Energy of a magnetic body: −m⋅δB or +B⋅δm?

“Energy of a magnetic body: -m dB or +B dm?” addresses a fraught question: what is the free-energy change when a B-field applied to a magnetic body (magnetic moment m) is changed? We define what is meant by an “applied field”. We show that the free-energy change is -m dB. The electric analogue -p dE is also described. A balls-and-spring model helps to understand an electric dipole, and by extension a magnetic dipole. In the magnetic case, we prepare the field using a reversible current generator driving a coil. The energy change is obtained by inserting the sample and (also, alternatively) by changing the field. There is much that is new in this chapter.

Characterization of Anomalous Forces in Dielectric Rotors

We performed several measurements of anomalous forces on a dielectric rotor under electrostatic conditions of operation. The device operated under constant and intense angular velocity for each high voltage applied. The measurements were made in the similar way than an analogue magnetic gyroscope, by considering clockwise and counterclockwise rotations. We found that there are significant weight reduction on the device in the clockwise case, with one order of magnitude higher than the magnetic case. In addition, we detected a similar asymmetry in the observation of the effect, that is, there are smaller results for the anomalous forces in counterclockwise rotation for higher values of the voltage applied on the device. We also propose a theoretical model to explain the quantitative effect based on average values of macroscopic observables of the device rotation and concluded that it is consistent with the experimental findings.

Plesio-geostrophy for Earth’s core: I. Basic equations, inertial modes and induction

An approximation is developed that lends itself to accurate description of the physics of fluid motions and motional induction on short time scales (e.g. decades), appropriate for planetary cores and in the geophysically relevant limit of very rapid rotation. Adopting a representation of the flow to be columnar (horizontal motions are invariant along the rotation axis), our characterization of the equations leads to the approximation we call plesio-geostrophy , which arises from dedicated forms of integration along the rotation axis of the equations of motion and of motional induction. Neglecting magnetic diffusion, our self-consistent equations collapse all three-dimensional quantities into two-dimensional scalars in an exact manner. For the isothermal magnetic case, a series of fifteen partial differential equations is developed that fully characterizes the evolution of the system. In the case of no forcing and absent viscous damping, we solve for the normal modes of the system, called inertial modes. A comparison with a subset of the known three-dimensional modes that are of the least complexity along the rotation axis shows that the approximation accurately captures the eigenfunctions and associated eigenfrequencies.

Equation of State of Strongly Magnetized Matter with Hyperons and Δ-Resonances

We construct a new equation of state for the baryonic matter under an intense magnetic field within the framework of covariant density functional theory. The composition of matter includes hyperons as well as Δ-resonances. The extension of the nucleonic functional to the hypernuclear sector is constrained by the experimental data on Λ and Ξ-hypernuclei. We find that the equation of state stiffens with the inclusion of the magnetic field, which increases the maximum mass of neutron star compared to the non-magnetic case. In addition, the strangeness fraction in the matter is enhanced. Several observables, like the Dirac effective mass, particle abundances, etc. show typical oscillatory behavior as a function of the magnetic field and/or density which is traced back to the occupation pattern of Landau levels.

On anisotropic Sobolev spaces

We investigate two types of characterizations for anisotropic Sobolev and BV spaces. In particular, we establish anisotropic versions of the Bourgain–Brezis–Mironescu formula, including the magnetic case both for Sobolev and BV functions.