[Book review] Symmetry - A Unifying Concept, István Hargittai and Magdolna Hargittai

Tony Mann provides a review of the book: István Hargittai and Magdolna Hargittai, Symmetry - A Unifying Concept, 1994, Ten Speed Press, 222pp. ISBN: 089815-590-8. £14.99

[Reviews] Finding moonshine: a mathematician's journey through symmetry

Review of 'Finding Moonshine: A Mathematician’s Journey Through Symmetry' by Marcus du Sautoy, published by Fourth Estate, 2008 (ISBN 0-007-214618).

Shortened duration of the annual Neocalanus plumchrus biomass peak in the Northeast Pacific

The calanoid copepod Neocalan us plumchrus (Marukawa) is a dominant member of the spring mesozooplankton in the subarctic North Pacific and Bering Sea. Previous studies have shown interdecadal and latitudinal variation in seasonal developmental timing, with peak biomass occurring earlier in years and places with warmer upper ocean temperatures. Because N. plumchrus normally has a single dominant annual cohort, its seasonal timing can be indexed from measurements of total population biomass or by following progressive changes in stage composition. Early studies empirically found that peak upper ocean biomass occurred when about half of the pre-dormant population had reached copepodite stage 5 (C5). However, more recent comparisons derived from recent Continuous Plankton Recorder (CPR) data now show peak biomass when a larger fraction (> 80%) of the population is at C5. CPR samples the surface 10 to 15 m, but comparisons to depth-resolved BIONESS data show that this discrepancy is not an artefact of sampling depth. Other causes are either a prolongation of duration of pre-dormant C5 or a narrowing of the age range making up the annual cohort. We assessed changes in cohort width using a modification of Greve's cumulative percentile method, and found that average cohort widths in the Alaska Gyre were significantly narrower in 2000-2007 than in 1957-1965 (1968-1980 were intermediate). Net tow sampling of Strait of Georgia populations showed a similar significant narrowing of cohorts in the 2003-2005 sampling period. This study provides evidence that in addition to the shift to an earlier occurrence of peak biomass reported previously, the duration of the peak has also decreased in the last decade.

Electron collisions with Fe-peak elements: Forbidden transitions between the low lying valence states 3d6, 3d54s, and 3d54p of Fe III:

Effective collision strengths are presented for the Fe-peak element Fe III at electron temperatures (Te in degrees Kelvin) in the range 2 × 103 to 1 × 106. Forbidden transitions results are given between the 3d6, 3d54s, and the 3d54p manifolds applicable to the modeling of laboratory and astrophysical plasmas.

Multiwavelength observations of the M15 intermediate-velocity cloud

We present Westerbork Synthesis Radio Telescope HI images, Lovell telescope multibeam H I wide-field mapping, William Herschel Telescope long-slit echelle Ca II observations, Wisconsin Halpha Mapper (WHAM) facility images, and IRAS ISSA 60- and 100-mum co-added images towards the intermediate- velocity cloud (IVC) at + 70 km s(-1), located in the general direction of the M15 globular cluster. When combined with previously published Arecibo data, the H I gas in the IVC is found to be clumpy, with a peak H I column density of similar to1.5 x 10(20) cm(-2), inferred volume density (assuming spherical symmetry) of similar to24 cm(-3)/D (kpc) and a maximum brightness temperature at a resolution of 81 x 14 arcsec(2) of 14 K. The major axis of this part of the IVC lies approximately parallel to the Galactic plane, as does the low- velocity H I gas and IRAS emission. The H I gas in the cloud is warm, with a minimum value of the full width at half-maximum velocity width of 5 km s(-1) corresponding to a kinetic temperature, in the absence of turbulence, of similar to540 K. From the H I data, there are indications of two-component velocity structure. Similarly, the Ca II spectra, of resolution 7 km s(-1), also show tentative evidence of velocity structure, perhaps indicative of cloudlets. Assuming that there are no unresolved narrow-velocity components, the mean values of log(10)[N(Ca II K) cm(2)] similar to 12.0 and Ca II/H I similar to2 5 x 10(-8) are typical of observations of high Galactic latitude clouds. This compares with a value of Ca II/H I>10(-6) for IVC absorption towards HD 203664, a halo star of distance 3 kpc, some 3.degrees1 from the main M15 IVC condensation. The main IVC condensation is detected by WHAM in Halpha with central local-standard-of-rest velocities of similar to60-70 km s(-1), and intensities uncorrected for Galactic extinction of up to 1.3 R, indicating that the gas is partially ionized. The FWHM values of the Halpha IVC component, at a resolution of 1degrees, exceed 30 km s(-1). This is some 10 km s(-1) larger than the corresponding H I value at a similar resolution, and indicates that the two components may not be mixed. However, the spatial and velocity coincidence of the Halpha and H I peaks in emission towards the main IVC component is qualitatively good. If the Halpha emission is caused solely by photoionization, the Lyman continuum flux towards the main IVC condensation is similar to2.7 x 10(6) photon cm(-2) s(-1). There is not a corresponding IVC Halpha detection towards the halo star HD 203664 at velocities exceeding similar to60 km s(- 1). Finally, both the 60- and 100-mum IRAS images show spatial coincidence, over a 0.675 x 0 625 deg(2) field, with both low- and intermediate-velocity H I gas (previously observed with the Arecibo telescope), indicating that the IVC may contain dust. Both the Halpha and tentative IRAS detections discriminate this IVC from high-velocity clouds, although the H I properties do not. When combined with the H I and optical results, these data point to a Galactic origin for at least parts of this IVC.

