Quantum signatures of classical multifractal measures

A clear signature of classical chaoticity in the quantum regime is the fractal Weyl law, which connects the density of eigenstates to the dimension $D_0$ of the classical invariant set of open systems. Quantum systems of interest are often {\it partially} open (e.g., cavities in which trajectories are partially reflected/absorbed). In the corresponding classical systems $D_0$ is trivial (equal to the phase-space dimension), and the fractality is manifested in the (multifractal) spectrum of R\'enyi dimensions $D_q$. In this paper we investigate the effect of such multifractality on the Weyl law. Our numerical simulations in area-preserving maps show for a wide range of configurations and system sizes $M$ that (i) the Weyl law is governed by a dimension different from $D_0=2$ and (ii) the observed dimension oscillates as a function of $M$ and other relevant parameters. We propose a classical model which considers an undersampled measure of the chaotic invariant set, explains our two observations, and predicts that the Weyl law is governed by a non-trivial dimension $D_\mathrm{asymptotic} < D_0$ in the semi-classical limit $M\rightarrow\infty$

RECOMMENDATIONS FOR DENTAL EDUCATION AND TECHNOLOGY ENHANCED LEARNING (TEL) IN MALAWI: REPORT OF A ROUND TABLE DISCUSSION

This report summarises the Malawian roundtable discussions held at the 10th Colloquium on Innovations in Education, Brescia University, Italy. The specific goal was to review the special circumstances for TEL implementation in Dentistry in Malawi and provide recommendations

