Negative specific heat in a Lennard-Jones-like gas with long-range interactions

We study, through molecular dynamics, a conservative two-dimensional Lennard-Jones-like gas (with attractive potential $\propto r^{-\alpha}$). We consider the effect of the range index $\alpha$ of interactions, number of particles, total energy and particle density. We detect negative specific heat when the interactions become long-ranged ($0\le \alpha/d<1$).Comment: LaTeX, 8 pages, 4 eps figures, contributed paper to the Proceedings of the International School and Workshop on Nonextensive Thermodynamics and physical applications, NEXT 2001, 23-30 May 2001, Cagliari (Italy) (Physica A) (New Title, new Fig. 4

CoachNet: The further development of a coordinated network for sport coaching in Europe

Leeds Metropolitan University (LMU), in partnership with the European Coaching Council (ECC), was successful in a bid to the European Commission under the Preparatory Action in the Field of Sport (EAC/18/2011). The project was designed to develop an innovative approach that would contribute to the strengthening of the organisation of sport in Europe as part of the ‘good governance, strand of the EU Preparatory Action in the Field of Sport. The primary objective was to examine ways in which the organisation of coaching could be enhanced in Europe, with a particular focus on the greater involvement of coaches in decisionmaking. In exploring ways to maximise the ‘voice of the coach’, the partnership between LMU and ECC was central to the project. ECC is the continental division of the International Council for Coaching Excellence (ICCE). Through its network, ECC was in a position to identify current organisational arrangements for coaching across Europe. LMU is a well established research and practice oriented university in the UK and played a lead role in coordinating the project and guiding the research methodology through its Sport Coaching and Physical Education (SCOPE) Research and Enterprise Centre. Varying arrangements for the development and management of coaching were observed through a study of European countries. Within this varied landscape, the representation of coaches was sporadic, ranging from no representative mechanism to a number of good practice examples that made provision for the tiered engagement of coaches depending on their role; sport and coaching status category. These examples included confederated models across sports; blended models across coaching status categories and single and multi-sport models for the engagement and representation of coaches. The study concluded that there is a need for a more considered approach to the involvement of coaches in decision-making, with a number of recommendations developed for consideration by member states and the European divisions of the International Federations. These recommendations proposed that the structure of ECC as the European arm of ICCE be reviewed, with the intention to more strongly engage organisations that have been established to represent the voice of coaches and leading to a re-structuring of the organisation. In this context, ICCE and ECC should play an even stronger advocacy, representative and action role in establishing coaching as a blended profession, which includes volunteer, part-time paid and full-time paid coaches. More coherent structures for the engagement of coaches in each sport and country are also recommended. This should occur as part of a wider commitment that the principle of listening to and hearing the voice of the coach should become more strongly embedded within the way in which sporting and related organisations operate. The EU is well placed to lead on this type of approach, ensuring the coaches are more fully engaged in social dialogue and in the process to further enhance the role of sport and coaching in Europe. Further research is also recommended on the nature, needs and demographics of the coaching workforce. All of these approaches need to be tempered with the realisation that coaches are individual decision-makers, operating in a wide variety of contexts and many of whom do not show a propensity for involvement in formal ‘representative’ structures. The need for alternative methods to connect with and engage coaches was, therefore, identified. These include a more segmented approach to engaging with coaches, depending on their coaching role and status, as well as the utilisation of more informal modes of web-based communication to connect directly with coaches in their daily lives. In all existing and future scenarios, the key role of federations at the national and international level in seeking, activating and allocating financial and other resources to connect with and support their coaches was highlighted. The findings have been notified to ICCE for formal consideration, leading to changes in the ways in which the voice of the coach is more clearly represented within the work of the organisation. ICCE should continue to work closely with the EU Sport Unit to ensure that the recommendations of this report are implemented and evaluated on an on-going basis

Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations

A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The H-theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck equations, in the presence of an external potential. For that, a relation involving terms of Fokker-Planck equations and general entropic forms is proposed. It is shown that, at equilibrium, this relation is equivalent to the maximum-entropy principle. Families of Fokker-Planck equations may be related to a single type of entropy, and so, the correspondence between well-known entropic forms and their associated Fokker-Planck equations is explored. It is shown that the Boltzmann-Gibbs entropy, apart from its connection with the standard -- linear Fokker-Planck equation -- may be also related to a family of nonlinear Fokker-Planck equations.Comment: 19 pages, no figure

On a generalization of the binomial distribution and its Poisson-like limit

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We discuss under which conditions this distribution can have a probabilistic interpretation.Comment: 17 pages, 6 figure

Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos

We consider nonequilibrium probabilistic dynamics in logistic-like maps $x_{t+1}=1-a|x_t|^z$, $(z>1)$ at their chaos threshold: We first introduce many initial conditions within one among $W>>1$ intervals partitioning the phase space and focus on the unique value $q_{sen}<1$ for which the entropic form $S_q \equiv \frac{1-\sum_{i=1}^{W} p_i^q}{q-1}$ {\it linearly} increases with time. We then verify that $S_{q_{sen}}(t) - S_{q_{sen}}(\infty)$ vanishes like $t^{-1/[q_{rel}(W)-1]}$ [$q_{rel}(W)>1$]. We finally exhibit a new finite-size scaling, $q_{rel}(\infty) - q_{rel}(W) \propto W^{-|q_{sen}|}$. This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.Comment: Final version with new Title and small modifications. REVTeX, 8 pages and 4 eps figure

On a generalised model for time-dependent variance with long-term memory

The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law probability density distribution of the random variable, it is not capable to reproduce further statistical properties of many of these time series such as: the strong persistence of the instantaneous variance characterised by large values of the Hurst exponent (H > 0.8), and asymptotic power-law decay of the absolute values self-correlation function. By means of considering an effective return obtained from a correlation of past returns that has a q-exponential form we are able to fix the limitations of the original model. Moreover, this improvement can be obtained through the correct choice of a sole additional parameter, $q_{m}$. The assessment of its validity and usefulness is made by mimicking daily fluctuations of SP500 financial index.Comment: 6 pages, 4 figure

Polarisation measurements with a CdTe pixel array detector for Laue hard X-ray focusing telescopes

Polarimetry is an area of high energy astrophysics which is still relatively unexplored, even though it is recognized that this type of measurement could drastically increase our knowledge of the physics and geometry of high energy sources. For this reason, in the context of the design of a Gamma-Ray Imager based on new hard-X and soft gamma ray focusing optics for the next ESA Cosmic Vision call for proposals (Cosmic Vision 2015-2025), it is important that this capability should be implemented in the principal on-board instrumentation. For the particular case of wide band-pass Laue optics we propose a focal plane based on a thick pixelated CdTe detector operating with high efficiency between 60-600 keV. The high segmentation of this type of detector (1-2 mm pixel size) and the good energy resolution (a few keV FWHM at 500 keV) will allow high sensitivity polarisation measurements (a few % for a 10 mCrab source in 106s) to be performed. We have evaluated the modulation Q factors and minimum detectable polarisation through the use of Monte Carlo simulations (based on the GEANT 4 toolkit) for on and off-axis sources with power law emission spectra using the point spread function of a Laue lens in a feasible configuration.Comment: 10 pages, 6 pages. Accepted for publication in Experimental Astronom

Option Pricing Formulas based on a non-Gaussian Stock Price Model

Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential equation, and some closed-form solutions are obtained. The standard B-S equation ($q=1$) which is used by economists to calculate option prices requires multiple values of the stock volatility (known as the volatility smile). Using $q=1.5$ which well models the empirical distribution of returns, we get a good description of option prices using a single volatility.Comment: final version (published