Chaotic dynamics and orbit stability in the parabolic oval billiard

Chaotic properties of the one-parameter family of oval billiards with parabolic boundaries are investigated. Classical dynamics of such billiard is mixed and depends sensitively on the value of the shape parameter. Deviation matrices of some low period orbits are analyzed. Special attention is paid to the stability of orbits bouncing at the singular joining points of the parabolic arcs, where the boundary curvature is discontinuous. The existence of such orbits is connected with the segmentation of the phase space into two or more chaotic components. The obtained results are illustrated by numerical calculations of the Poincaré sections and compared with the properties of the elliptical stadium billiards

Classical and quantum chaos in the generalized parabolic lemon-shaped billiard

Two-dimensional billiards of a generalized parabolic lemonlike shape are investigated classically and quantum mechanically depending on the shape parameter δ. Quantal spectra are analyzed by means of the nearest-neighbor spacing distribution method. Calculated results are well accounted for by the proposed new two-parameter distribution function P(s), which is a generalization of Brody and Berry-Robnik distributions. Classically, Poincaré diagrams are shown and interpreted in terms of the lowest periodic orbits. For δ=2, the billiard has some unique characteristics resulting from the focusing property of the parabolic mirror. Comparison of the classical and quantal results shows an accordance with the Bohigas, Giannoni, and Schmit conjecture and confirms the relevance of the new distribution for the analysis of realistic spectral data

Chaotic behavior in lemon-shaped billiards with elliptical and hyperbolic boundary arcs

Chaotic properties of a new family, ellipse hyperbola billiards (EHB), of lemon-shaped two-dimensional billiards, interpolating between the square and the circle, whose boundaries consist of hyperbolic, parabolic, or elliptical segments, depending on the shape parameter δ, are investigated classically and quantally. Classical chaotic fraction is calculated and compared with the quantal level density fluctuation measures obtained by fitting the calculated level spacing sequences with the Brody, Berry-Robnik, and Berry-Robnik-Brody distributions. Stability of selected classical orbits is investigated, and for some special hyperbolic points in the Poincaré sections, the “blinking island” phenomenon is observed. Results for the EHB billiards are compared with the properties of the family of generalized power-law lemon-shaped billiards

Chemistry in Edication: Kilogram and Mole in a New Attire – On Radical Changes in the International System of Units (SI)

Od 20. svibnja 2019. jedinice Međunarodnog sustava SI definirane su s pomoću sedam prirodnih konstanti, νCs, c, h, e, kB, NA i Kcd. Promjene su prihvaćene na 26. sjednici Opće konferencije za utege i mjere (Conférence générale des poids et mesures, CGPM), održanoj u Versaillesu u Francuskoj 18. studenoga 2018. U članku su navedene stare i nove definicije osnovnih jedinica sustava SI, kao i matematički izrazi koji se dobiju rješavanjem algebarskih jednadžbi implicitno sadržanih u novim definicijama. Posebna je pozornost posvećena povijesti i novim definicijama jedinica kilogram i mol te metodičkim aspektima njihova tumačenja. Navedeni su i odabrani numerički primjeri, korisni za primjenu u srednjoškolskoj i sveučilišnoj nastavi kemije. Ovo djelo je dano na korištenje pod licencom Creative Commons Imenovanje 4.0 međunarodna.At the end of the year 2018, news of a radical transformation of the International System of Units (SI) spread worldwide. Particular excitement was caused by the abandonment of the 140-year-old prototype of kilogram, the base SI unit of mass, stored under the glass bell in Sèvres near Paris, France, and by the introduction of a new definition of kilogram using the quantum-mechanical Planck constant h. The changes were accepted at the 26th session of the General Conference on Weights and Measures (CGPM) held in Versailles, France, on November 18, 2018, and entered into force on May 20, 2019. In the new definitions the SI units are derived by means of seven natural constants, νCs, c, h, e, kB, NA, and Kcd. The article presents the old and the new definitions of the seven base units of the SI system together with the mathematical expressions obtained by solving algebraic equations implicitly contained in the new definitions. The newly defined set of natural units for the base and derived quantities is discussed. The properties and the history of units kilogram and mole as well as the educational aspects of their interpretation are given special attention. Some selected numerical examples are proposed for use in the high school and university chemistry classes. This work is licensed under a Creative Commons Attribution 4.0 International License

