The Glass Transition and the Jarzynski Equality

A simple model featuring a double well potential is used to represent a liquid that is quenched from an ergodic state into a history dependent glassy state. Issues surrounding the application of the Jarzynski Equality to glass formation are investigated. We demonstrate that the Jarzynski Equality gives the free energy difference between the initial state and the state we would obtain if the glass relaxed to true thermodynamic equilibrium. We derive new variations of the Jarzynski Equality which are relevant to the history dependent glassy state rather than the underlying equilibrium state. It is shown how to compute the free energy differences for the nonequilibrium history dependent glassy state such that it remains consistent with the standard expression for the entropy and with the second law inequality.Comment: 16 pages, 5 figure

Dust in a Type Ia Supernova Progenitor: Spitzer Spectroscopy of Kepler's Supernova Remnant

Characterization of the relatively poorly-understood progenitor systems of Type Ia supernovae is of great importance in astrophysics, particularly given the important cosmological role that these supernovae play. Kepler's Supernova Remnant, the result of a Type Ia supernova, shows evidence for an interaction with a dense circumstellar medium (CSM), suggesting a single-degenerate progenitor system. We present 7.5-38 $\mu$m infrared (IR) spectra of the remnant, obtained with the {\it Spitzer Space Telescope}, dominated by emission from warm dust. Broad spectral features at 10 and 18 $\mu$m, consistent with various silicate particles, are seen throughout. These silicates were likely formed in the stellar outflow from the progenitor system during the AGB stage of evolution, and imply an oxygen-rich chemistry. In addition to silicate dust, a second component, possibly carbonaceous dust, is necessary to account for the short-wavelength IRS and IRAC data. This could imply a mixed chemistry in the atmosphere of the progenitor system. However, non-spherical metallic iron inclusions within silicate grains provide an alternative solution. Models of collisionally-heated dust emission from fast shocks ($>$ 1000 km s$^{-1}$) propagating into the CSM can reproduce the majority of the emission associated with non-radiative filaments, where dust temperatures are $\sim 80-100$ K, but fail to account for the highest temperatures detected, in excess of 150 K. We find that slower shocks (a few hundred km s$^{-1}$) into moderate density material ($n_{0} \sim 50-250$ cm$^{-3}$) are the only viable source of heating for this hottest dust. We confirm the finding of an overall density gradient, with densities in the north being an order of magnitude greater than those in the south.Comment: Accepted by ApJ. 11 pages, 5 figures, 1 table. Produced using emulateapj forma

Identification of structure in condensed matter with the topological cluster classification

We describe the topological cluster classification (TCC) algorithm. The TCC detects local structures with bond topologies similar to isolated clusters which minimise the potential energy for a number of monatomic and binary simple liquids with $m\leq13$ particles. We detail a modified Voronoi bond detection method that optimizes the cluster detection. The method to identify each cluster is outlined, and a test example of Lennard-Jones liquid and crystal phases is considered and critically examined.Comment: 28 pages, 28 figure

Magnetic-Field Amplification in the Thin X-ray Rims of SN1006

Several young supernova remnants (SNRs), including SN1006, emit synchrotron X-rays in narrow filaments, hereafter thin rims, along their periphery. The widths of these rims imply 50 to 100 $\mu$G fields in the region immediately behind the shock, far larger than expected for the interstellar medium compressed by unmodified shocks, assuming electron radiative losses limit rim widths. However, magnetic-field damping could also produce thin rims. Here we review the literature on rim width calculations, summarizing the case for magnetic-field amplification. We extend these calculations to include an arbitrary power-law dependence of the diffusion coefficient on energy, $D \propto E^{\mu}$. Loss-limited rim widths should shrink with increasing photon energy, while magnetic-damping models predict widths almost independent of photon energy. We use these results to analyze Chandra observations of SN 1006, in particular the southwest limb. We parameterize the full widths at half maximum (FWHM) in terms of energy as FWHM $\propto E^{m_E}_{\gamma}$. Filament widths in SN1006 decrease with energy; $m_E \sim -0.3$ to $-0.8$, implying magnetic field amplification by factors of 10 to 50, above the factor of 4 expected in strong unmodified shocks. For SN 1006, the rapid shrinkage rules out magnetic damping models. It also favors short mean free paths (small diffusion coefficients) and strong dependence of $D$ on energy ($\mu \ge 1$).Comment: Accepted by ApJ, 49 pages, 10 figure

The First Reported Infrared Emission from the SN 1006 Remnant

We report results of infrared imaging and spectroscopic observations of the SN 1006 remnant, carried out with the Spitzer Space Telescope. The 24 micron image from MIPS clearly shows faint filamentary emission along the northwest rim of the remnant shell, nearly coincident with the Balmer filaments that delineate the present position of the expanding shock. The 24 micron emission traces the Balmer filaments almost perfectly, but lies a few arcsec within, indicating an origin in interstellar dust heated by the shock. Subsequent decline in the IR behind the shock is presumably due largely to grain destruction through sputtering. The emission drops far more rapidly than current models predict, however, even for a higher proportion of small grains than would be found closer to the Galactic plane. The rapid drop may result in part from a grain density that has always been lower -- a relic effect from an earlier epoch when the shock was encountering a lower density -- but higher grain destruction rates still seem to be required. Spectra from three positions along the NW filament from the IRS instrument all show only a featureless continuum, consistent with thermal emission from warm dust. The dust-to-gas mass ratio in the pre-shock interstellar medium is lower than that expected for the Galactic ISM -- as has also been observed in the analysis of IR emission from other SNRs but whose cause remains unclear. As with other SN Ia remnants, SN 1006 shows no evidence for dust grain formation in the supernova ejecta.Comment: 24 pages, 6 figure

Chandra and Hubble Study of a New Transient X-ray Source in M31

We present X-ray and optical observations of a new transient X-ray source in M31 first detected 23-May-2004 at R.A.=00:43:09.940 +/- 0.65'', Dec.=41:23:32.49 +/- 0.66''. The X-ray lightcurve shows two peaks separated by several months, reminiscent of many Galactic X-ray novae. The location and X-ray spectrum of the source suggest it is a low mass X-ray binary (LMXB). Follow-up HST ACS observations of the location both during and after the outburst provide a high-confidence detection of variability for one star within the X-ray position error ellipse. This star has $\Delta$B ~ 1 mag, and there is only a ~1% chance of finding such a variable in the error ellipse. We consider this star a good candidate for the optical counterpart of the X-ray source. The luminosity of this candidate provides a prediction for the orbital period of the system of 2.3$^{+3.7}_{-1.2}$ days.Comment: 17 pages, 3 figures, 4 tables, accepted for publication in Ap