The electric potential and field of an axially symmetric electric system can be computed by expansion of the central and remote zonal harmonics, using the Legendre polynomials. Garrett showed the usefulness of the zonal harmonic expansion for magnetic field calculations, and the similar radial series expansion has been widely used in electron optics. In this paper, we summarize our experience o...

In anticipation of new observational results for Jupiter’s axial moment of inertia and gravitational zonal harmonic coefficients from the forthcoming Juno orbiter, we present a number of preliminary Jupiter interior models. We combine results from ab initio computer simulations of hydrogen-helium mixtures, including immiscibility calculations, with a new nonperturbative calculation of Jupiter’s...

We investigate the stability of growing vesicles using the formalism of nonequilibrium thermodynamics. The vesicles are growing due to the accretion of lipids to the bilayer which forms the vesicle membrane. The thermodynamic description is based on the hydrodynamics of a water and lipid mixture together with a model of the vesicle as a discontinuous system in the sense of linear nonequilibrium...

Neoclassical shielding is the dominant mechanism reducing the collisionless zonal flow in a tokamak. Previously, this phenomenon was analyzed in the case of an essentially homogeneous equilibrium since the wavelength of the zonal flow perturbation was assumed to be much less than the scale length of background plasma parameters. This assumption is not appropriate in a tokamak pedestal. Therefor...

The magnetic field of an axially symmetric coil or magnetic material system can be computed by expansion of the central and remote zonal harmonics, using the Legendre polynomials. This method can be 100–1000 times faster than the more widely known elliptic integral method and is more general than the similar radial series expansion. We present the zonal harmonic method for field, scalar and vec...

Turbulence and its structure formation are universal in neutral fluids and in plasmas. Turbulence annihilates global structures but can organize flows and eddies. The mutual-interactions between flow and the eddy give basic insights into the understanding of non-equilibrium and nonlinear interaction by turbulence. In fusion plasma, clarifying structure formation by Drift-wave turbulence, driven...

We consider the Navier–Stokes equations on two-dimensional unit sphere and study linear stability of two-jet Kolmogorov type flow which is a stationary solution given by zonal spherical harmonic function degree two. prove for an arbitrary viscosity coefficient showing exponential decay to linearized equation towards equilibrium grows as tends zero. The main result this paper nonexistence nonzer...