Fractal Dimensions in Classical and Quantum Mechanical Open Chaotic Systems

Fractals have long been recognized to be a characteristic feature arising from chaotic dynamics; be it in the form of strange attractors, of fractal boundaries around basins of attraction, or of fractal and multifractal distributions of asymptotic measures in open systems. In this thesis we study fractal and multifractal measure distributions in leaky Hamiltonian systems. Leaky systems are created by introducing a fully or partially transparent hole in an otherwise closed system, allowing trajectories to escape or lose some of their intensity. This dynamics results in intricate (multi)fractal distributions of the surviving trajectories. These systems are suitable models for experimental setups such as optical microcavities or microwave resonators. In this thesis we perform an improved investigation of the fractality in these systems using the concept of effective dimensions. They are defined as the dimensions far from the usually considered asymptotics of infinite evolution time $t$, infinite sample size $S$, and infinite resolution (infinitesimal box-size $varepsilon$). Yet, as we show, effective dimensions can be considered as intrinsic to the dynamics of the system. We present a detailed discussion of the behaviour of the numerically observed dimension $D_mathrm{obs}(S,t,varepsilon)$. We show that the three parameters can be expressed in terms of limiting length scales that define the parameter ranges in which $D_mathrm{obs}(S,t,varepsilon)$ is an effective dimension of the system. We provide dynamical and statistical arguments for the dependence of these scales on $S$, $t$, and $varepsilon$ in strongly chaotic systems and show that the knowledge of the scales allows us to define meaningful effective dimensions. We apply our results to three main fields. In the context of numerical algorithms to calculate dimensions, we show that our findings help to numerically find the range of box sizes leading to accurate results. We further show that they allow us to minimize the computational cost by providing estimates of the required sample-size and iteration time needed. A second application field of our results is systems exhibiting non-trivial dependencies of the effective dimension $D_mathrm{eff}$ on $t$ and $varepsilon$. We numerically explore this in weakly chaotic leaky systems. There, our findings provide insight into the dynamics of the systems, since deviations from our predictions based on strongly chaotic systems at a given parameter range are a sign that the stickiness inherent to such systems needs to be taken into account in that range. Lastly, we show that in quantum analogues of chaotic maps with a partial leak, a related effective dimension can be used to explain the numerically observed deviation from the predictions provided by the fractal Weyl law for systems with fully absorbing leaks. Here, we provide an analytical description of the expected scaling based on the classical dynamics of the system and compare it with numerical results obtained in the studied quantum maps.Es ist seit langem bekannt, dass Fraktale eine charakteristische Begleiterscheinung chaotischer Dynamik sind. Sie treten in Form von seltsamen Attraktoren, von fraktalen Begrenzungen der Einzugsbereiche von Attraktoren oder von fraktalen und multifraktalen Verteilungen asymptotischer Maße in offenen Systemen auf. In dieser Arbeit betrachten wir fraktal und multifraktal verteilte Maße in geöffneten hamiltonschen Systemen. Geöffnete Systeme werden dadurch erzeugt, dass man ein völlig oder teilweise transparentes Loch im Phasenraum definiert, durch das Trajektorien entkommen können oder in dem sie einen Teil ihrer Intensität verlieren. Die Dynamik in solchen Systemen erzeugt komplexe (multi)fraktale Verteilungen der verbleibenden Trajektorien, beziehungsweise ihrer Intensitäten. Diese Systeme sind zur Modellierung experimenteller Aufbauten, wie zum Beispiel optischer Mikrokavitäten oder Mikrowellenresonatoren, geeignet. In dieser Arbeit führen wir eine verbesserte Untersuchung der Fraktalität in derartigen Systemen durch, die auf dem Konzept der effektiven Dimensionen beruht. Diese sind als die Dimensionen definiert, die weit weg von den üblicherweise betrachteten Limites unendlicher Iterationszeit $t$, unendlicher Stichprobengröße $S$ und unendlicher Auflösung, also infinitesimaler Boxgröße $varepsilon$ auftreten. Dennoch können effektive Dimensionen, wie wir zeigen, als der Dynamik des Systems inhärent angesehen werden. Wir führen eine detaillierte Diskussion der numerisch beobachteten Dimension $D_mathrm{obs}(S,t,varepsilon)$ durch und zeigen, dass die drei Parameter $S$, $t$ und $varepsilon$ in Form grenzwertiger Längenskalen ausgedrückt werden können, die die Parameterbereiche definieren, in denen $D_mathrm{obs}(S,t,varepsilon)$ den Wert einer effektiven Dimension des Systems annimmt. Wir beschreiben das Verhalten dieser Längenskalen in stark chaotischen Systemen als Funktionen von $S$, $t$ und $varepsilon$ anhand statistischer Überlegungen und anhand von auf der Dynamik basierenden Aussagen. Weiterhin zeigen wir, dass das Wissen um diese Längenskalen die Definition aussagekräftiger effektiver Dimensionen ermöglicht. Wir wenden unsere Ergebnisse hauptsächlich in drei Bereichen an: Im Kontext numerischer Algorithmen zur Dimensionsberechnung zeigen wir, dass unsere Ergebnisse es erlauben, diejenigen $varepsilon$-Bereiche zu finden, die zu korrekten Ergebnissen führen. Weiterhin zeigen wir, dass sie es uns erlauben, den Rechenaufwand zu minimieren, indem sie uns eine Abschätzung der benötigten Stichprobengröße und Iterationszeit ermöglichen. Ein zweiter Anwendungsbereich sind Systeme, die sich durch eine nichttriviale Abhängigkeit von $D_mathrm{eff}$ von $t$ und $varepsilon$ auszeichnen. Hier ermöglichen unsere Ergebnisse ein besseres Verständnis der Systeme, da Abweichungen von den Vorhersagen basierend auf der Annahme von starker Chaotizität ein Anzeichen dafür sind, dass im entsprechenden Parameterbereich die Eigenschaft dieser Systeme, dass Bereiche in ihrem Phasenraum Trajektorien für eine begrenzte Zeit einfangen können, relevant ist. Zuletzt zeigen wir, dass in quantenmechanischen Analoga chaotischer Abbildungen mit partiellen Öffnungen eine verwandte effektive Dimension genutzt werden kann, um die numerisch beobachteten Abweichungen vom fraktalen weyl'schen Gesetz für völlig transparente Öffnungen zu erklären. In diesem Zusammenhang zeigen wir eine analytische Beschreibung des erwarteten Skalierungsverhaltens auf, die auf der klassischen Dynamik des Systems basiert, und vergleichen sie mit numerischen Erkenntnissen, die wir über die Quantenabbildungen gewonnen haben

