Dispersion of tracer particles in a compressible flow

The turbulent diffusion of Lagrangian tracer particles has been studied in a flow on the surface of a large tank of water and in computer simulations. The effect of flow compressibility is captured in images of particle fields. The velocity field of floating particles has a divergence, whose probability density function shows exponential tails. Also studied is the motion of pairs and triplets of particles. The mean square separation is fitted to the scaling form ~ t^alpha, and in contrast with the Richardson-Kolmogorov prediction, an extended range with a reduced scaling exponent of alpha=1.65 pm 0.1 is found. Clustering is also manifest in strongly deformed triangles spanned within triplets of tracers.Comment: 6 pages, 4 figure

Particle Acceleration and Magnetic Field Generation in Electron-Positron Relativistic Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic electron-positron jet front propagating into an ambient electron-positron plasma with and without initial magnetic fields. We find small differences in the results for no ambient and modest ambient magnetic fields. New simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. Furthermore, the non-linear fluctuation amplitudes of densities, currents, electric, and magnetic fields in the electron-positron shock are larger than those found in the electron-ion shock studied in a previous paper at the comparable simulation time. This comes from the fact that both electrons and positrons contribute to generation of the Weibel instability. Additionally, we have performed simulations with different electron skin depths. We find that growth times scale inversely with the plasma frequency, and the sizes of structures created by the Weibel instability scale proportional to the electron skin depth. This is the expected result and indicates that the simulations have sufficient grid resolution. The simulation results show that the Weibel instability is responsible for generating and amplifying nonuniform, small-scale magnetic fields which contribute to the electron's (positron's) transverse deflection behind the jet head.Comment: 18 pages, 8 figures, revised and accepted for ApJ, A full resolution of the paper can be found at http://gammaray.nsstc.nasa.gov/~nishikawa/apjep1.pd

Particle Acceleration in Relativistic Jets due to Weibel Instability

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. While some Fermi acceleration may occur at the jet front, the majority of electron acceleration takes place behind the jet front and cannot be characterized as Fermi acceleration. The simulation results show that this instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields, which contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation (Medvedev 2000) from deflected electrons has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.Comment: ApJ, in press, Sept. 20, 2003 (figures with better resolution: http://gammaray.nsstc.nasa.gov/~nishikawa/apjweib.pdf

Particle Acceleration and Radiation associated with Magnetic Field Generation from Relativistic Collisionless Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. The simulation results show that this instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields, which contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation from deflected electrons has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.Comment: 4 pages, 1 figure, submitted to Proceedings of 2003 Gamma Ray Burst Conferenc

Particle acceleration, magnetic field generation, and emission in relativistic pair jets

Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating into an ambient plasma. We find that the growth times of Weibel instability are proportional to the Lorentz factors of jets. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction.Comment: 4 pages, 2 figures, submitted to Il nuovo cimento (4th Workshop Gamma-Ray Bursts in the Afterglow Era, Rome, 18-22 October 2004

Development of a carbon fibre composite active mirror: Design and testing

Carbon fibre composite technology for lightweight mirrors is gaining increasing interest in the space- and ground-based astronomical communities for its low weight, ease of manufacturing, excellent thermal qualities and robustness. We present here first results of a project to design and produce a 27 cm diameter deformable carbon fibre composite mirror. The aim was to produce a high surface form accuracy as well as low surface roughness. As part of this programme, a passive mirror was developed to investigate stability and coating issues. Results from the manufacturing and polishing process are reported here. We also present results of a mechanical and thermal finite element analysis, as well as early experimental findings of the deformable mirror. Possible applications and future work are discussed.Comment: Accepted by Optical Engineering. Figures 1-7 on http://www.star.ucl.ac.uk/~sk/OEpaper_files

Thermodynamic properties of a small superconducting grain

The reduced BCS Hamiltonian for a metallic grain with a finite number of electrons is considered. The crossover between the ultrasmall regime, in which the level spacing, $d$, is larger than the bulk superconducting gap, $\Delta$, and the small regime, where $\Delta \gtrsim d$, is investigated analytically and numerically. The condensation energy, spin magnetization and tunneling peak spectrum are calculated analytically in the ultrasmall regime, using an approximation controlled by $1/\ln N$ as small parameter, where $N$ is the number of interacting electron pairs. The condensation energy in this regime is perturbative in the coupling constant $\lambda$, and is proportional to $d N \lambda^2 = \lambda^2 \omega_D$. We find that also in a large regime with $\Delta>d$, in which pairing correlations are already rather well developed, the perturbative part of the condensation energy is larger than the singular, BCS, part. The condition for the condensation energy to be well approximated by the BCS result is found to be roughly $\Delta > \sqrt{d \omega_D}$. We show how the condensation energy can, in principle, be extracted from a measurement of the spin magnetization curve, and find a re-entrant susceptibility at zero temperature as a function of magnetic field, which can serve as a sensitive probe for the existence of superconducting correlations in ultrasmall grains. Numerical results are presented which suggest that in the large $N$ limit the 1/N correction to the BCS result for the condensation energy is larger than $\Delta$.Comment: 17 pages, 7 figures, Submitted to Phys. Rev.

Evidence for Proportionate Partition Between the Magnetic Field and Hot Gas in Turbulent Cassiopeia A

We present a deep X-ray observation of the young Galactic supernova remnant Cas A, acquired with the ROSAT High Resolution Imager. This high dynamic range (232 ks) image reveals low-surface-brightness X-ray structure, which appears qualitatively similar to corresponding radio features. We consider the correlation between the X-ray and radio morphologies and its physical implications. After correcting for the inhomogeneous absorption across the remnant, we performed a point by point (4" resolution) surface brightness comparison between the X-ray and radio images. We find a strong (r = 0.75) log-log correlation, implying an overall relationship of $\log(\Sigma_{_{\rm X-ray}}) \propto (2.21\pm0.05) \times \log(\Sigma_{_{\rm radio}})$. This is consistent with proportionate partition (and possibly equipartition) between the local magnetic field and the hot gas --- implying that Cas A's plasma is fully turbulent and continuously amplifying the magnetic field.Comment: 8 pages with embedded bitmapped figures, Accepted by ApJ Letters 5/1/9

Using Stories in Coach Education

The purpose of this paper is to illustrate how storied representations of research can be used as an effective pedagogical tool in coach education. During a series of continuing professional development seminars for professional golf coaches, we presented our research in the form of stories and poems which were created in an effort to evoke and communicate the lived experiences of elite professional golfers. Following these presentations, we obtained written responses to the stories from 53 experienced coaches who attended the seminars. Analysis of this data revealed three ways in which coaches responded to the stories: (i) questioning; (ii) summarising; and (iii) incorporating. We conclude that these responses illustrate the potential of storied forms of representation to enhance professional development through stimulating reflective practice and increasing understanding of holistic, person-centred approaches to coaching athletes in high-performance sport