Abstract:
In 1973, Le Bellac and Levy-Leblond (Nuovo Cimento B 14, 217-234) discovered that Maxwell's equations possess two non-relativistic Galilei-covariant limits, corresponding to E >> cB (electric limit) or E << cB (magnetic limit). Here, we provide a systematic, yet simple, derivation of these two limits based on a dimensionless form of Maxwell's equations and an expansion of the electric and magnetic fields in a power series of some small parameters. Using this procedure, all previously known results are recovered in a natural and unambiguous way. Some further extensions are also proposed.

Abstract:
When an unmagnetized plasma comes in contact with a material surface, the difference in mobility between the electrons and the ions creates a nonneutral layer known as the Debye sheath (DS). However, in magnetic fusion devices, the open magnetic field lines intersect the structural elements of the device with near grazing incidence angles. The magnetic field tends to align the particle flow along its own field lines, thus counteracting the mechanism that leads to the formation of the DS. Recent work using a fluid model [P. Stangeby, Nucl. Fusion {\bf 52}, 083012 (2012)] showed that the DS disappears when the incidence angle is smaller than a critical value (around $5^\circ$ for ITER-like parameters). Here, we study this transition by means of numerical simulations of a kinetic model both in the collisionless and weakly collisional regimes. We show that the main features observed in the fluid model are preserved: for grazing incidence, the space charge density near the wall is reduced, the ion flow is subsonic, and the electric field and plasma density profiles are spread out over several ion Larmor radii instead of a few Debye lengths as in the unmagnetized case. As there is no singularity at the DS entrance in the kinetic model, this phenomenon depends smoothly on the magnetic field incidence angle and no particular critical angle arises. The simulation results and the predictions of the fluid model are in good agreement, although some discrepancies subsist, mainly due to the assumptions of isothermal closure and diagonality of the pressure tensor in the fluid model.

Abstract:
Magnetic fusion devices operate at regimes characterized by extremely high temperatures and low densities, for which the charged particles motion is well described by classical mechanics. This is not true, however, for solid-state metallic objects: their density approaches $10^{28} \rm m^{-3}$, so that the average interparticle distance is shorter than the de Broglie wavelength, which characterizes the spread of the electron wave function. Under these conditions, the conduction electrons behave as a true quantum plasma even at room temperature. Here, we shall illustrate the impact of quantum phenomena on the electron dynamics in metallic objects of nanometric size, particularly thin metallic films excited by short laser pulses. Further, we will discuss more recent results on regimes that involve spin and relativistic effects.

Abstract:
Nonneutral plasmas can be trapped for long times by means of combined electric and magnetic fields. Adiabatic cooling is achieved by slowly decreasing the trapping frequency and letting the plasma occupy a larger volume. We develop a fully kinetic time-dependent theory of adiabatic cooling for plasmas trapped in a one-dimensional well. This approach is further extended to three dimensions and applied to the cooling of antiproton plasmas, showing excellent agreement with recent experiments [G. Gabrielse et al., Phys. Rev. Lett. 106, 073002 (2011)].

Abstract:
Self-consistent simulations of the ultrafast electron dynamics in thin metal films are performed. A regime of nonlinear oscillations is observed, which corresponds to ballistic electrons bouncing back and forth against the film surfaces. When an oscillatory laser field is applied to the film, the field energy is partially absorbed by the electron gas. Maximum absorption occurs when the period of the external field matches the period of the nonlinear oscillations, which, for sodium films, lies in the infrared range. Possible experimental implementations are discussed.

Abstract:
In recent decades, oxidative stress has become a focus of interest in most biomedical disciplines and many types of clinical research. Increasing evidence shows that oxidative stress is associated with the pathogenesis of diabetes, obesity, cancer, ageing, inflammation, neurodegenerative disorders, hypertension, apoptosis, cardiovascular diseases, and heart failure. Based on these studies, an emerging concept is that oxidative stress is the “final common pathway” through which the risk factors for several diseases exert their deleterious effects. Oxidative stress causes a complex dysregulation of cell metabolism and cell–cell homeostasis; in particular, oxidative stress plays a key role in the pathogenesis of insulin resistance and β-cell dysfunction. These are the two most relevant mechanisms in the pathophysiology of type 2 diabetes and its vascular complications, the leading cause of death in diabetic patients.

Abstract:
The ability to control the magnetization switching in nanoscale devices is a crucial step for the development of fast and reliable techniques to store and process information. Here we show that the switching dynamics can be controlled efficiently using a microwave field with slowly varying frequency (autoresonance). This technique allowed us to reduce the applied field by more than $30%$ compared to competing approaches, with no need to fine-tune the field parameters. For a linear chain of nanoparticles the effect is even more dramatic, as the dipolar interactions tend to cancel out the effect of the temperature. Simultaneous switching of all the magnetic moments can thus be efficiently triggered on a nanosecond timescale.

Abstract:
We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical way. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. This hydrodynamic model is closed using a maximum entropy principle in the case of three or four constraints on the fluid moments, both for Maxwell-Boltzmann and Fermi-Dirac statistics.

Abstract:
Electron-positron clusters are studied using a quantum hydrodynamic model that includes Coulomb and exchange interactions. A variational Lagrangian method is used to determine their stationary and dynamical properties. The cluster static features are validated against existing Hartree-Fock calculations. In the linear response regime, we investigate both dipole and monopole (breathing) modes. The dipole mode is reminiscent of the surface plasmon mode usually observed in metal clusters. The nonlinear regime is explored by means of numerical simulations. We show that, by exciting the cluster with a chirped laser pulse with slowly varying frequency (autoresonance), it is possible to efficiently separate the electron and positron populations on a timescale of a few tens of femtoseconds.

Abstract:
Using a variational approach based on a Lagrangian formulation and Gaussian trial functions, we derive a simple dynamical system that captures the main features of the time-dependent Schr\"odinger-Newton equations. With little analytical or numerical effort, the model furnishes information on the ground state density and energy eigenvalue, the linear frequencies, as well as the nonlinear long-time behaviour. Our results are in good agreement with those obtained through analytical estimates or numerical simulations of the full Schr\"odinger-Newton equations.