Massimo Marino

Capacitive mixing with electrodes of the same kind for energy production from salinity differences

The capacitive mixing technique is aimed at producing renewable energy from salinity differences, for example between sea and river water. The technique makes use of two electrodes that modify their potential in opposite directions when the concentration of the solution in which they are immersed is changed, as a consequence of the dynamics of the electric double layer which forms in the ionic solution. Unfortunately, it is difficult to find two electrodes presenting both optimal performances and opposite potential variations. In order to overcome this problem, we present here a cell scheme with electrodes of the same kind (and thus identical dependence of potential on concentration) which can be operated with a CapMix cycle; it is based on a concentration cell with identical electrodes dipped into two compartments separated by a non-perm-selective porous diaphragm. Thanks to the cyclic operation, the actual cell voltage rise and the power production are close to the values obtained with the traditional scheme, or even higher, depending on the features of the ion transport in the liquid junction region. We present an experimental demonstration of the working principles and we study the power production and energy efficiency in the light of the theory of ion transport in fluids. We show that our technique is competitive with respect to the other CapMix techniques, with the relevant advantage that we make use of only one kind of electrode.

Boosting the voltage of a salinity-gradient-power electrochemical cell by means of complex-forming solutions

We report experiments on a concentration cell with zinc electrodes and ZnCl2 solutions at different concentrations, separated by a porous diaphragm. The cell is aimed at the conversion of the free energy associated to the concentration difference into electrical energy, for renewable and clean energy applications. Usually, the diffusion of the solute across the diaphragm constitutes a waste of free energy, which impairs the voltage generation of the concentration cell with respect to other well-known techniques that work quasi-reversibly, such as reverse electrodialysis or the “mixing entropy battery.” Quite surprisingly, we find that the voltage produced by our concentration cell is significantly higher than the voltage obtained with the other quasi-reversible techniques. We show that the surplus voltage comes from the active transformation of the mixing free energy into electrical energy performed by the liquid junction, and we show the connection with the negative apparent transference number of the zi...

Classical Electrodynamics of Point Charges

Abstract A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once removed without affecting the locality and the relativistic covariance of the theory, and with no need for mass renormalization. The procedure is first used to obtain a finite expression for the electromagnetic energy-momentum of the system. We show that the relativistic Lorentz-Dirac equation can be deduced from the conservation of this electromagnetic energy-momentum plus the usual mechanical term. Then we derive a finite lagrangian, which depends on the particle variables and on the actual electromagnetic potentials at a given time. From this lagrangian the equations of motion of both particles and fields can be derived via Hamiltons variational principle. The hamiltonian formulation of the theory can be obtained in a straightforward way. This leads to an interesting comparison between the resulting divergence-free expression of the hamiltonian functional and the standard renormalization rules for perturbative quantum electrodynamics.

Transition from order to chaos, and density limit, in magnetized plasmas

It is known that a plasma in a magnetic field, conceived microscopically as a system of point charges, can exist in a magnetized state, and thus remain confined, inasmuch as it is in an ordered state of motion, with the charged particles performing gyrational motions transverse to the field. Here, we give an estimate of a threshold, beyond which transverse motions become chaotic, the electrons being unable to perform even one gyration, so that a breakdown should occur, with complete loss of confinement. The estimate is obtained by the methods of perturbation theory, taking as perturbing force acting on each electron that due to the so-called microfield, i.e., the electric field produced by all the other charges. We first obtain a general relation for the threshold, which involves the fluctuations of the microfield. Then, taking for such fluctuations, the formula given by Iglesias, Lebowitz, and MacGowan for the model of a one component plasma with neutralizing background, we obtain a definite formula for the threshold, which corresponds to a density limit increasing as the square of the imposed magnetic field. Such a theoretical density limit is found to fit pretty well the empirical data for collapses of fusion machines.

Classical light dispersion theory in a regular lattice

Abstract We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by all the other particles, and to the radiation reaction expressed according to the Lorentz–Dirac equation. Exact normal mode solutions, describing the propagation of plane electromagnetic waves through the lattice, are obtained for the complete linearized system of infinitely many oscillators. At variance with all the available results, our method is valid for any values of the frequency, or of the ratio between wavelength and lattice parameter. A remarkable feature is that the proper inclusion of radiation reaction in the dynamics of the individual oscillators does not give rise to any extinction coefficient for the global normal modes of the lattice. The dispersion relations resulting from our solution are numerically studied for the case of a simple cubic lattice. New predictions are obtained in this way about the behavior of the crystal at frequencies near the proper oscillation frequency of the dipoles.

A generalized thermodynamics for power-law statistics

We show that there exists a natural way to define a condition of generalized thermal equilibrium between systems governed by Tsallis thermostatistics, under the hypotheses that (i) the coupling between the systems is weak, (ii) the structure functions of the systems have a power-law dependence on the energy. It is found that the q values of two such systems at equilibrium must satisfy a relationship involving the respective numbers of degrees of freedom. The physical properties of a Tsallis distribution can be conveniently characterized by a new parameter η which can vary between 0 and +∞, these limits corresponding, respectively, to the two opposite situations of a microcanonical distribution and of a distribution with a predominant power-tail at high energies. We prove that the statistical expression of the thermodynamic functions is univocally determined by the requirements that (a) systems at thermal equilibrium have the same temperature, (b) the definitions of temperature and entropy are consistent with the second law of thermodynamics. We find that, for systems satisfying the hypotheses (i) and (ii) specified above, the thermodynamic entropy is given by Renyi entropy.

On the classical and quantum integrability of systems of resonant oscillators

We study in this paper systems of harmonic oscillators with resonant frequencies. For these systems we present general procedures for the construction of sets of functionally independent constants of motion, which can be used for the definition of generalized actionangle variables, in accordance with the general description of degenerate integrable systems which was presented by Nekhoroshev in a seminal paper in 1972. We then apply to these classical integrable systems the procedure of quantization which has been proposed to the author by Nekhoroshev during his last years of activity at Milan University. This procedure is based on the construction of linear operators by means of the symmetrization of the classical constants of motion mentioned above.For 3 oscillators with resonance 1: 1: 2, by using a computer program we have discovered an exceptional integrable system, which cannot be obtained with the standard methods based on the obvious symmetries of the Hamiltonian function. In this exceptional case, quantum integrability can be realized only by means of a modification of the symmetrization procedure.

On the nonradiating motion of point charges

We investigate the possible existence of nonradiating motions of systems of point charges, according to classical electrodynamics with retarded potentials. We prove that two point particles of arbitrary electric charges cannot move for an infinitely long time within a finite region of space without radiating electromagnetic energy. We show however with an example that nonradiating accelerated motions of systems of point charges do in general exist.