Illustrating Dynamical Symmetries in Classical Mechanics: The Laplace-Runge-Lenz Vector Revisited

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and degeneracy associated with this vector and with analogous dynamical symmetris. We define a conserved dynamical variable $\alpha$ that characterizes the orientation of the orbit in two-dimensional configuration space for the Kepler problem and an analogous variable $\beta$ for the isotropic harmonics oscillator. This orbit orientation variable is canonically conjugate to the angular momentum component normal to the plane of motion. We explore the canoncial one-parameter group of transformations generated by $\alpha (\beta).$ Because we have an obvious pair of conserved canonically conjugate variables, it is desirable to us them as a coordinate-momentum pair. In terms of these phase space coordinates, the form of the Hamiltonian is nearly trivial because neither member of the pair can occur explicitly in the Hamiltonian. From these considerations we gain a simple picture of the dynamics in phase space. The procedure we use is in the spirit of the Hamilton-Jacobi method.Comment: 15 pages, 1 figure, to be published in American Journal of Physic

Cognitive Rhythms Reluctantly Revisited

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.In response to the Power (1983) - Beattie (1984) controversy, a more general critique of the construct of cognitive rhythms is presented. It is argued that the term itself is a misnomer, that the relevance of articulation rate has been neglected, that fluent and hesitant phases of cognitive rhythms have been assessed both subjectively and intuitively, that the speech-production model underlying the concept is simplistic, and that the empirical evidence is based on an extraordinarily small corpus which has been described inadequately in the research literature

Integrating physical and psychological wellbeing in child health

Research shows that the integration of physical and mental healthcare in paediatric settings is beneficial in terms of clinical and cost effectiveness (Kahana, Drotar, & Frazier, 2008; Douglas & Benson 2008, Griffin & Christie, 2008). Due to the high rates of mental health problems within this population, several studies have shown that referral to paediatric psychology should be increased (e.g. Wagner & Smith, 2007). However, there are few studies investigating factors influencing healthcare professionals’ referral behaviour. The current study used theory of planned behaviour (Ajzen, 1988; 1991) to develop a questionnaire which explores factors influencing the referral of children and families to paediatric psychology. Psychometric properties of the questionnaire were examined. Findings indicate that the questionnaire holds good reliability and validity and that the main constructs of theory of planned behaviour are useful in predicting intention to refer to paediatric psychology. Specific beliefs about referral were also shown to influence intention to refer. Findings that individual referrer factors such as attitudes and beliefs can impact healthcare professionals’ referral behaviour indicates that multidisciplinary interventions and inter-professional education relating to the psychological aspects of illness are required. Recommendations for future research are discussed

The classical double copy for Taub-NUT spacetime

The double copy is a much-studied relationship between gauge theory and gravity amplitudes. Recently, this was generalised to an infinite family of classical solutions to Einstein's equations, namely stationary Kerr-Schild geometries. In this paper, we extend this to the Taub-NUT solution in gravity, which has a double Kerr-Schild form. The single copy of this solution is a dyon, whose electric and magnetic charges are related to the mass and NUT charge in the gravity theory. Finally, we find hints that the classical double copy extends to curved background geometries.Comment: 13 pages, no figures. Minor edits to match journal versio

Constraints on New Physics from Baryogenesis and Large Hadron Collider Data

We demonstrate the power of constraining theories of new physics by insisting that they lead to electroweak baryogenesis, while agreeing with current data from the Large Hadron Collider. The general approach is illustrated with a singlet scalar extension of the Standard Model. Stringent bounds can already be obtained, which reduce the viable parameter space to a small island.Comment: 4 pages, 2 figures. References added, figures updated. Version to appear in PR

Analysis of permanent magnets as elasmobranch bycatch reduction devices in hook-and-line and longline trials

Previous studies indicate that elasmobranch fishes (sharks, skates and rays) detect the Earth’s geomagnetic field by indirect magnetoreception through electromagnetic induction, using their ampullae of Lorenzini. Applying this concept, we evaluated the capture of elasmobranchs in the presence of permanent magnets in hook-and-line and inshore longline fishing experiments. Hooks with neodymium-iron-boron magnets significantly reduced the capture of elasmobranchs overall in comparison with control and procedural control hooks in the hook-and-line experiment. Catches of Atlantic sharpnose shark (Rhizoprionodon terraenovae) and smooth dogfish (Mustelus canis) were signif icantly reduced with magnetic hook-and-line treatments, whereas catches of spiny dogfish (Squalus acanthias) and clearnose skate (Raja eglanteria) were not. Longline hooks with barium-ferrite magnets significantly reduced total elasmobranch capture when compared with control hooks. In the longline study, capture of blacktip sharks (Carcharhinus limbatus) and southern stingrays (Dasyatis americana) was reduced on magnetic hooks, whereas capture of sandbar shark (Carcharhinus plumbeus) was not affected. Teleosts, such as red drum (Sciaenops ocellatus), Atlantic croaker (Micropogonias undulatus), oyster toadfish (Opsanus tau), black sea bass (Centropristis striata), and the bluefish (Pomatomas saltatrix), showed no hook preference in either hook-and-line or longline studies. These results indicate that permanent magnets, although eliciting species-specific capture trends, warrant further investigation in commercial longline and recreational fisheries, where bycatch mortality is a leading contributor to declines in elasmobranch populations