Nos\'e-Hoover and Langevin thermostats do not reproduce the nonequilibrium behavior of long-range Hamiltonians

We compare simulations performed using the Nos\'e-Hoover and the Langevin thermostats with the Hamiltonian dynamics of a long-range interacting system in contact with a reservoir. We find that while the statistical mechanics equilibrium properties of the system are recovered by all the different methods, the Nos\'e-Hoover and the Langevin thermostats fail in reproducing the nonequilibrium behavior of such Hamiltonian.Comment: Contribution to the proceeding of the "International Conference on the Frontiers of Nonlinear and Complex Systems" in honor of Prof. Bambi Hu, Hong Kong, May 200

Hamiltonian dynamics reveals the existence of quasi-stationary states for long-range systems in contact with a reservoir

We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the Hamiltonian Mean Field model and the equilibrium ensemble equivalence. We find that long-lasting quasi-stationary states persist in presence of the interaction with the environment. Our results indicate that quasi-stationary states are indeed reproducible in real physical experiments.Comment: Title changed, throughout revision of the tex

Anomalous scaling due to correlations: Limit theorems and self-similar processes

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling forms, justify their universal character, and specify universality domains in the spaces of joint probability density functions of the summand variables. These density functions are assumed to be invariant under arbitrary permutations of their arguments. Examples from the theory of critical phenomena are discussed. The novel notion of stability implied by the limit theorems also allows us to define sequences of random variables whose sum satisfies anomalous scaling for any finite number of summands. If regarded as developing in time, the stochastic processes described by these variables are non-Markovian generalizations of Gaussian processes with uncorrelated increments, and provide, e.g., explicit realizations of a recently proposed model of index evolution in finance.Comment: Through text revision. 15 pages, 3 figure

Incomplete equilibrium in long-range interacting systems

We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasi-stationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution, we find that the Central Limit Theorem implies the Boltzmann expression in Gibbs' $\Gamma$-space. We identify the nonequilibrium sub-manifold of $\Gamma$-space characterizing the anomalous behavior and show that by restricting the Boltzmann-Gibbs approach to this sub-manifold we obtain the statistical mechanics of the quasi-stationary states.Comment: Title changed, throughout revision of the tex

Microcanonical quasi-stationarity of long-range interacting systems in contact with a heat bath

On the basis of analytical results and molecular dynamics simulations we clarify the nonequilibrium dynamics of a long-range interacting system in contact with a heat bath. For small couplings with the bath, we show that the system can first be trapped in a Vlasov quasi-stationary state, then a microcanonical one follows, and finally canonical equilibrium is reached at the bath temperature. We compare a Langevin mesoscopic thermostat with Hamiltonian reservoirs microscopically coupled with the system and demonstrate the equivalence of the two descriptions. Our identification of the parameters determining the quasi-stationary lifetimes could be exploited to control experimental systems such as the Free Electron Laser, in the presence of external noise or inherent imperfections

The impact of acute intoxications in a toxicological unit care in North East Italy

Retrospective study in a Toxicological Unit Care (TUC) performed to know the epidemiology of acute intoxication (AI) in Verona (Italy) during years 2008-2009. All data regarding patients with a diagnosis of certain/suspected AI were collected and evaluated: some demographic information, the characteristics of the agent involved, the pattern of exposure, the triage at the admission to TUC and the outcome. 244 cases were analyzed: 45.9% males and 54.9% females, mean age respectively 45.1 and 43.9 years. The monthly distribution of admitted patients resulted fairly constant, except from a light rising prevalence in autumn, with a majority of yellow (45.9%) and green (43.4%) triage code. The pattern of exposure resulted: ingestion (82.7% of cases; age peaks: 18-34 and 35-51 years old; mostly due to food (as mushrooms), drinks, detergents, soap, pharmaceutical, drugs of abuse, caustics substances), contact (10.2% of cases; age peak 18-51) and inhalation (6.9% of cases). In 17.2% of cases the poisoning exposure was intentional. In 63.5% the patients were sent to their general practitioners (45.5% of the yellow and 81.1% of the green coded patients) and in 22.1% of cases they were admitted to clinical rooms (44.6% of the yellow coded patients). In most cases the triage code assigned to the studied patients resulted yellow and green. Considering that the seriousness of the symptoms can appear after several hours from the exposure to toxic substances, a quick and specific intervention to obtain the best therapeutical effectiveness is suitable, in order to save lives or to avoid irremediable health damages

Mapping dynamical systems onto complex networks

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent the transitions between these regions. Parameters used to quantify the properties of complex networks, including those related to higher order neighborhoods, are used in the analysis. The methodology is tested for the logistic map, focusing the onset of chaos and chaotic regimes. It is found that the corresponding networks show distinct features, which are associated to the particular type of dynamics that have generated them.Comment: 13 pages, 8 eps files in 5 figure

Classical Infinite-Range-Interaction Heisenberg Ferromagnetic Model: Metastability and Sensitivity to Initial Conditions

A N-sized inertial classical Heisenberg ferromagnet, which consists in a modification of the well-known standard model, where the spins are replaced by classical rotators, is studied in the limit of infinite-range interactions. The usual canonical-ensemble mean-field solution of the inertial classical $n$-vector ferromagnet (for which $n=3$ recovers the particular Heisenberg model considered herein) is briefly reviewed, showing the well-known second-order phase transition. This Heisenberg model is studied numerically within the microcanonical ensemble, through molecular dynamics.Comment: 18 pages text, and 7 EPS figure

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie

High-Resolution Chandra X-Ray Imaging And Spectroscopy Of The Sigma Orionis Cluster

We present results of a 90 ks Chandra X-ray observation of the young sigma Orionis cluster ( age similar to 3 Myr) obtained with the HETGS. We use the high-resolution grating spectrum and moderate-resolution CCD spectrum of the massive central star sigma Ori AB (O9.5 V + B0.5 V) to test wind shock theories of X-ray emission and also analyze the high spatial resolution zero-order ACIS-S image of the central cluster region. Chandra detected 42 X-ray sources on the primary CCD (ACIS-S3). All but five have near-IR or optical counterparts and about one-fourth are variable. Notable high-mass stellar detections are sigma Ori AB, the magnetic B star sigma Ori E, and the B5 V binary HD 37525. Most of the other detections have properties consistent with lower mass K- or M-type stars. We present the first X-ray spectrum of the unusual infrared source IRS 1, located approximate to 3 \u27\u27 north of sigma Ori AB. Its X-ray properties and elongated mid-IR morphology suggest that it is an embedded low-mass T Tauri star whose disk/envelope is being photoevaporated by sigma Ori AB. We focus on the radiative wind shock interpretation of the soft luminous X-ray emission from sigma Ori AB, but also consider possible alternatives including magnetically confined wind shocks and colliding wind shocks. Its emission lines show no significant asymmetries or centroid shifts and are moderately broadened to HWHM approximate to 264 km s(-1), or one-fourth the terminal wind speed. Forbidden lines in He-like ions are formally undetected, implying strong UV suppression. The Mg XI triplet forms in the wind acceleration zone within one stellar radius above the surface. These X-ray properties are consistent in several respects with the predictions of radiative wind shock theory for an optically thin wind, but explaining the narrow line widths presents a challenge to the theory