inhomogeneous magnetic…
Building on the Utiyama principle we formulate an approach to Lagrangian field theory in which exterior covariant differentials of vector-valued forms replace partial derivatives, in the sense that they take up the role played by the latter…
On the basis of the gauge principle of field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…
One approach to studying the dynamics of a singular Lagrangian system is to attempt to regularize it, that is, to find an equivalent and regular system. In the case of time-independent singular Lagrangians, an approach due to \textit{A.…
We consider a classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the…
Non-Riemannian generalization of the standard Born-Infeld (BI) Lagrangian is introduced and analized from a theory of gravitation with dynamical torsion field. The field equations derived from the proposed action lead to a trace free…
It is well known that the Lagrangian and the Hamiltonian formalisms can be combined and lead to "covariant symplectic" methods. For that purpose a "pre-symplectic form" has been constructed from the Lagrangian using the so-called Noether…
Motivated by the possibility of radiation driven instabilities in rotating magnetic stars, we study the stability properties of general linear perturbations of a stationary and axisymmetric, infinitely conducting perfect fluid configuration…