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

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

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

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

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

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

Investigation of asymmetrical shaft power increase during ship maneuvers by means of simulation techniques

Marine propulsion plants can experience large power fluctuations during tight maneuvers, with increases of shaft torque up to and over 100% of the steady values in straight course and considerable asymmetry between internal and external shafts during turning circle. This phenomenon (studied in Viviani et al 2007a and 2007b can be of particular interest for twin screw ships propulsion systems with coupled shaftlines, in which asymmetrical loads can represent a challenge for the whole propulsion system (e.g. unique reduction gear, shaftlines, automation). A joint research has been set up in order to deeply investigate the phenomenon, by means of large scale model testing and related numerical simulations. In the present work, preliminary simulation results with different simplified automation systems and with an automation system more similar to the real one are reported, allowing to get a better insight into this complex problem

The hydrostatic equilibrium and Tsallis equilibrium for self-gravitating systems

Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We obtain a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium of self-gravitating systems. It is suggested that the nonextensive parameter in Tsallis statistics has a clear physical meaning with regard to the non-isothermal nature of the systems with long-range interactions and Tsallis equilibrium distribution for the self-gravitating systems describes the property of hydrostatic equilibrium of the systems.Comment: 7 pages, 9 Reference