Decorated hypertrees

C. Jensen, J. McCammond and J. Meier have used weighted hypertrees to compute the Euler characteristic of a subgroup of the automorphism group of a free product. Weighted hypertrees also appear in the study of the homology of the hypertree poset. We link them to decorated hypertrees after a general study on decorated hypertrees, which we enumerate using box trees.     

Structures of tin cluster cations Sn3(+) to Sn15(+)

We employ a combination of ion mobility measurements and an unbiased systematic structure search with density functional theory methods to study structure and energetics of gas phase tin cluster cations, Sn(n)(+), in the range of n = 3-15. For Sn(13)(+) we also carry out trapped ion electron diffraction measurements to ascertain the results obtained by the other procedures. The structures for the smaller systems are most easily described by idealized point group symmetries, although they are all Jahn-Teller distorted: D(3h) (trigonal bipyramid), D(4h) (octahedron), D(5h) (pentagonal bipyramid) for n = 5, 6, and 7. For the larger systems we find capped D(5h) for Sn(8)(+) and Sn(9)(+), D(3h) (tricapped trigonal prism) and D(4d) (bicapped squared antiprism) plus adatoms for n = 10, 11, 14, and 15. A centered icosahedron with a peripheral atom removed is the dominant motif in Sn(12)(+). For Sn(13)(+) the calculations predict a family of virtually isoenergetic isomers, an icosahedron and slightly distorted icosahedra, which are about 0.25 eV below two C(1) structures. The experiments indicate the presence of two structures, one from the I(h) family and a prolate C(1) isomer based on fused deltahedral moieties.     

Origins of life and biochemistry under high-pressure conditions

Life on Earth can be traced back to as far as 3.8 billion years (Ga) ago. The catastrophic meteoritic bombardment ended between 4.2 and 3.9 Ga ago. Therefore, if life emerged, and we know it did, it must have emerged from nothingness in less than 400 million years. The most recent scenarios of Earth accretion predict some very unstable physico-chemical conditions at the surface of Earth, which, in such a short time period, would impede the emergence of life from a proto-biotic soup. A possible alternative would be that life originated in the depth of the proto-ocean of the Hadean Earth, under high hydrostatic pressure. The large body of water would filter harmful radiation and buffer physico-chemical variations, and therefore would provide a more stable radiation-free environment for pre-biotic chemistry. After a short introduction to Earth history, the current tutorial review presents biological and physico-chemical arguments in support of high-pressure origin for life on Earth.     

Differential non-destructive image current detection in a fourier transform quadrupole ion trap

Dual-detector differential non-destructive Fourier transform detection in a quadrupole ion trap is shown to improve signal intensity and reduce noise compared with spectra recorded using a single detector. A larger area detector in each end-cap electrode is machined to fit its hyperbolic shape and so minimize field imperfections on the z-axis. Argon, acetophenone and bromobenzene spectra were recorded to allow a comparison between single- and dual-detector (differential) modes of detection and to demonstrate the improvement achieved with differential detection. Copyright 1999 John Wiley & Sons, Ltd.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.