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

Sequencing Renewables: Groundwater, Recycled Water, and Desalination

Optimal recycling of minerals can be thought of as an integral part of the theory of the mine. In this paper, we consider the role that wastewater recycling plays in the optimal extraction of groundwater, a renewable resource. We develop a two-sector dynamic optimization model to solve for the optimal trajectories of groundwater extraction and water recycling. For the case of spatially increasing recycling costs, recycled water serves as a supplemental resource in transition to the steady state. For constant unit recycling cost, recycled wastewater is eventually used as a sector-specific backstop for agricultural users, while desalination supplements household groundwater in the steady state. In both cases, recycling water increases welfare by shifting demand away from the aquifer, thus delaying implementation of costly desalination. The model provides guidance on when and how much to develop resource alternatives.Renewable resources, dynamic optimization, groundwater allocation, wastewater reuse, recycling, reclamation, water quality, Environmental Economics and Policy, Resource /Energy Economics and Policy, Q25, Q28, C6,

Partly melted DNA conformations obtained with a probability peak finding method

Peaks in the probabilities of loops or bubbles, helical segments, and unzipping ends in melting DNA are found in this article using a peak finding method that maps the hierarchical structure of certain energy landscapes. The peaks indicate the alternative conformations that coexist in equilibrium and the range of their fluctuations. This yields a representation of the conformational ensemble at a given temperature, which is illustrated in a single diagram called a stitch profile. This article describes the methodology and discusses stitch profiles vs. the ordinary probability profiles using the phage lambda genome as an example.Comment: 11 pages, 9 figures; v3: major changes; v4: applications sectio

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

Non-equilibrium hydrodynamics of a rotating filament

The nonlinear dynamics of an elastic filament that is forced to rotate at its base is studied by hydrodynamic simulation techniques; coupling between stretch, bend, twist elasticity and thermal fluctuations is included. The twirling-overwhirling transition is located and found to be strongly discontinuous. For finite bend and twist persistence length, thermal fluctuations lower the threshold rotational frequency, for infinite persistence length the threshold agrees with previous analytical predictions

Density PDFs of diffuse gas in the Milky Way

The probability distribution functions (PDFs) of the average densities of the diffuse ionized gas (DIG) and the diffuse atomic gas are close to lognormal, especially when lines of sight at |b|5 degree are considered separately. Our results provide strong support for the existence of a lognormal density PDF in the diffuse ISM, consistent with a turbulent origin of density structure in the diffuse gas.Comment: 4 pages, 1 figure. To be published in the proceedings of the August 2008 conference (held in Eapinho, Portugal) "The Role of Disk-Halo Interaction in Galaxy Evolution: Outflow vs Infall?", Ed. M. A. de Avillez, EAS Publications Serie

Obscuring Material around Seyfert Nuclei with Starbursts

The structure of obscuring matter in the environment of active galactic nuclei with associated nuclear starbursts is investigated using 3-D hydrodynamical simulations. Simple analytical estimates suggest that the obscuring matter with energy feedback from supernovae has a torus-like structure with a radius of several tens of parsecs and a scale height of about 10 pc. These estimates are confirmed by the fully non-linear numerical simulations, in which the multi-phase inhomogeneous interstellar matter and its interaction with the supernovae are consistently followed. The globally stable, torus-like structure is highly inhomogeneous and turbulent. To achieve the high column densities (> 10^{24} cm^{-2}) as suggested by observations of some Seyfert 2 galaxies with nuclear starbursts, the viewing angle should be larger than about 70 degree from the pole-on for a 10^8 solar mass massive black hole. Due to the inhomogeneous internal structure of the torus, the observed column density is sensitive to the line-of-sight, and it fluctuates by a factor of order 100. The covering fraction for N > 10^{23} cm^{-2} is about 0.4. The average accretion rate toward R < 1 pc is 0.4 solar mass/yr, which is boosted to twice that in the model without the energy feedback.Comment: ApJL in press (4 pages, 3 figures) A gziped ps file with high resolution figures is available at http://th.nao.ac.jp/~wada/AGN

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

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