In this article, a systematic procedure has been explored to studying general Zq-equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z12-equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-...

Two-dimensional, nonlinear, Hall-magnetohydrodynamical ~MHD! numerical simulations are used to investigate the scaling of the rate of forced magnetic reconnection in the so-called Taylor problem. In this problem, a small amplitude boundary perturbation is suddenly applied to a tearing stable, slab plasma equilibrium. The perturbation is such as to drive magnetic reconnection within the plasma. ...

The problem of sharp boundary, ideal magnetohydrodynamic equilibria in three-dimensional toroidal geometry is addressed. The sharp boundary, which separates a uniform pressure, current-free plasma from a vacuum, is determined by a magnetic surface of a given vacuum magnetic field. The pressure balance equation has the form of a Hamilton-Jacobi equation with a Hamiltonian that is quadratic in th...