Circular-like Maps: Sensitivity to the Initial Conditions, Multifractality and Nonextensivity

We generalize herein the usual circular map by considering inflexions of arbitrary power $z$, and verify that the scaling law which has been recently proposed [Lyra and Tsallis, Phys.Rev.Lett. 80 (1998) 53] holds for a large range of $z$. Since, for this family of maps, the Hausdorff dimension $d_f$ equals unity for all $z$ values in contrast with the nonextensivity parameter $q$ which does depend on $z$, it becomes clear that $d_f$ plays no major role in the sensitivity to the initial conditions.Comment: 15 pages (revtex), 8 fig

Validity and Failure of the Boltzmann Weight

The dynamics and thermostatistics of a classical inertial XY model, characterized by long-range interactions, are investigated on $d$-dimensional lattices ($d=1,2,$ and 3), through molecular dynamics. The interactions between rotators decay with the distance $r_{ij}$ like~$1/r_{ij}^{\alpha}$ ($\alpha \geq 0$), where $\alpha\to\infty$ and $\alpha=0$ respectively correspond to the nearest-neighbor and infinite-range interactions. We verify that the momenta probability distributions are Maxwellians in the short-range regime, whereas $q$-Gaussians emerge in the long-range regime. Moreover, in this latter regime, the individual energy probability distributions are characterized by long tails, corresponding to $q$-exponential functions. The present investigation strongly indicates that, in the long-range regime, central properties fall out of the scope of Boltzmann-Gibbs statistical mechanics, depending on $d$ and $\alpha$ through the ratio $\alpha/d$.Comment: 10 pages, 6 figures. To appear in EP

Possible Implication of a Single Nonextensive pTp_T Distribution for Hadron Production in High-Energy pppp Collisions

Multiparticle production processes in $pp$ collisions at the central rapidity region are usually considered to be divided into independent "soft" and "hard" components. The first is described by exponential (thermal-like) transverse momentum spectra in the low-$p_T$ region with a scale parameter $T$ associated with the temperature of the hadronizing system. The second is governed by a power-like distributions of transverse momenta with power index $n$ at high-$p_T$ associated with the hard scattering between partons. We show that the hard-scattering integral can be approximated as a nonextensive distribution of a quasi-power-law containing a scale parameter $T$ and a power index $n=1/(q -1)$, where $q$ is the nonextensivity parameter. We demonstrate that the whole region of transverse momenta presently measurable at LHC experiments at central rapidity (in which the observed cross sections varies by $14$ orders of magnitude down to the low $p_T$ region) can be adequately described by a single nonextensive distribution. These results suggest the dominance of the hard-scattering hadron-production process and the approximate validity of a "no-hair" statistical-mechanical description of the $p_T$ spectra for the whole $p_T$ region at central rapidity for $pp$ collisions at high-energies.Comment: 10 pages, 3 figures; presented by G.Wilk at the XLIV International Symposium on Multiparticle Dynamics; 8 - 12 September 2014 - Bologna, ITAL

Seepage in earth slopes with longitudinal drainage trenches

The major objective of this study was to determine the effect of hydraulic conductivity on the effectiveness and efficiency of longitudinal drains and on the time to reach steady state seepage under controlled laboratory conditions. An apparatus capable of simulating different slope angles and trench spacing was utilized in this study. By using this apparatus it was possible to obtain data regarding flow pattern, pressure heads, saturation time, influence of slope angle (theta), the trench spacing (W = 2w) and seepage depth (h) under steady state and transient conditions for different values of hydraulic conductivity. Two different soil types with different values of hydraulic conductivity (k) were tested at three slope angles. For each of these slopes, three different values of trench spacing were tested. For each of these, tests were conducted at three seepage levels. Measurements of seepage removal rate were taken along the longitudinal direction of the trench under transient and steady state conditions. The piezometric pressures at selected locations in the soil slope were measured

Resilience, Acculturative Stress, and Family Norms Against Disclosure of Mental Health Problems Among Foreign-Born Filipino American Women

The present study explores the relationships between resilience, acculturative stress, and family norms against disclosure of mental health problems among foreign-born Filipino American women. The sample consisted of 159 foreign-born Filipino American women aged 18 years and above and residing in Las Vegas, Nevada, United States. Participants completed paper-and-pencil questionnaires. Results indicated high levels of resilience and moderate levels of acculturative stress. Findings also showed a significant negative correlation between resilience and acculturative stress, and a significant predictive effect of resilience on acculturative stress. We also found a significant negative relationship between resilience and family norms against disclosure of mental health problems but no significant mediating effect of resilience on the relationship between acculturative stress and family norms. This lack of significant findings related to the mediating effect of resilience on the relationship between acculturative stress and family norms against disclosure of mental illness may be due to the absence of theoretical models and research regarding the role of resilience in the context of acculturation among Filipino American women. Our findings imply the need to further explore underlying mechanisms that explain the relationships between resilience, acculturative stress, and family norms. The findings of the study also confirm the need to develop interventions and resources that ameliorate acculturative stress and promote an increase of the disclosure and reporting of mental health problems among Filipino American women

Thermodynamics is more powerful than the role to it reserved by Boltzmann-Gibbs statistical mechanics

We brief{}ly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermodynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs~(BG) statistical mechanics is suff{}icient but not necessary. Indeed, the $N\to\infty$ limit of statistical mechanics is expected to be consistent with thermodynamics. For systems whose elements are generically independent or quasi-independent in the sense of the theory of probabilities, it is well known that the BG theory (based on the additive BG entropy) does satisfy this expectation. However, in complete analogy, other thermostatistical theories (\emph{e.g.}, $q$-statistics), based on nonadditive entropic functionals, also satisfy the very same expectation. We illustrate this standpoint with systems whose elements are strongly correlated in a specific manner, such that they escape the BG realm.Comment: The final publication is available at link.springer.co