Semiclassical trace formulae using coherent states

We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately obvious that classical periodic orbits make separate contributions to the trace of the quantum-mechanical time evolution operator. In addition, our approach is manifestly canonically invariant at all stages, and leads to the simplest possible derivation of Gutzwiller's formula.Comment: 19 pages, 1 figur

Precise asymptotics for a variable-range hopping model

For a system of localised electron states the DC conductivity vanishes at zero temperature, but localised electrons can conduct at finite temperature. Mott gave a theory for the low-temperature conductivity in terms of a variable-range hopping model, which is hard to analyse. Here we give precise asymptotic results for a modified variable-range hopping model proposed by S. Alexander [Phys. Rev. B 26, 2956 (1982)].Comment: 7 pages, 2 figure

Advective collisions

Small particles advected in a fluid can collide (and therefore aggregate) due to the stretching or shearing of fluid elements. This effect is usually discussed in terms of a theory due to Saffman and Turner [J. Fluid Mech., 1, 16-30, (1956)]. We show that in complex or random flows the Saffman-Turner theory for the collision rate describes only an initial transient (which we evaluate exactly). We obtain precise expressions for the steady-state collision rate for flows with small Kubo number, including the influence of fractal clustering on the collision rate for compressible flows. For incompressible turbulent flows, where the Kubo number is of order unity, the Saffman-Turner theory is an upper bound.Comment: 4 pages, 1 figur

A study of radiation environment in space and its biological effects

Biological effects on man in space resulting from galactic and solar cosmic radiation are discussed. Importance of secondary ions which contribute to galactic cosmic radiation hazards is analyzed. Mathematical model to show rate of production of secondary ions of given atomic number at various points in absorber is presented

Galactic cosmic ray heavy primary secondary doses

Results of a calculation which estimates the heavy primary secondary doses from cosmic ray interaction data are reported. The incident galactic cosmic ray heavy primary spectrum is represented as the sum of helium, nitrogen, magnesium, and iron components. The incident iron nuclei are allowed to fragment into lesser Z secondaries, which are assumed to travel in the same direction and start with the same energy per nucleon as the interacting primary. The total emergent particle energy spectra and dose are then presented for the galactic heavy primary spectrum incident on aluminum and tissue slabs. The importance of the fragmentation parameters assumed is also evaluated. The total dose from the heavy primaries and their secondaries is found to be reduced by only a factor of two in 20 g/sq cm of shielding

Stokes trapping and planet formation

It is believed that planets are formed by aggregation of dust particles suspended in the turbulent gas forming accretion disks around developing stars. We describe a mechanism, termed 'Stokes trapping', by which turbulence limits the growth of aggregates of dust particles, so that their Stokes number (defined as the ratio of the damping time of the particles to the Kolmogorov dissipation timescale) remains close to unity. We discuss possible mechanisms for avoiding this barrier to further growth. None of these is found to be satisfactory and we introduce a new theory which does not involve the growth of small clusters of dust grains.Comment: 30 pages, 4 figures. Revised version has improved concluding remarks, extended discussion of sticking velocit

Ergodic and non-ergodic clustering of inertial particles

We compute the fractal dimension of clusters of inertial particles in mixing flows at finite values of Kubo (Ku) and Stokes (St) numbers, by a new series expansion in Ku. At small St, the theory includes clustering by Maxey's non-ergodic 'centrifuge' effect. In the limit of St to infinity and Ku to zero (so that Ku^2 St remains finite) it explains clustering in terms of ergodic 'multiplicative amplification'. In this limit, the theory is consistent with the asymptotic perturbation series in [Duncan et al., Phys. Rev. Lett. 95 (2005) 240602]. The new theory allows to analyse how the two clustering mechanisms compete at finite values of St and Ku. For particles suspended in two-dimensional random Gaussian incompressible flows, the theory yields excellent results for Ku < 0.2 for arbitrary values of St; the ergodic mechanism is found to contribute significantly unless St is very small. For higher values of Ku the new series is likely to require resummation. But numerical simulations show that for Ku ~ St ~ 1 too, ergodic 'multiplicative amplification' makes a substantial contribution to the observed clustering.Comment: 4 pages, 2 figure

Absorption of Energy at a Metallic Surface due to a Normal Electric Field

The effect of an oscillating electric field normal to a metallic surface may be described by an effective potential. This induced potential is calculated using semiclassical variants of the random phase approximation (RPA). Results are obtained for both ballistic and diffusive electron motion, and for two and three dimensional systems. The potential induced within the surface causes absorption of energy. The results are applied to the absorption of radiation by small metal spheres and discs. They improve upon an earlier treatment which used the Thomas-Fermi approximation for the effective potential.Comment: 19 pages (Plain TeX), 2 figures, 1 table (Postscript