Numerical Study of the Oscillatory Convergence to the Attractor at the Edge of Chaos

This paper compares three different types of ``onset of chaos'' in the logistic and generalized logistic map: the Feigenbaum attractor at the end of the period doubling bifurcations; the tangent bifurcation at the border of the period three window; the transition to chaos in the generalized logistic with inflection 1/2 ($x_{n+1} = \mu x_{n}^{1/2}$), in which the main bifurcation cascade, as well as the bifurcations generated by the periodic windows in the chaotic region, collapse in a single point. The occupation number and the Tsallis entropy are studied. The different regimes of convergence to the attractor, starting from two kinds of far-from-equilibrium initial conditions, are distinguished by the presence or absence of log-log oscillations, by different power-law scalings and by a gap in the saturation levels. We show that the escort distribution implicit in the Tsallis entropy may tune the log-log oscillations or the crossover times.Comment: 10 pages, 5 figure

Thermal distributions in stellar plasmas, nuclear reactions and solar neutrinos

The physics of nuclear reactions in stellar plasma is reviewed with special emphasis on the importance of the velocity distribution of ions. Then the properties (density and temperature) of the weak-coupled solar plasma are analysed, showing that the ion velocities should deviate from the Maxwellian distribution and could be better described by a weakly-nonexstensive (|q-1|<0.02) Tsallis' distribution. We discuss concrete physical frameworks for calculating this deviation: the introduction of higher-order corrections to the diffusion and friction coefficients in the Fokker-Plank equation, the influence of the electric-microfield stochastic distribution on the particle dynamics, a velocity correlation function with long-time memory arising from the coupling of the collective and individual degrees of freedom. Finally, we study the effects of such deviations on stellar nuclear rates, on the solar neutrino fluxes, and on the pp neutrino energy spectrum, and analyse the consequences for the solar neutrino problem.Comment: ReVTeX, 23 pages, 3 figures, to appear in the special issue (Nonextensive statistical mechanics and thermodynamics) of the Brazilian Journal of Physic

Parametric study of the influence of the wind assisted propulsion on ships

nologies to increase energy efficiency and reduce ship fuel consumption. Several measures have been identified, or even applied, with the potential to achieve substantial fuel consumption and emission reductions, like slow-steaming, bio-fuels, and alternative propulsion technologies. Slow steaming has been already analysed to a great extent, whereas biofuels have raised concerns about environmental impact and availability. Among alternative propulsion technologies, a resurgence in wind-assisted propulsion is observed in recent years, primarily due to its high potential for fuel consumption and emission reduction. Wind power is currently being developed through both conventional sails and modern alternatives. These include Flettner rotors, kites or spinnakers, soft sails, wing sails and wind turbines. In particular, Flettner rotors are rotating cylinders generating lift when immersed in a fluid stream. This paper presents a ship propulsion model study, able to account for the thrust force produced by the rotor accounting for different vessel speed and weather scenario. This paper aims to assess the improvement of the ship’s energy efficiency and optimise the ship operating conditions in terms of daily performance. The result clearly shows the potential reduction achieved in the propeller delivered power given using the rotor as an auxiliary propulsion device

Deuterium burning in Jupiter interior

We show that moderate deviations from the Maxwell-Boltzmann energy distribution can increase deuterium reaction rates enough to contribute to the heating of Jupiter. These deviations are compatible with the violation of extensivity expected from temperature and density conditions inside Jupiter.Comment: 6 pages, use elsart + 1 encaspulated postscript figure. Submitted to Physica

Numerical modelling of the quantum-tail effect on fusion rates at low energy

Results of numerical simulations of fusion rate d(d,p)t, for low-energy deuteron beam, colliding with deuterated metallic matrix (Raiola et al. Phys. Lett.B 547 (2002) 193 and Eur. Phys J. A 13 (2002) 377) confirm analytical estimate given in Coraddu et al. nucl-th/0401043, taking into account quantum tails in the momentum distribution function of target particles, and predict an enhanced astrophysical factor in the 1 keV region in qualitative agreement with experiments.Comment: 6 pages, without figure

The nonrelativistic limit of the Magueijo-Smolin model of deformed special relativity

We study the nonrelativistic limit of the motion of a classical particle in a model of deformed special relativity and of the corresponding generalized Klein-Gordon and Dirac equations, and show that they reproduce nonrelativistic classical and quantum mechanics, respectively, although the rest mass of a particle no longer coincides with its inertial mass. This fact clarifies the meaning of the different definitions of velocity of a particle available in DSR literature. Moreover, the rest mass of particles and antiparticles differ, breaking the CPT invariance. This effect is close to observational limits and future experiments may give indications on its effective existence.Comment: 10 pages, plain TeX. Discussion of generalized Dirac equation and CPT violation adde

Kappa-deformed random-matrix theory based on Kaniadakis statistics

We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index {\kappa} (Boltzmann-Gibbs entropy is recovered in the limit {\kappa}\rightarrow0), we propose the non-Gaussian deformations ({\kappa} \neq 0) of the conventional orthogonal and unitary ensembles of random matrices. The joint eigenvalue distributions for the {\kappa}-deformed ensembles are derived by applying the principle maximum entropy to Kaniadakis entropy. The resulting distribution functions are base invarient as they depend on the matrix elements in a trace form. Using these expressions, we introduce a new generalized form of the Wigner surmise valid for nearly-chaotic mixed systems, where a basis-independent description is still expected to hold. We motivate the necessity of such generalization by the need to describe the transition of the spacing distribution from chaos to order, at least in the initial stage. We show several examples about the use of the generalized Wigner surmise to the analysis of the results of a number of previous experiments and numerical experiments. Our results suggest the entropic index {\kappa} as a measure for deviation from the state of chaos. We also introduce a {\kappa}-deformed Porter-Thomas distribution of transition intensities, which fits the experimental data for mixed systems better than the commonly-used gamma-distribution.Comment: 18 pages, 8 figure

Weak insensitivity to initial conditions at the edge of chaos in the logistic map

We extend existing studies of weakly sensitive points within the framework of Tsallis non-extensive thermodynamics to include weakly insensitive points at the edge of chaos. Analyzing tangent points of the logistic map we have verified that the generalized entropy with suitable entropic index q correctly describes the approach to the attractor.Comment: 6 pages, 3 figure

Collisional cross sections and momentum distributions in astrophysical plasmas: dynamics and statistical mechanics link

We show that, in stellar core plasmas, the one-body momentum distribution function is strongly dependent, at least in the high velocity regime, on the microscopic dynamics of ion elastic collisions and therefore on the effective collisional cross sections, if a random force field is present. We take into account two cross sections describing ion-dipole and ion-ion screened interactions. Furthermore we introduce a third unusual cross section, to link statistical distributions and a quantum effect originated by the energy-momentum uncertainty owing to many-body collisions, and propose a possible physical interpretation in terms of a tidal-like force. We show that each collisional cross section gives rise to a slight peculiar correction on the Maxwellian momentum distribution function in a well defined velocity interval. We also find a possible link between microscopical dynamics of ions and statistical mechanics interpreting our results in the framework of non-extensive statistical mechanics.Comment: 8 page