Single- and multiphoton detachment of K

Single- and multiphoton detachment rates have been calculated for K- using the R-matrix Floquet approach. Single-photon detachment rates, obtained at a laser field peak intensity of 10(9) W cm(-2), are discussed and compared with other theoretical work. Two-photon detachment rates at the same intensity have also been obtained, and similarities with results from earlier calculations for Li- and Na- are discussed. Three-photon rates are also presented at this laser intensity, and are compared and contrasted with those arising in the single-photon case, since both involve resonance structure with P-1(o) symmetry. The influence of resonances such as the 5s(2) S-1(e) doubly excited state and excitations of the residual atom are also considered.

Shifting of the electron-capture-to-the-continuum peak in proton-helium collisions at 10 and 20 keV

A refined theoretical approach has been developed to study the double-differential cross sections (DDCS's) in proton-helium collisions as a function of the ratio of ionized electron velocity to the incident proton velocity. The refinement is done in the present coupled-channel calculation by introducing a continuum distorted wave in the final state coupled with discrete states including direct as well as charge transfer channels. It is confirmed that the electron-capture-to-the-continuum (ECC) peak is slightly shifted to a lower electron velocity than the equivelocity position. Comparing measurements and classical trajectory Monte Carlo (CTMC) calculations at 10 and 20 keV proton energies, excellent agreement of the ECC peak heights is achieved at both energies. However, a minor disagreement in the peak positions between the present calculation and the CTMC results is noted. A smooth behavior of the DDCS is found in the present calculation on both sides of the peak whereas the CTMC results show some oscillatory behavior particularly to the left of the peak, associated with the statistical nature of CTMC calculations.

Fast heating of ultrahigh-density plasma as a step towards laser fusion ignition

ate studies(2) and fusion energy research(3,4). Laser-driven implosions of spherical polymer shells have, for example, achieved an increase in density of 1,000 times relative to the solid state(5). These densities are large enough to enable controlled fusion, but to achieve energy gain a small volume of compressed fuel (known as the 'spark') must be heated to temperatures of about 10(8) K (corresponding to thermal energies in excess of 10 keV). In the conventional approach to controlled fusion, the spark is both produced and heated by accurately timed shock waves(4), but this process requires both precise implosion symmetry and a very large drive energy. In principle, these requirements can be significantly relaxed by performing the compression and fast heating separately(6-10); however, this 'fast ignitor' approach(7) also suffers drawbacks, such as propagation losses and deflection of the ultra-intense laser pulse by the plasma surrounding the compressed fuel. Here we employ a new compression geometry that eliminates these problems; we combine production of compressed matter in a laser-driven implosion with picosecond-fast heating by a laser pulse timed to coincide with the peak compression. Our approach therefore permits efficient compression and heating to be carried out simultaneously, providing a route to efficient fusion energy production.

Symmetry, delocalization, and molecular conductance

Molecules bonded between two metal contacts form the simplest possible molecular devices. Coupled by the molecule, the left and right contact-based states form symmetric and antisymmetric pairs near the Fermi level. We relate the size of the resulting energy splitting DeltaE to the symmetry and degree of delocalization of the coupling molecular orbital. Qualitative trends in molecular conductances are then estimated from the variations in DeltaE. We examine benzenedithiol and other molecules of interest in transport. (C) 2005 American Institute of Physics.

Broken symmetry and pseudogaps in ropes of carbon nanotubes

Since the discovery of carbon nanotubes, it has been speculated that these materials should behave like nanoscale wires with unusual electronic properties and exceptional strength. Recently, 'ropes' of close-packed single-wall nanotubes have been synthesized in high yield. The tubes in these ropes are mainly of the (10,10) type3, which is predicted to be metallic. Experiments on individual nanotubes and ropes indicate that these systems indeed have transport properties that qualify them to be viewed as nanoscale quantum wires at low temperature. It has been expected that the close-packing of individual nanotubes into ropes does not change their electronic properties significantly. Here, however, we present first-principles calculations which show that a broken symmetry of the (10,10) tube caused by interactions between tubes in a rope induces a pseudogap of about 0.1 eV at the Fermi level. This pseudogap strongly modifies many of the fundamental electronic properties: we predict a semimetal-like temperature dependence of the electrical conductivity and a finite gap in the infrared absorption spectrum. The existence of both electron and hole charge carriers will lead to qualitatively different thermopower and Hall-effect behaviours from those expected for a normal metal.

Broken symmetry and pseudogaps in ropes of carbon nanotubes

We investigate the influence of tube-tube interactions in ropes of (10,10) carbon nanotubes, and find that these effects induce a pseudogap in the density of state (DOS) of the rope of width 0.1 eV at the Fermi level. In an isolated (n,n) carbon nanotube there are two bands that cross in a linear fashion at the Fermi level, making the nanotube metallic with a DOS that is constant in a 1.5 eV wide window around the Fermi energy. The presence of the neighbouring tubes causes these two bands to repel, opening up a band gap that can be as large as 0.3 eV. The small dispersion in the plane perpendicular to the rope smears out this gap for a rope with a large cross-sectional area, and we see a pseudogap at the Fermi energy in the DOS where the DOS falls to one third of its value for the isolated tube. This phenomenon should affect many properties of the behavior of ropes of (n,n) nanotubes, which should display a more semimetallic character than expected in transport and doping experiments, with the existence of both hole and electron carriers leading to qualitatively different thermopower and Hall-effect behaviors from those expected for a normal metal. Band repulsion like this can be expected to occur for any tube perturbed by a sufficiently strong interaction, for example, from contact with a surface or with other tubes.