HOMFLY for twist knots and exclusive Racah matrices in representation [333]

Next step is reported in the program of Racah matrices extraction from the differential expansion of HOMFLY polynomials for twist knots: from the double-column rectangular representations R=[rr] to a triple-column and triple-hook R=[333]. The main new phenomenon is the deviation of the particular coefficient $f_{[332]}^{[21]}$ from the corresponding skew dimension, what opens a way to further generalizations.Comment: 10 page

Studying the small scale ISM structure with supernovae

AIMS. In this work we explore the possibility of using the fast expansion of a Type Ia supernova photosphere to detect extra-galactic ISM column density variations on spatial scales of ~100 AU on time scales of a few months. METHODS. We constructed a simple model which describes the expansion of the photodisk and the effects of a patchy interstellar cloud on the observed equivalent width of Na I D lines. Using this model we derived the behavior of the equivalent width as a function of time, spatial scale and amplitude of the column density fluctuations. RESULTS. The calculations show that isolated, small (<100 AU) clouds with Na I column densities exceeding a few 10^11 cm^-2 would be easily detected. In contrast, the effects of a more realistic, patchy ISM become measurable in a fraction of cases, and for peak-to-peak variations larger than ~10^12 cm^-2 on a scale of 1000 AU. CONCLUSIONS. The proposed technique provides a unique way to probe the extra-galactic small scale structure, which is out of reach for any of the methods used so far. The same tool can also be applied to study the sub-AU Galactic ISM structure.Comment: 6 pages, 3 figures. Accepted for publication in Astronomy & Astrophysic

Tracking ground state Ba+ ions in an expanding laser–plasma plume using time-resolved vacuum ultraviolet photoionization imaging

We report results from a study of the integrated column density and expansion dynamics of ground-state-selected Ba+ ions in a laser–plasma plume using a new experimental system—VPIF (vacuum-ultraviolet photoabsorption imaging facility). The ions are tracked by recording the attenuation of a pulsed and collimated vacuum ultraviolet beam, tuned to the 5p–6d inner-shell resonance of singly ionized barium, as the expanding plasma plume moves across it. The attenuated beam is allowed to fall on a CCD array where the spatial distribution of the absorption is recorded. Time-resolved ion velocity and integrated column density maps are readily extracted from the photoionization images

Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect

A flux line in a Type-II superconductor with a single nonuniform columnar defect is studied by a perturbative diagrammatic expansion around an annealed approximation. The system undergoes a finite temperature depinning transition for the (rather unphysical) on-the-average repulsive columnar defect, provided that the fluctuations along the axis are sufficiently large to cause some portions of the column to become attractive. The perturbative expansion is convergent throughout the weak pinning regime and becomes exact as the depinning transition is approached, providing an exact determination of the depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st

Identification of the Sequence of Steps Intrinsic to Spheromak Formation

A planar coaxial electrostatic helicity source is used for studying the relaxation process intrinsic to spheromak formation Experimental observations reveal that spheromak formation involves: (1) breakdown and creation of a number of distinct, arched, filamentary, plasma-filled flux loops that span from cathode to anode gas nozzles, (2) merging of these loops to form a central column, (3) jet-like expansion of the central column, (4) kink instability of the central column, (5) conversion of toroidal flux to poloidal flux by the kink instability. Steps 1 and 3 indicate that spheromak formation involves an MHD pumping of plasma from the gas nozzles into the magnetic flux tube linking the nozzles. In order to measure this pumping, the gas puffing system has been modified to permit simultaneous injection of different gas species into the two ends of the flux tube linking the wall. Gated CCD cameras with narrow-band optical filters are used to track the pumped flows

Spectral properties of zero temperature dynamics in a model of a compacting granular column

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table