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We present the calculation of the stability region of a perfect diamagnet levitated in a magnetic field created by a circular current loop. We make use of the machine learning technique of automatic differentiation to illustrate the calculations with the elliptic integrals involved.

We report on nanomechanical resonators with very high-quality factors operated as mechanical probes in liquid helium \(^4\mathrm{He}\), with special attention to the superfluid regime down to millikelvin temperatures. Such resonators have been used to map out the full range of damping mechanisms in the liquid on the nanometer scale from \(10\,\mathrm{mK}\) up to \(\sim3\,\mathrm{K}\). The high sensitivity of these doubly-clamped beams to thermal excitations in the superfluid \(^4\mathrm{He}\) makes it possible to drive them using the momentum transfer from phonons generated by a nearby heater. This so-called "\textit{phonon wind}" is an inverse thermomechanical effect that until now has never been demonstrated, and provides the possibility to perform a new type of optomechanical experiments in quantum fluids., Comment: The manuscript has been split into two publications currently accepted in PRB and PRL. The splitted manuscripts will be uploaded to arxiv

The Fourier transform method can be applied to obtain electromagnetic knots, which are solutions of Maxwell equations in vacuum with non-trivial topology of the field lines and especial properties. The program followed in this work allows to present the main ideas and the explicit calculations at undergraduate level, so they are not obscured by a more involved formulation. We make use of helicity basis for calculating the electromagnetic helicity and the photon content of the fields.

We calculate analytically the spin-orbital decomposition of the angular momentum using completely non-paraxial fields that have certain degree of linkage of electric and magnetic lines. The split of the angular momentum into spin-orbital components is worked out for non-null knotted electromagnetic fields. The relation between magnetic and electric helicities and spin-orbital decomposition of the angular momentum is considered. We demonstrate that even if the total angular momentum and the values of the spin and orbital momentum are the same, the behaviour of the local angular momentum density is rather different. By taking cases with constant and non-constant electric and magnetic helicities, we show that the total angular momentum density present different characteristics during time evolution.

We study the collision of two hopfions or Hopf-Ra\~nada electromagnetic fields. The superposition of two of such fields, travelling in opposite directions, yields different topology for the electric and magnetic field lines. Controlling the angular momentum of such fields, we can control the topology of the flow associated to the field lines, and the energy distribution. The concept of electromagnetic helicity and the exchange between its magnetic and electric components are used to explain the different behaviours observed when the angular momentum is reversed.

Intense electromagnetic pulses interacting with a plasma can create a wake of plasma oscillations. Electrons trapped in such oscillations can be accelerated under certain conditions to very high energies. We study the conditions for the wakefield acceleration to produce MeV electrons in atmospheric plasmas. This mechanism may explain the origin of MeV or runaway electrons needed in the current theories for the production of Terrestrial Gamma ray Flashes., Comment: 11 pages, 3 figures

In this paper we consider the classical relativistic motion of charged particles in a knotted electromagnetic field. After reviewing how to construct electromagnetic knots from maps between the three-sphere and the two-sphere, we introduce a mean quadratic radius of the energy density distribution in order to study some properties of this field. We study the classical relativistic motion of electrons in the electromagnetic field of the Hopf map, and compute their trajectories. It is observed that these electrons initially at rest are strongly accelerated by the electromagnetic force, becoming ultrarelativistic in a period of time that depends on the knot energy and size.

In this paper we study the effects of photoionization processes on the propagation of both negative and positive streamer discharges. We show that negative fronts accelerate in the presence of photoionization events. The appearance and propagation of positive streamers travelling with constant velocity is explained as the result of the combined effects of photoionization and electron diffusion. The photoionization range plays an important role for the selection of the velocity of the streamer as we show in this work.

We explain a mechanism for branching of a planar negative front. Branching occurs as the result of a balance between the destabilizing effect of impact ionization and the stabilizing effect of electron diffusion on ionization fronts. The dispersion relation for transversal perturbation is obtained analytically and reads: $s = |k|/[2 (1 + |k|)] - D |k|^2$, where $D$, which is assumed to be small, is the ratio between the electron diffusion coefficient and the intensity of the externally imposed electric field. We estimate the spacing $\lambda$ between streamers in a planar discharge and deduce a scaling law $\lambda \sim D^{1/3}$.

It has been long admitted that a consequence of the virial theorem is that there can be no equilibrium configurations of a system of charges in electromagnetic interaction in the absence of external forces. However, recent results have shown that the virial theorem can not preclude the existence of certain nontrivial equilibrium configurations. Although some of these new results are based on an effective microscopic field theory, they are important for a theory of ball lightning that has been developed by the authors of the present work. Other theoretical results relative to magnetic force-free fields with field aligned currents and self-organized filamentary structures are also found to be relevant for this model., Comment: 15 pages TeX format and 1 epsfigure

We present a topological mechanism of discretization, which gives for the fundamental electric charge a value equal to the square root of the Planck constant times the velocity of light, which is about 3.3 times the electron charge. Its basis is the following recently proved property of the standard linear classical Maxwell equations: they can be obtained by change of variables from an underlying topological theory, using two complex scalar fields, the level curves of which coincide with the magnetic and the electric lines, respectively., Comment: 10 pages, LaTeX file