Abstract:
By considering an electrolyte solution in motion in a duct under a transverse magnetic field, we notice that a so called Faraday voltage arises because of the Lorentz force acting on anions and cations in the fluid. When salt water is considered, hydrogen production takes place at one of the electrodes if an electric current, generated by Faraday voltage, flows in an external circuit. The maximum amount of hydrogen production rate is calculated by basic electrochemical concepts.

A detailed analysis of the magnetic response of field-cooled type-I superconducting hollow cylinders shows that the so-called “paramagnetic Meissner effect” can take place in opportunely devised multiply connected superconductors. Adopting simple circuital analogs of the latter superconducting systems, the magnetic susceptibility of micro-cylinders with one or two holes is studied by means of energy considerations.

Abstract:
The parallelism between diffraction and interference in optics and
quantum interference in Josephson junctions is discussed and studied in
details. The interdisciplinary character of the present work is highlighted
through specific examples. The Fraunhofer-like pattern of the maximum Josephson
current in a single Josephson junction and the periodic field dependence of the
critical current in two-junction and in multi-junction quantum interferometers
is analyzed and discussed in comparison with the homologous classical optical
phenomena.

Abstract:
looking closely to the mechanism which make sliding doors move, one sees that the motion of the commonly used objects can be understood by solving a problem related to the motion of blocks and pulleys. the system is by itself interesting to be modelled as a problem in newtonian mechanics, and the solution of the equation of the motion can lead us to estimate the time it takes for a sliding door to open or close.

Abstract:
A simple problem in Newtonian mechanics is considered. The problem consists in finding the maximum value of the length xUP of the portion of string slowly dragged on a step of height h, when the string itself is initially placed to match the vertical profile of the step, the remaining part lying on the ground and the final portion being in static equilibrium during the dragging process. A straightforward analysis is required to find the solution. The problem can be proposed in a lecture or a demonstration in class on the role played by the coefficient of static friction in mechanics.

Abstract:
A preliminary study of a boiler generating superheated steam by means of solar power is presented. Steam generationin this system does not need convection fluids, which in general are utilized in traditional solar thermal systems. Theapparatus is conceived by considering the idea of sunlight trap, consisting of a sunlight collector and a black body.

Abstract:
A discussion of asymptotic weak and strong Poincare' charges in metric gravity is given to identify the proper Hamiltonian boundary conditions. The asymptotic part of the lapse and shift functions is put equal to their analogues on Minkowski hyperplanes. By adding Dirac's ten extra variables at spatial infinity, metric gravity is extended to incorporate Dirac's ten extra first class constraints (the new ten momenta equal to the weak Poincare' charges) and this allows its deparametrization to parametrized Minkowski theories restricted to spacelike hyperplanes. The absence of supertranslations implies: i) boundary conditions identifying the family of Christodoulou-Klainermann spacetimes; ii) the restriction of foliations to those (Wigner-Sen-Witten hypersurfaces) corresponding to Wigner's hyperplanes of Minkowski rest-frame instant form. These results are generalized to tetrad gravity in the new formulation given in gr-qc/9807072, gr-qc/9807073. The evolution in the parameter labelling the leaves of the foliation is generated by the weak ADM energy. Some comments on the quantization in a completely fixed special 3-orthogonal gauge are made.

Abstract:
In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of {\it non-harmonic} 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) $r_{\bar a}(\tau ,\vec \sigma)$, $\pi_{\bar a}(\tau ,\vec \sigma)$, $\bar a = 1,2$. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, {\it without introducing any background 4-metric}, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in ${\hat E}_{ADM}$. {\it We solve all the constraints} of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's $r_{\bar a}(\tau ,\vec \sigma)$, which replace the two polarizations of the TT harmonic gauge, and that {\it linearized Einstein's equations are satisfied} . Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.

Abstract:
A Hamiltonian linearization of the rest-frame instant form of tetrad gravity (gr-qc/0302084), where the Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, in a completely fixed (non harmonic) 3-orthogonal Hamiltonian gauge is defined. For the first time this allows to find an explicit solution of all the Hamiltonian constraints and an associated linearized solution of Einstein's equations. It corresponds to background-independent gravitational waves in a well defined post-Minkowskian Christodoulou-Klainermann space-time.

Abstract:
We show that magnetic fields stronger than about $10^{15}$ G are able to suppress the development of the hydrodynamical bar-mode instability in relativistic stars. The suppression is due to a change in the rest-mass density and angular velocity profiles due to the formation and to the linear growth of a toroidal component that rapidly overcomes the original poloidal one, leading to an amplification of the total magnetic energy. The study is carried out performing three-dimensional ideal-magnetohydrodynamics simulations in full general relativity, superimposing to the initial (matter) equilibrium configurations a purely poloidal magnetic field in the range $10^{14}-10^{16}$ G. When the seed field is a few parts in $10^{15}$ G or above, all the evolved models show the formation of a low-density envelope surrounding the star. For much weaker fields, no effect on the matter evolution is observed, while magnetic fields which are just below the suppression threshold are observed to slow down the growth-rate of the instability.