The impact of COVID-19 on the practice of Oral and Maxillofacial Pathology in the United States and Canada

Background: The COVID-19 pandemic has significantly disrupted the delivery of healthcare, including oral healthcare services. The restrictions imposed for mitigating spread of the virus forced dental practitioners to adopt significant changes in their workflow pattern. The aim of this study was to investigate the impact of the pandemic on the practice of oral and maxillofacial pathology in two countries in regard to educational activities, and clinical and diagnostic pathology services

ON MULTIPLE BROODS AND THE BREEDING STRATEGY OF ARCTIC SANDERLINGS

Sanderlings on Bathurst Island in the Canadian arctic have two patterns of incubation. At some nests the eggs are covered soon after the fourth egg has been laid and at others incubation is delayed for 5–6 days. Because the delay is about the same time required to lay a second clutch and because a single individual alone incubates at any one nest, we suspected that Sanderlings might normally lay two clutches in a season, the male caring for one brood and the female for the other. Histological and gross examination of the ovaries of two females taken as the birds began incubation showed eight freshly ovulated follicles in each female. The size gradation and histological appearance of the follicles indicated that two clutches of four eggs each had been laid within 8–10 days by a single female. The ovary of one female had additional large yolky follicles, suggesting a physiological capability of further ovulations. Field conditions in the arctic summer are highly variable, and the small eggs and the rapid sequence of broods of Sanderlings may be breeding adaptations that permit them to multiply the traditional wader clutch of four eggs by 2 or 3 in favourable years. Selection for mating systems characterised by brief pair bonds and by polyandry is expected in precocial birds where some broods are incubated and cared for by the male, but further field work is required to determine the precise mating system of Sanderlings.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74788/1/j.1474-919X.1973.tb02638.x.pd

Host species determines egg size in Oriental cuckoo

© 2018 The Zoological Society of London.The Oriental cuckoo Cuculus optatus is an obligate brood parasite associated with species of the genus Phylloscopus. Four distinct phenotypes of Oriental cuckoo eggs, matching eggshell colour patterns of Arctic warbler Phylloscopus borealis, common chiffchaff (Siberian) P. collybita tristis, yellow-browed warbler P. inornatus and Pallas's leaf warbler P. proregulus, have been identified in the Russian part of its breeding area. We compared egg length, breadth and volume of Oriental cuckoo egg phenotypes with eggs of the corresponding hosts from three geographical regions in Russia: the Urals, Siberia and the Far East. We found significant oometric differences between Oriental cuckoo egg phenotypes. Egg breadth of each cuckoo group matched the egg breadth of the host species, while the length of cuckoo eggs did not match egg length in host species. Our results can be explained in terms of clutch geometry. An egg sticking out above the clutch is likely to be rejected by the host and so breadth should match the host's egg. This constrains cuckoos in maintaining large egg volumes, which are essential for providing a cuckoo chick with the energy required to eject the host eggs and chicks. An increased egg length might compensate for breadth constraints. We suggest that the size of cuckoo eggs might also be affected by parental care - when only one parent is involved in feeding, eggs need to be larger. This might explain why the longest cuckoo eggs belonged to the phenotype parasitizing the smallest host, Pallas's leaf warbler, where only one parent feeds the chicks. In our view, differences in egg sizes of Oriental cuckoo phenotypes provide evidence of their adaptations to brood parasitism on small leaf warbler species.Peer reviewe

Spectral data for doubly excited states of helium with non-zero total angular momentum

A spectral approach is used to evaluate energies and widths for a wide range of singlet and triplet resonance states of helium. Data for total angular momentum $L=1,...,4$ is presented for resonances up to below the 5th single ionization threshold. In addition the expectation value of $\cos(\theta_{12})$ is given for the calculated resonances.Comment: 35 pages, 16 tables, to be published in Atomic Data and Nuclear Data Table

Framework for E‐Learning Assessment in Dental Education: A Global Model for the Future

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153544/1/jddj002203372013775tb05504x.pd