One-dimensional chaos in a system with dry friction: analytical approach

We introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of a domain of parameters where a chaotic dynamics can be observed. We prove existence of an infinite set of periodic points of arbitrarily big period. Moreover, a reduction of the considered map to a compact subset of the segment is semi-conjugated to a shift on the set of one-sided infinite boolean sequences. We find conditions, sufficient for existence of a superstable periodic point of the base map. The obtained result partially solves a general problem: theoretical confirmation of chaotic and periodic regimes numerically and experimentally observed for models of percussion drilling

Multiplicity Distributions in Canonical and Microcanonical Statistical Ensembles

The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand canonical partition function. Taylor expansion of the generating function is used to separate contributions to the partition function in their power in volume. We employ Laplace's asymptotic expansion to show that any equilibrium distribution of multiplicity, charge, energy, etc. tends to a multivariate normal distribution in the thermodynamic limit. Gram-Charlier expansion allows additionally for calculation of finite volume corrections. Analytical formulas are presented for inclusion of resonance decay and finite acceptance effects directly into the system partition function. This paper consolidates and extends previously published results of current investigation into properties of statistical ensembles.Comment: 53 pages, 7 figure

Particle Number Fluctuations in Statistical Model with Exact Charge Conservation Laws

Even though the first momenta i.e. the ensemble average quantities in canonical ensemble (CE) give the grand canonical (GC) results in large multiplicity limit, the fluctuations involving second moments do not respect this asymptotic behaviour. Instead, the asymptotics are strikingly different, giving a new handle in study of statistical particle number fluctuations in relativistic nuclear reactions. Here we study the analytical large volume asymptotics to general case of multispecies hadron gas carrying fixed baryon number, strangeness and electric charge. By means of Monte Carlo simulations we have also studied the general multiplicity probability distributions taking into account the decay chains of resonance states.Comment: 4 pages, 2 figures. The report of the talk given in Strangeness in Quark Matter 2004, Cape Town. Submitted to J. Phys. G: Nucl. Part. Phy

Particle Number Fluctuations in the Microcanonical Ensemble

Particle number fluctuations are studied in the microcanonical ensemble. For the Boltzmann statistics we deduce exact analytical formulae for the microcanonical partition functions in the case of non-interacting massless neutral particles and charged particles with zero net charge. The particle number fluctuations are calculated and we find that in the microcanonical ensemble they are suppressed in comparison to the fluctuations in the canonical and grand canonical ensembles. This remains valid in the thermodynamic limit too, so that the well-known equivalence of all statistical ensembles refers to average quantities, but does not apply to fluctuations. In the thermodynamic limit we are able to calculate the particle number fluctuations in the system of massive bosons and fermions when the exact conservation laws of both the energy and charge are taken into account.Comment: REVTeX, 17 pages, 9 figures, v3: misprints a correcte

Trace element analysis provides insight into the diets of early Late Miocene ungulates from the Rudabánya II locality (Hungary)

The early Late Miocene vertebrate locality of Rudabánya II (R. II) in northeastern Hungary preserves an abundance of forest-adapted ungulate species. To better understand the ecological relationships within this ancient ecosystem, we used analysis of enamel strontium/calcium (Sr/Ca) ratios to infer dietary preferences. The goals of the analysis were to: i) determine whether these ungulate species specialized in specific plants or plant parts; ii) discern whether the Sr/Ca ratios support what was previously suggested about the ecology of these species; and iii) evaluate the factors that may have acted to promote coexistence within this diverse community of predominantly browsing herbivores. Results show significant differences in the diets of the sampled species. The highest Sr/Ca ratios were displayed by the suids Parachleuastochoerus kretzoii [B1] and Propotamochoerus palaeochoerus implying a preference for Sr-rich underground plant parts. Elevated Sr/Ca ratios yielded by the cervid Lucentia aff. pierensis and equid Hippotherium intrans are indicative of intermediate feeding. The bovid Miotragocerus sp. showed higher Sr/Ca ratios than the gomphothere Tetralophodon longirostris, which is incongruent with morphological and stable isotope data, and suggested browsing by both taxa. This finding is likely the result of a difference in digestive physiology (ruminant vs. monogastric) rather than a difference in dietary behaviour. The lowest Sr/Ca ratios were displayed by the traguild Dorcatherium naui and moschid Micromeryx flourensianussuggesting a preference for Sr-poor fruits. Resource specialization and partitioning within the local environment likely acted to decrease interspecific competition and promote coexistence within the diverse ungulate community at R. II

Particle Number Fluctuations in Relativistic Bose and Fermi Gases

Particle number fluctuations are studied in relativistic Bose and Fermi gases. The calculations are done within both the grand canonical and canonical ensemble. The fluctuations in the canonical ensemble are found to be different from those in the grand canonical one. Effects of quantum statistics increase in the grand canonical ensemble for large chemical potential. This is, however, not the case in the canonical ensemble. In the limit of large charge density a strongest difference between the grand canonical and canonical ensemble results is observed.Comment: 13 pages, 6 figure

Methods to study event-by-event fluctuations in the NA61/SHINE experiment at the CERN SPS

Theoretical calculations locate the critical point of strongly interacting matter (CP) at energies accessible at the CERN SPS. Event-by-event transverse momentum and multiplicity fluctuations are considered as one of the most important tools to search for the CP. Pilot studies of the energy dependence and the system size dependence of both $p_T$ and multiplicity fluctuations were performed by the NA49 experiment. The NA61/SHINE ion program is a continuation of these efforts. After briefly recalling the essential NA49 results on fluctuations we will discuss the technical methods (removing Non-Target interactions) which we plan to apply for future transverse momentum and multiplicity fluctuation analyses.Comment: Proceedings of CPOD 2010, 23-29 August, JINR, Dubn

Multiplicity Fluctuations in Hadron-Resonance Gas

The charged hadron multiplicity fluctuations are considered in the canonical ensemble. The microscopic correlator method is extended to include three conserved charges: baryon number, electric charge and strangeness. The analytical formulae are presented that allow to include resonance decay contributions to correlations and fluctuations. We make the predictions for the scaled variances of negative, positive and all charged hadrons in the most central Pb+Pb (Au+Au) collisions for different collision energies from SIS and AGS to SPS and RHIC.Comment: 19 pages, 4 figure