Discrete Routh Reduction

This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical $J_2$ correction, as well as the double spherical pendulum. The $J_2$ problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the noncanonical nature of the symplectic structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added, fixed typo

Transport and stirring induced by vortex formation

The purpose of this study is to analyse the transport and stirring of fluid that occurs owing to the formation and growth of a laminar vortex ring. Experimental data was collected upstream and downstream of the exit plane of a piston-cylinder apparatus by particle-image velocimetry. This data was used to compute Lagrangian coherent structures to demonstrate how fluid is advected during the transient process of vortex ring formation. Similar computations were performed from computational fluid dynamics (CFD) data, which showed qualitative agreement with the experimental results, although the CFD data provides better resolution in the boundary layer of the cylinder. A parametric study is performed to demonstrate how varying the piston-stroke length-to-diameter ratio affects fluid entrainment during formation. Additionally, we study how regions of fluid are stirred together during vortex formation to help establish a quantitative understanding of the role of vortical flows in mixing. We show that identification of the flow geometry during vortex formation can aid in the determination of efficient stirring. We compare this framework with a traditional stirring metric and show that the framework presented in this paper is better suited for understanding stirring/mixing in transient flow problems. A movie is available with the online version of the paper

Cometary Astrometry

Modern techniques for making cometary astrometric observations, reducing these observations, using accurate reference star catalogs, and computing precise orbits and ephemerides are discussed in detail and recommendations and suggestions are given in each area

Equivariant differential characters and symplectic reduction

We describe equivariant differential characters (classifying equivariant circle bundles with connections), their prequantization, and reduction

Routh's procedure for non-Abelian symmetry groups

We extend Routh's reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a symmetry group which is not necessarily Abelian. To do so we analyse the restriction of the Euler-Lagrange field to a level set of momentum in velocity phase space. We present a new method of analysis based on the use of quasi-velocities. We discuss the reconstruction of solutions of the full Euler-Lagrange equations from those of the reduced equations.Comment: 30 pages, to appear in J Math Phy

Knowledge, Food and Place: a way of producing a way of knowing

The article examines the dynamics of knowledge in the valorisation of local food, drawing on the results from the CORASON project (A cognitive approach to rural sustainable development: the dynamics of expert and lay knowledge), funded by the EU under its Framework Programme 6. It is based on the analysis of several in-depth case studies on food relocalisation carried out in 10 European countries

Discovery of a New 89 Second X-ray Pulsar XTE J1906+09

We report on the discovery of a new pulsating X-ray source during Rossi X-ray Timing Explorer observations of a low galactic latitude field centered at RA (J2000) = 19 hr 05 m 43 s and Dec (J2000) = +08 deg 58 arcmin 48 arcsec. Significant pulsations were detected by both the PCA and HEXTE instruments aboard RXTE at a fundamental period of 89.17 +/- 0.02 seconds, with higher harmonics also visible in the 2-10 keV power spectrum. The folded lightcurve from the source is multiply peaked at lower energies, and changes to single peaked morphology above ~20 keV. The phase averaged spectrum from the source is well fit by strongly absorbed power law or thermal bremsstrahlung spectral models of photon index 1.9 +/- 0.1 or temperature 19.5 +/- 4.6 keV, respectively. The mean neutral hydrogen column density is approximately 10^23 cm^-2, suggesting a distance of >10 kpc to the source and a minimum 2-10 keV X-ray luminosity of 2*10^{35} ergs s^{-1}. By comparison with other pulsars with similar periods and luminosities, we suggest that XTE J1906+09 has a supergiant companion with an underfilled Roche lobe. We speculate further that one of the M stars in a peculiar M star binary system may be the companion.Comment: 14 pages, 2 figures. Accepted by ApJ Letter

Psychotic symptoms in methamphetamine psychotic in-patients

The present study was aimed at exploring the prevalence and factor structure of methamphetamine (MA) psychotic symptoms. The data were obtained from a cross-country evaluation of substance use, health, and treatment in MA psychotic in-patients. The prevalence rates of lifetime and current psychotic symptoms were determined by using Mini-International Neurospychiatric Interview-Plus, Module M. The Manchester scale was used to assess the severity of psychotic symptoms during the week prior to assessment. All eight items of the Manchester scale were subjected to principal-component analysis, eigenvalue one test, and varimax rotation. The data of 168 patients (127 male and 41 female) included in the analyses were obtained from Australia, Japan, the Philippines and Thailand. Persecutory delusion was the most common lifetime psychotic symptom found in 130 participants (77.4%), followed by auditory hallucinations, strange or unusual beliefs, and thought reading. Auditory hallucinations were the most common current symptom found in 75 participants (44.6%), followed by strange or unusual beliefs and visual hallucinations. Current negative symptoms were also found in 36 patients (21.4%). Apart from a factor of anxiety and depression, the results yielded a two-factor model of MA psychotic symptoms, which were negative and positive/disorganized syndromes. The negative syndrome comprised poverty of speech, psychomotor retardation, and flattened/incongruous affects. The positive syndrome consisted of delusions, hallucinations, and incoherent speech. Both positive/disorganized and negative syndromes should be taken into account in assessing MA psychotic symptoms. The clinical findings do not support the shortcomings of amphetamine-induced psychosis in modelling the negative symptoms of schizophrenia.Manit Srisurapanont, Robert Ali, John Marsden, Agueda Sunga, Kiyoshi Wada and Maristela Monteir

Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the symplectic structure in the case $\epsilon=0$. In the case $0<\epsilon\ll 1$ the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order