Temperature dependence of modified CNO nuclear reaction rates in dense stellar plasmas

We study the dependence of the CNO nuclear reaction rates on temperature, in the range of $10^7\div 10^8$ K, the typical range of temperature evolution from a Sun-like star towards a white dwarf. We show that the temperature dependence of the CNO nuclear reaction rates is strongly affected by the presence of non-extensive statistical effects in the dense stellar core. A very small deviation from the Maxwell-Boltzmann particle distribution implies a relevant enhancement of the CNO reaction rate and could explain the presence of heavier elements (e.g. Fe, Mg) in the final composition of a white dwarf core. Such a behavior is consistent with the recent experimental upper limit to the fraction of energy that the Sun produces via the CNO fusion cycle.Comment: Presented at NEXT2003 (Second International Conference on "News and Expectations in Thermostatistics"), Villasimius (Cagliari)- Italy in 21-28 September 2003. 7 pages including 3 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

Metastable and stable equilibrium states of stellar electron-nuclear plasmas

By minimizing free energy density, we show that the stellar core of a hydrogen burning star is not in a global thermodynamical equilibrium unless density, temperature, mass and composition assume given values. The core (as the solar interior) may be viewed more appropriately as a metastable state with very long lifetime. Slightly non-extensive distribution function could be the natural distribution for a weakly non-ideal plasma like a stellar core and represents a more appropriate approximation to this system than a Maxwellian distribution, without affecting bulk properties of stars.Comment: 14 pages, to appear in Phys. Lett.

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

LNG fueled barge for cold ironing: feasibility study for the emission abatement in the Port of Genoa

The scientific analysis presented in this paper aims at studying some maritime technical solutions for the electric energy generation and delivery to ships moored in port by means of LNG fueled generators installed onboard a floating unit. Two different scenarios regarding the LNG supply chain are supposed and some options for producing cleaner electric energy are then investigated. The reference area considered in this study is the old port of Genoa where the traffic of both passenger and cargo ships takes place. The paper presents an analysis concerning the main technical features of the considered solutions for an actual port calls scenario. The results regard dimensions and weights of the proposed floating units and the most significant characteristics of the generation equipment, as far as average load factor, fuel consumption and cost are concerned

Anomalous enhancements of low-energy fusion rates in plasmas: the role of ion momentum distributions and inhomogeneous screening

Non-resonant fusion cross-sections significantly higher than corresponding theoretical predictions are observed in low-energy experiments with deuterated matrix target. Models based on thermal effects, electron screening, or quantum-effect dispersion relations have been proposed to explain these anomalous results: none of them appears to satisfactory reproduce the experiments. Velocity distributions are fundamental for the reaction rates and deviations from the Maxwellian limit could play a central role in explaining the enhancement. We examine two effects: an increase of the tail of the target Deuteron momentum distribution due to the Galitskii-Yakimets quantum uncertainty effect, which broadens the energy-momentum relation; and spatial fluctuations of the Debye-H\"{u}ckel radius leading to an effective increase of electron screening. Either effect leads to larger reaction rates especially large at energies below a few keV, reducing the discrepancy between observations and theoretical expectations.Comment: 6 pages, 3 figure

Our Sun. IV. The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters

Helioseismology provides a powerful tool to explore the deep interior of the Sun: for example, the adiabatic sound speed can be inferred with an accuracy of a few parts in 10,000. This has become a serious challenge to theoretical models of the Sun. Therefore, we have undertaken a self-consistent, systematic study of sources of uncertainties in the standard solar model, which must be understood before the helioseismic observations can be used as constraints on theory. We find that the largest uncertainty in the sound speed in the solar interior, namely, 3 parts in 1000, arises from uncertainties in the observed photospheric abundances of the elements; uncertainties of 1 part in 1000 arise from (1) the 4% uncertainty in the OPAL opacities, (2) the 5% uncertainty in the basic pp nuclear reaction rate, (3) the 15% uncertainty in the diffusion constants for the gravitational settling of helium, and (4) the 50% uncertainties in diffusion constants for the heavier elements. (Other investigators have shown that similar uncertainties arise from uncertainties in the interior equation of state and in rotation-induced turbulent mixing.) The predicted pre-main-sequence solar lithium depletion is a factor of order 20 (an order of magnitude larger than that predicted by earlier models that neglected gravitational settling and used older opacities), and is uncertain by a factor of 2. The predicted neutrino capture rate is uncertain by 30% for the Cl-37 experiment and by 3% for the Ga-71 experiments (not including uncertainties in the capture cross sections), while the B-8 neutrino flux is uncertain by 30%.Comment: LaTeX, 38 pages (including 8 figures); ApJ, in press. Added figures/color figurea available at http://www.cita.utoronto.ca/~boothroy/sun4.htm

Enhancement of fusion rates due to quantum effects in the particles momentum distribution in nonideal media

This study concerns a situation when measurements of the nonresonant cross-section of nuclear reactions appear highly dependent on the environment in which the particles interact. An appealing example discussed in the paper is the interaction of a deuteron beam with a target of deuterated metal Ta. In these experiments, the reaction cross section for d(d,p)t was shown to be orders of magnitude greater than what the conventional model predicts for the low-energy particles. In this paper we take into account the influence of quantum effects due to the Heisenberg uncertainty principle for particles in a non-ideal medium elastically interacting with the medium particles. In order to calculate the nuclear reaction rate in the non-ideal environment we apply both the Monte Carlo technique and approximate analytical calculation of the Feynman diagram using nonrelativistic kinetic Green's functions in the medium which correspond to the generalized energy and momentum distribution functions of interacting particles. We show a possibility to reduce the 12-fold integral corresponding to this diagram to a fivefold integral. This can significantly speed up the computation and control accuracy. Our calculations show that quantum effects significantly influence reaction rates such as p +7Be, 3He +4He, p +7Li, and 12C +12C. The new reaction rates may be much higher than the classical ones for the interior of the Sun and supernova stars. The possibility to observe the theoretical predictions under laboratory conditions is discussed

Variation in The Vitamin D Receptor Gene is Associated With Multiple Sclerosis in an Australian Population

Multiple Sclerosis (MS) is a chronic inflammatory demyelinating disease of the central nervous system (CNS) resulting in accumulating neurological disability. The disorder is more prevalent at higher latitudes. To investigate VDR gene variation using three intragenic restriction fragment length polymorphisms (Apa I, Taq I and Fok I) in an Australian MS case-control population, one hundred and four Australian MS patients were studied with patients classified clinically as Relapsing Remitting MS (RR-MS), Secondary Progressive MS (SP-MS) or Primary Progressive MS (PP-MS). Also, 104 age-, sex-, and ethnicity-matched controls were investigated as a comparative group. Our results show a significant difference of genotype distribution frequency between the case and control groups for the functional exon 9 VDR marker Taq I (p_Gen = 0.016) and interestingly, a stronger difference for the allelic frequency (p_All = 0.0072). The Apa I alleles were also found to be associated with MS (p_All = 0.04) but genotype frequencies were not significantly different from controls (p_Gen = 0.1). The Taq and Apa variants are in very strong and significant linkage disequilibrium (D' = 0.96, P < 0.0001). The genotypic associations are strongest for the progressive forms of MS (SP-MS and PP-MS). Our results support a role for the VDR gene increasing