Ray helicity: a geometric invariant for multi-dimensional resonant wave conversion

For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning it must be invariant under two groups of transformations: congruence transformations (which shuffle components of the multi-component wave field) and canonical transformations (which act on the ray phase space). It is shown that for conversion between two waves there is a new invariant not previously discussed: the intrinsic helicity of the ray

Different mechanics of snap-trapping in the two closely related carnivorous plants Dionaea muscipula and Aldrovanda vesiculosa

The carnivorous aquatic Waterwheel Plant (Aldrovanda vesiculosa L.) and the closely related terrestrial Venus Flytrap (Dionaea muscipula SOL. EX J. ELLIS) both feature elaborate snap-traps, which shut after reception of an external mechanical stimulus by prey animals. Traditionally, Aldrovanda is considered as a miniature, aquatic Dionaea, an assumption which was already established by Charles Darwin. However, videos of snapping traps from both species suggest completely different closure mechanisms. Indeed, the well-described snapping mechanism in Dionaea comprises abrupt curvature inversion of the two trap lobes, while the closing movement in Aldrovanda involves deformation of the trap midrib but not of the lobes, which do not change curvature. In this paper, we present the first detailed mechanical models for these plants, which are based on the theory of thin solid membranes and explain this difference by showing that the fast snapping of Aldrovanda is due to kinematic amplification of the bending deformation of the midrib, while that of Dionaea unambiguously relies on the buckling instability that affects the two lobes.Comment: accepted in Physical Review

A q-analog of the ADHMN construction and axisymmetric multi-instantons

In the preceding paper (Phys. Lett. B463 (1999) 257), the authors presented a q-analog of the ADHMN construction and obtained a family of anti-selfdual configurations with a parameter q for classical SU(2) Yang-Mills theory in four-dimensional Euclidean space. The family of solutions can be seen as a q-analog of the single BPS monopole preserving (anti-)selfduality. Further discussion is made on the relation to axisymmetric ansatz on anti-selfdual equation given by Witten in the late seventies. It is found that the q-exponential functions familiar in q-analysis appear as analytic functions categorizing the anti-selfdual configurations yielded by axisymmetric ansatz.Comment: 11pages, Latex2e, to appear in Journal of Physics A: Mathematical and General as a `Special Issue/Difference Equations

Religion as a Cross-cultural Determinant of Depression in Elderly Europeans: Results from the EURODEP Collaboration

Background. The protective effects of religion against late life depression may depend on the broader sociocultural environment. This paper examines whether the prevailing religious climate is related to cross-cultural differences of depression in elderly Europeans. Methods. Two approaches were employed, using data from the EURODEP collaboration. First, associations were studied between church-attendance, religious denomination and depression at the syndrome level for six EURODEP study centres (five countries, N = 8398). Secondly, ecological associations were computed by multi-level analysis between national estimates of religious climate, derived from the European Value Survey and depressive symptoms, for the pooled dataset of 13 EURODEP study centres (11 countries, N = 17739). Results. In the first study, depression rates were lower among regular church-attenders, most prominently among Roman Catholics. In the second study, fewer depressive symptoms were found among the female elderly in countries, generally Roman Catholic, with high rates of regular church-attendance. Higher levels of depressive symptoms were found among the male elderly in Protestant countries. Conclusions. Religious practice is associated with less depression in elderly Europeans, both on the individual and the national level. Religious practice, especially when it is embedded within a traditional value-orientation, may facilitate coping with adversity in later life