We build corotational symmetric solutions to the harmonic map flow from the unit disc into the unit sphere which have constant degree. First, we prove the existence of such solutions, using a time semi-discrete scheme based on the idea that the harmonic map flow is the L-gradient of the relaxed Dirichlet energy. We prove a partial uniqueness result concerning these solutions. Then, we compute n...

We present an efficient method for computing numerically the solution to the time-dependent Maxwell equations in an axisymmetric domain, with arbitrary (not necessarily axisymmetric) data. The method is an extension of those introduced in [20] for Poisson’s equation, and in [4] for Maxwell’s equations in the fully axisymmetric setting (i.e., when the data is also axisymmetric). It is based on a...

We investigate the axisymmetric magnetosphere of an aligned rotating magnetic dipole surrounded by an ideal force-free plasma. We concentrate on the magnetic field structure around the point of intersection of the separatrix between the openand closed-field line regions and the equatorial plane. We first study the case in which this intersection point is located at the light cylinder. We find t...

Output-driven mesh adaptation is used in conjunction with an embedded-boundary Cartesian meshing scheme for sonic-boom simulations. The approach automatically refines the volume mesh in order to minimize discretization errors in output functionals, specifically pressure signals, defined at locations several body-lengths away from the surface geometry. Techniques and strategies used to improve a...

We extend our previous immersed boundary (IB) method for 3D axisymmetric inextensible vesicle in Navier-Stokes flows, [W.-F. Hu, Y. Kim, M.-C. Lai, An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier-Stokes flows, J. Comput. Phys. 257 (2014)] to general three dimensions. Despite a similar spirit in numerical algorithms to the axisymmetric...

Centrifugally driven interchange instabilities are observed in a laboratory plasma confined by a dipole magnetic field. The instabilities appear when an equatorial mesh is biased to drive a radial current that causes rapid axisymmetric plasma rotation. The observed instabilities are quasicoherent in the laboratory frame of reference; they have global radial mode structures and low azimuthal mod...