Dependence of chaotic behavior on the residual interaction in the odd-odd nucleus 106Ag

Dependence of the level-density fluctuations on the interaction strengths for the 106Ag energy spectrum calculated in the interacting-boson-fermion-fermion model is investigated. Breaking of symmetry is accompanied by a rapid transition from a nearly Poissonian distribution to the intermediate pattern between Poisson and Gaussian-orthogonal-ensemble distributions. Fluctuation measures show sensitivity to details of nuclear dynamics. Possible connection with the degree of chaos is discussed

Neutron-capture gamma-ray study of levels in Ba135 and description of nuclear levels in the interacting-boson-fermion model

We have performed neutron-capture gamma-ray studies on natural and enriched targets of 134Ba in order to investigate the nuclear levels of 135Ba. The low-energy level spectra were compared with the calculations using the interacting-boson-fermion model (IBFM) and the cluster-vibration model. The level densities up to 5 MeV that are calculated within the IBFM are in accordance with the constant temperature Fermi gas model. From the spin distribution we have determined the corresponding spin cutoff parameter σ and compared it to the prediction from nuclear systematics

Study of ^194 Ir via thermal neutron capture and (d,p) reactions

Levels of ^194 Ir were studied using thermal neutron capture reaction. A pair spectrometer was used to measure the high-energy gamma-ray spectrum from thermal-neutron capture in enriched ^193 Ir target over the energy range 4640 - 6100 keV. The low-energy gamma-radiation from the reaction was studied with crystal diffraction spectrometers, and conversion electrons were observed with magnetic spectrometers. The high-sensitivity measurements at the Grenoble reactor, evaluated for transition energies up to 500 keV, are compared with lower-sensitivity measurements at the Wuerenlingen and Salaspils reactors. The comparison helped to obtain reliable isotopic identification for a number of ^194 Ir lines. The multipolarity admixtures for 29 gamma-transitions were determined on the basis of conversion lines from different electron subshells. Prompt and delayed gamma-gamma coincidences were measured using semiconductor and scintillation detectors. The ^193 Ir(d,p) high-resolution spectra, observed with a magnetic spectrometer, are given. All these data contributed to establishing a detailed level scheme of ^194 Ir. Additional data and the interpretation of the results in terms of current models will be presented in a forthcoming paper

Study of ^194 Ir via thermal neutron capture and (d,p) reactions

Levels of ^194 Ir were studied using thermal neutron capture reaction. A pair spectrometer was used to measure the high-energy gamma-ray spectrum from thermal-neutron capture in enriched ^193 Ir target over the energy range 4640 - 6100 keV. The low-energy gamma-radiation from the reaction was studied with crystal diffraction spectrometers, and conversion electrons were observed with magnetic spectrometers. The high-sensitivity measurements at the Grenoble reactor, evaluated for transition energies up to 500 keV, are compared with lower-sensitivity measurements at the Wuerenlingen and Salaspils reactors. The comparison helped to obtain reliable isotopic identification for a number of ^194 Ir lines. The multipolarity admixtures for 29 gamma-transitions were determined on the basis of conversion lines from different electron subshells. Prompt and delayed gamma-gamma coincidences were measured using semiconductor and scintillation detectors. The ^193 Ir(d,p) high-resolution spectra, observed with a magnetic spectrometer, are given. All these data contributed to establishing a detailed level scheme of ^194 Ir. Additional data and the interpretation of the results in terms of current models will be presented in a forthcoming paper