Geodesic equations and algebro-geometric methods

For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all possible geodesic motions. Such a thorough analysis can be accomplished most effectively by using analytical methods to solve the geodesic equation. In this contribution, the use of elliptic functions and their generalizations for solving the geodesic equation in a wide range of well known space-times, which are part of the general Pleba\'nski-Demia\'nski family of solutions, will be presented. In addition, the definition and calculation of observable effects like the perihelion shift will be presented and further applications of the presented methods will be outlined.Comment: 8 pages, no figures; based on presentation at the conference "Relativity and Gravitation: 100 Years after Einstein in Prague," Prague, 2012. Relativity and Gravitation, volume 157 of Springer Proceedings in Physics, p 91. Springer International Publishing, 201

Functional morphology and efficiency of the antenna cleaner in Camponotus rufifemur ants

Contamination of body surfaces can negatively affect many physiological functions. Insects have evolved different adaptations for removing contamination, including surfaces that allow passive self-cleaning and structures for active cleaning. Here, we study the function of the antenna cleaner in Camponotus rufifemur ants, a clamp-like structure consisting of a notch on the basitarsus facing a spur on the tibia, both bearing cuticular ’combs’ and ’brushes’. The ants clamp one antenna tightly between notch and spur, pull it through, and subsequently clean the antenna cleaner itself with the mouthparts. We simulated cleaning strokes by moving notch or spur over antennae contaminated with fluorescent particles. The notch removed particles more efficiently than the spur, but both components eliminated >60% of the particles with the first stroke. Ablation of bristles, brush and comb strongly reduced the efficiency, indicating that they are essential for cleaning. To study how comb and brush remove particles of different sizes, we contaminated antennae of living ants, and anaesthetized them immediately after they had performed the first cleaning stroke. Different sized beads were trapped in distinct zones of the notch, consistent with the gap widths between cuticular outgrowths. This suggests that the antenna cleaner operates like a series of sieves that remove the largest objects first, followed by smaller ones, down to the smallest particles that get caught by adhesion.To AH: Research grant from the Konrad-Adenauer-Foundation To DL: Research grant from the Cusanuswerk To WF: UK Biotechnology and Biological Sciences Research Council (BB/I008667/1)This is the final version of the article. It first appeared from RSC via http://dx.doi.org/10.1098/rsos.15012

Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times

We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic function. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the "Misner string" in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub, and the analytic extension of Miller, Kruskal and Godfrey, and compare with the Reissner-Nordstr\"om space-time.Comment: 22 pages, 14 figures, accepted for publication in PR

Analytical solution of the geodesic equation in Kerr-(anti) de Sitter space-times

The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic p, zeta, and sigma functions as well as hyperelliptic Kleinian sigma functions restricted to the one-dimensional theta-divisor. We analyze the dependency of timelike geodesics on the parameters of the space-time metric and the test-particle and compare the results with the situation in Kerr space-time with vanishing cosmological constant. Furthermore, we systematically can find all last stable spherical and circular orbits and derive the expressions of the deflection angle of flyby orbits, the orbital frequencies of bound orbits, the periastron shift, and the Lense-Thirring effect.Comment: 18 pages, 11 figure

Nucleonic resonance excitations with linearly polarized photon in γp→ωp\gamma p\to \omega p

In this work, an improved quark model approach to the $\omega$ meson photo-production with an effective Lagrangian is presented. The {\it t}-channel {\it natural}-parity exchange is taken into account through the Pomeron exchange, while the {\it unnatural}-parity exchange is described by the $\pi^0$ exchange. With a very limited number of parameters, the available experimental data in the low energy regime can be consistently accounted for. We find that the beam polarization observables show sensitivities to some {\it s}-channel individual resonances in the $SU(6)\otimes O(3)$ quark model symmetry limit. Especially, the two resonances $P_{13}(1720)$ and $F_{15}(1680)$, which belong to the representation $[{\bf 56, ^2 8}, 2, 2, J]$, have dominant contributions over other excited states. Concerning the essential motivation of searching for "missing resonances" in meson photo-production, this approach provides a feasible framework, on which systematic investigations can be done.Comment: 16 pages, Revtex, 9 eps figures, to appear in PR

Relating Differently to Intrusive Images: The Impact of Mindfulness Based Cognitive Therapy (MBCT) on Intrusive Images in Patients With Severe Health Anxiety (Hypochondriasis).

Recurrent distressing intrusive images are a common experience in hypochondriasis. The aim of the current study was to assess the impact of Mindfulness-Based Cognitive Therapy (MBCT) for hypochondriasis on the occurrence and nature of distressing intrusive imagery in hypochondriasis. A semi-structured interview was used to assess intrusive imagery, and an adapted version of the Southampton Mindfulness Questionnaire (SMQ) was used to assess participants’ relationship with their intrusive images. A consecutive series of participants (N = 20) who were receiving MBCT for hypochondriasis as part of an ongoing research program were assessed prior to participating in an 8-week MBCT intervention, immediately following the intervention, and at three month follow-up. As compared to the baseline assessment, the frequency of intrusive images, the distress associated with them, and the intrusiveness of the images were all significantly reduced at the post-MBCT assessment. Participants’ adapted SMQ scores were significantly increased following the MBCT intervention, suggesting that participants’ relationship with their intrusive images had changed in that they had developed a more ‘mindful’ and compassionate response to the images when they did occur. Effect sizes from pre- to post-intervention were medium to large (Cohen’s d = 0.75 - 1.50). All treatment gains were maintained at 3 month follow-up. Results suggest that MBCT may be an effective intervention for addressing intrusive imagery in hypochondriasis