Canonical partition function for anomalous systems described by the κ\kappa-entropy

Starting from the $\kappa$-distribution function, obtained by applying the maximal entropy principle to the $\kappa$-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical $\kappa$-partition function and discuss its main properties. It is shown that all important macroscopical quantities of the system can be expressed employing only the $\kappa$-partition function. The relationship between the associated $\kappa$-free energy and the $\kappa$-entropy is also discussed.Comment: 8 pages, no figures. Work presented at the International conference Complexity and Nonextensivity: New Trends in Statistical Mechanics. - Yukawa Institute for Theoretical Physics - (14-18 March 2005) Kyoto, Japa

Composition law of κ\kappa-entropy for statistically independent systems

The intriguing and still open question concerning the composition law of $\kappa$-entropy $S_{\kappa}(f)=\frac{1}{2\kappa}\sum_i (f_i^{1-\kappa}-f_i^{1+\kappa})$ with $0<\kappa<1$ and $\sum_i f_i =1$ is here reconsidered and solved. It is shown that, for a statistical system described by the probability distribution $f=\{ f_{ij}\}$, made up of two statistically independent subsystems, described through the probability distributions $p=\{ p_i\}$ and $q=\{ q_j\}$, respectively, with $f_{ij}=p_iq_j$, the joint entropy $S_{\kappa}(p\,q)$ can be obtained starting from the $S_{\kappa}(p)$ and $S_{\kappa}(q)$ entropies, and additionally from the entropic functionals $S_{\kappa}(p/e_{\kappa})$ and $S_{\kappa}(q/e_{\kappa})$, $e_{\kappa}$ being the $\kappa$-Napier number. The composition law of the $\kappa$-entropy is given in closed form, and emerges as a one-parameter generalization of the ordinary additivity law of Boltzmann-Shannon entropy recovered in the $\kappa \rightarrow 0$ limit.Comment: 14 page

A suggested standardized format for cosmic ray ground-level event data

A standardized format is suggested for the archival storage and exchange of neutron monitor data obtained during solar flare initiated ground level cosmic ray events. Using the data for the 7 May 1978 ground level event, a format has been developed that incorporates hourly data preceding and following the event and small time interval data immediately before and during the event. Provision has been made for the inclusion of uncorrected and corrected data as well as the atmospheric pressure. The cosmic ray intensity data are then reduced to a standard counting rate of counts per second facilitating the graphing and comparison of these data for various analyses

Time-resolved infrared emission from radiation-driven central obscuring structures in Active Galactic Nuclei

The central engines of Seyfert galaxies are thought to be enshrouded by geometrically thick gas and dust structures. In this article, we derive observable properties for a self-consistent model of such toroidal gas and dust distributions, where the geometrical thickness is achieved and maintained with the help of X-ray heating and radiation pressure due to the central engine. Spectral energy distributions (SEDs) and images are obtained with the help of dust continuum radiative transfer calculations with RADMC-3D. For the first time, we are able to present time-resolved SEDs and images for a physical model of the central obscurer. Temporal changes are mostly visible at shorter wavelengths, close to the combined peak of the dust opacity as well as the central source spectrum and are caused by variations in the column densities of the generated outflow. Due to the three-component morphology of the hydrodynamical models -- a thin disc with high density filaments, a surrounding fluffy component (the obscurer) and a low density outflow along the rotation axis -- we find dramatic differences depending on wavelength: whereas the mid-infrared images are dominated by the elongated appearance of the outflow cone, the long wavelength emission is mainly given by the cold and dense disc component. Overall, we find good agreement with observed characteristics, especially for those models, which show clear outflow cones in combination with a geometrically thick distribution of gas and dust, as well as a geometrically thin, but high column density disc in the equatorial plane.Comment: 16 pages, 12 figures, accepted for publication in MNRA

Discrete elastic model for stretching-induced flagellar polymorphs

Force-induced reversible transformations between coiled and normal polymorphs of bacterial flagella have been observed in recent optical-tweezer experiment. We introduce a discrete elastic rod model with two competing helical states governed by a fluctuating spin-like variable that represents the underlying conformational states of flagellin monomers. Using hybrid Brownian dynamics Monte-Carlo simulations, we show that a helix undergoes shape transitions dominated by domain wall nucleation and motion in response to externally applied uniaxial tension. A scaling argument for the critical force is presented in good agreement with experimental and simulation results. Stretching rate-dependent elasticity including a buckling instability are found, also consistent with the experiment

A non self-referential expression of Tsallis' probability distribution function

The canonical probability distribution function (pdf) obtained by optimizing the Tsallis entropy under the linear mean energy constraint (first formalism) or the escort mean energy constraint (third formalism) suffer self-referentiality. In a recent paper [Phys. Lett. A {\bf335} (2005) 351-362] the authors have shown that the pdfs obtained in the two formalisms are equivalent to the pdf in non self-referential form. Based on this result we derive an alternative expression, which is non self-referential, for the Tsallis distributions in both first and third formalisms.Comment: 3 page

Altitude variations of cosmic-ray soft and hard components observed by airborne detectors

The altitude variations of cosmic-ray total and hard components were measured up to 12,000 m on board a jet liner over Japan island on December, 1981. Observed results together with soft component are presented comparing with the model calculations through the atmosphere by applying the hadronic cascade

The life cycle of starbursting circumnuclear gas discs

High-resolution observations from the sub-mm to the optical wavelength regime resolve the central few 100pc region of nearby galaxies in great detail. They reveal a large diversity of features: thick gas and stellar discs, nuclear starbursts, in- and outflows, central activity, jet interaction, etc. Concentrating on the role circumnuclear discs play in the life cycles of galactic nuclei, we employ 3D adaptive mesh refinement hydrodynamical simulations with the RAMSES code to self-consistently trace the evolution from a quasi-stable gas disc, undergoing gravitational (Toomre) instability, the formation of clumps and stars and the disc's subsequent, partial dispersal via stellar feedback. Our approach builds upon the observational finding that many nearby Seyfert galaxies have undergone intense nuclear starbursts in their recent past and in many nearby sources star formation is concentrated in a handful of clumps on a few 100pc distant from the galactic centre. We show that such observations can be understood as the result of gravitational instabilities in dense circumnuclear discs. By comparing these simulations to available integral field unit observations of a sample of nearby galactic nuclei, we find consistent gas and stellar masses, kinematics, star formation and outflow properties. Important ingredients in the simulations are the self-consistent treatment of star formation and the dynamical evolution of the stellar distribution as well as the modelling of a delay time distribution for the supernova feedback. The knowledge of the resulting simulated density structure and kinematics on pc scale is vital for understanding inflow and feedback processes towards galactic scales.Comment: accepted by MNRA