Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems

In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy-momentum confinement, KAM, and Nekhoroshev stability, and we explain the transitions between these. We apply our results to the Kirchhoff model for the motion of an axisymmetric underwater vehicle, and we numerically study dissipation induced instability of KAM stable relative equilibria for this system.Comment: Minor revisions. Typographical errors correcte

The native architecture of a photosynthetic membrane

In photosynthesis, the harvesting of solar energy and its subsequent conversion into a stable charge separation are dependent upon an interconnected macromolecular network of membrane-associated chlorophyll–protein complexes. Although the detailed structure of each complex has been determined, the size and organization of this network are unknown. Here we show the use of atomic force microscopy to directly reveal a native bacterial photosynthetic membrane. This first view of any multi-component membrane shows the relative positions and associations of the photosynthetic complexes and reveals crucial new features of the organization of the network: we found that the membrane is divided into specialized domains each with a different network organization and in which one type of complex predominates. Two types of organization were found for the peripheral light-harvesting LH2 complex. In the first, groups of 10–20 molecules of LH2 form light-capture domains that interconnect linear arrays of dimers of core reaction centre (RC)–light-harvesting 1 (RC–LH1–PufX) complexes; in the second they were found outside these arrays in larger clusters. The LH1 complex is ideally positioned to function as an energy collection hub, temporarily storing it before transfer to the RC where photochemistry occurs: the elegant economy of the photosynthetic membrane is demonstrated by the close packing of these linear arrays, which are often only separated by narrow 'energy conduits' of LH2 just two or three complexes wide