Fractional Statistics in terms of the r-Generalized Fibonacci Sequences

We develop the basis of the two dimensional generalized quantum statistical systems by using results on $r$-generalized Fibonacci sequences. According to the spin value $s$ of the 2d-quasiparticles, we distinguish four classes of quantum statistical systems indexed by $s=0,1/2:mod(1)$, $s=1/M:mod(1)$, $s=n/M:mod(1)$ and $0\leq s\leq 1:mod(1)$. For quantum gases of quasiparticles with $s=1/M:mod(1)$, $M\geq 2,$, we show that the statistical weights densities $\rho_M$ are given by the integer hierarchies of Fibonacci sequences. This is a remarkable result which envelopes naturally the Fermi and Bose statistics and may be thought of as an alternative way to the Haldane interpolating statistical method.Comment: Late

Determination of Lightning Currents from Far Electromagnetic Fields: Effect of a Strike Object

We discuss in this paper the influence of the presence of an elevated strike object on the peak of the lightning return stroke current determined from remote field measurements. We develop analytical expressions relating the lightning return stroke channel-base current and the far electromagnetic field for different specific cases, namely, (1) ground-initiated return strokes (classical transmission line (TL) model), (2) ground-initiated return strokes including possible reflections at ground level, (3) tall strike objects for which the current's zero-to-peak time is smaller than the travel time along the object, and (4) electrically short strike objects. It is shown that for tall structures, the field enhancement relative to a return stroke initiated at ground level is expressed through a factor equal to ktall = [1 + c / v (1 - 2 ρt)] / (1 - ρt), where v and c are the return stroke front speed and the speed of light in vacuum, respectively, and ρt is the top reflection coefficient. For very short towers and/or very slow return stroke current wavefronts, when the condition tf very much greater than h / c applies, expressions relating the far electromagnetic field and the return stroke current were also derived. For case (2), return strokes initiated at ground level, the field enhancement relative to a return stroke initiated at ground level, case (1), is expressed through a factor equal to kshort = (1 + (c / v) ρch - g) / (1 + ρch - g), where ρch-g represents the reflection coefficient between the lightning channel and the grounding impedance

Time Reversal to Localise Multiple Partial Discharges in Power Cables

The paper studies the suitability of the electromagnetic time reversal (EMTR) technique to localise multiple sources of partial discharges (PD) in power cables. In particular, the localisation of two PDs in a homogeneous power line is investigated both in the presence or absence of noise. The investigation, which is based on numerical simulations, shows that an EMTR-based PD localisation method is able to localise two PDs occurring simultaneously in a line using only a measurement at one observation point (OP), indiscriminately collecting the direct and reflected signals coming from the two PD sources. The EMTR procedure to localise multiple PD sources, using a Transmission Line Matrix model digital twin for the time reversal simulations, is described and the challenges that must be addressed to develop an EMTR-based device for the on-line location of multiple PDs are discussed