Two-Particle Circular Billiards Versus Randomly Perturbed One-Particle Circular Billiards

We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an "intermittent" system. This billiard system behaves chaotically, but the time scale on which chaos manifests can become arbitrarily long as the sizes of the confined particles become smaller. The finite-time dynamics of this system depends on the relative frequencies of (chaotic) particle-particle collisions versus (integrable) particle-boundary collisions, and investigating these dynamics is computationally intensive because of the long time scales involved. To help improve understanding of such two-particle dynamics, we compare the results of diagnostics used to measure chaotic dynamics for a two-particle circular billiard with those computed for two types of one-particle circular billiards in which a confined particle undergoes random perturbations. Importantly, such one-particle approximations are much less computationally demanding than the original two-particle system, and we expect them to yield reasonable estimates of the extent of chaotic behavior in the two-particle system when the sizes of confined particles are small. Our computations of recurrence-rate coefficients, finite-time Lyapunov exponents, and autocorrelation coefficients support this hypothesis and suggest that studying randomly perturbed one-particle billiards has the potential to yield insights into the aggregate properties of two-particle billiards, which are difficult to investigate directly without enormous computation times (especially when the sizes of the confined particles are small).Comment: 9 pages, 7 figures (some with multiple parts); published in Chao

Quantum clocks and their synchronisation - the Alternate Ticks Game

Time plays a crucial role in the intuitive understanding of the world around us. Within quantum mechanics, however, time is not usually treated as an observable quantity; it enters merely as a parameter in the laws of motion of physical systems. Here we take an operational approach to time. Towards this goal we consider quantum clocks, i.e., quantum systems that generate an observable time scale. We then study the quality of quantum clocks in terms of their ability to stay synchronised. To quantify this, we introduce the "Alternate Ticks Game" and analyse a few strategies pertinent to this game

Trace level voltammetric determination of Zn(II) in selected nutrition related samples by bismuth-oxychloride-multiwalled carbon nanotube composite based electrode

Bismuth-oxychloride-multiwalled carbon nanotube composite material was applied as surface modifier of glassy carbon electrode (BiOCl-MWCNT/GCE) for rapid and reliable trace level determination of Zn(II) in selected foodstuffs. The method development encompasses the optimization of electrode preparation including the transmission electron microscopic study of the modifier suspension, selection of the supporting electrolyte pH, the adjustment of the operation parameters of the SW-ASV measurements and the investigation of matrix effects. The BiOCl-MWCNT/GCE showed an excellent linear response towards Zn reoxidation peak maxima in the concentration range from 2.50 to 80.0 μg L−1 with the calculated LOD of 0.75 μg L−1 which was associated with 120 s accumulation time and accumulation potential −1.40 V vs SCE in acetate buffer pH 4.5. A satisfactory repeatability expressed as relative standard deviation of 4.8% was obtained in the case of 10.0 μg L−1 Zn(II) in model solution. The Zn(II) reoxidation signal from BiOCl-MWCNT/GCE received by the optimized SW-ASV method was compared with those recorded with bare, classical bismuth-film, multiwalled carbon nanotubes and by in situ made advanced bismuth-film-MWCNTs working electrodes. The applicability of the proposed BiOCl-MWCNT/GCE based method was corroborated via measuring the target analyte in two nutrition related real samples: in a dietary supplement and in a brewer's yeast sample. Comparative flame atomic absorption spectrometric measurements verified the obtained results in the case of yeast sample