739 research outputs found
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 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
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