A Thermal Gradient Approach for the Quasi-Harmonic Approximation and its Application to Improved Treatment of Anisotropic Expansion

We present a novel approach to efficiently implement thermal expansion in the quasi-harmonic approximation (QHA) for both isotropic and more importantly, anisotropic expansion. In this approach, we rapidly determine a crystal's equilibrium volume and shape at a given temperature by integrating along the gradient of expansion from zero Kelvin up to the desired temperature. We compare our approach to previous isotropic methods that rely on a brute-force grid search to determine the free energy minimum, which is infeasible to carry out for anisotropic expansion, as well as quasi-anisotropic approaches that take into account the contributions to anisotropic expansion from the lattice energy. We compare these methods for experimentally known polymorphs of piracetam and resorcinol and show that both isotropic methods agree to within error up to 300 K. Using the Gr\"{u}neisen parameter causes up to 0.04 kcal/mol deviation in the Gibbs free energy, but for polymorph free energy differences there is a cancellation in error with all isotropic methods within 0.025 kcal/mol at 300 K. Anisotropic expansion allows the crystals to relax into lattice geometries 0.01-0.23 kcal/mol lower in energy at 300 K relative to isotropic expansion. For polymorph free energy differences all QHA methods produced results within 0.02 kcal/mol of each other for resorcinol and 0.12 kcal/mol for piracetam, the two molecules tested here, demonstrating a cancellation of error for isotropic methods. We also find that when expanding in more than a single volume variable, there is a non-negligible rate of failure of the basic approximations of QHA. Specifically, while expanding into new harmonic modes as the box vectors are increased, the system often falls into alternate, structurally distinct harmonic modes unrelated by continuous deformation from the original harmonic mode.Comment: 38 pages, including 9 pages supporting informatio

Feasibility study for a secondary Na/S battery

The feasibility of a moderate temperature Na battery was studied. This battery is to operate at a temperature in the range of 100-150 C. Two kinds of cathode were investigated: (1) a soluble S cathode consisting of a solution of Na2Sn in an organic solvent and (2) an insoluble S cathode consisting of a transition metal dichalcogenide in contact with a Na(+)ion conducting electrolyte. Four amide solvents, dimethyl acetamide, diethyl acetamide, N-methyl acetamide and acetamide, were investigated as possible solvents for the soluble S cathode. Results of stability and electrochemical studies using these solvents are presented. The dialkyl substituted amides were found to be superior. Although the alcohol 1,3-cyclohexanediol was found to be stable in the presence of Na2Sn at 130 C, its Na2Sn solutions did not appear to have suitable electrochemical properties

The Star Formation History of the Hubble Sequence: Spatially Resolved Colour Distributions of Intermediate Redshift Galaxies in the Hubble Deep Field

We analyse the spatially resolved colours of distant galaxies of known redshift in the Hubble Deep Field, using a new technique based on matching resolved four-band internal colour data to the predictions of evolutionary synthesis models. We quantify the relative age, dispersion in age, ongoing star-formation rate, star-formation history, and dust content of these galaxies. To demonstrate the potential of the method, we study the near-complete sample of 32 I ~ 0.5 studied by Bouwens et al (1997). The dispersion of the internal colours of a sample of 0.4<z<1 early-type field galaxies in the HDF indicates that ~40% [4/11] show evidence of star formation which must have occurred within the past third of their ages at the epoch of observation. For a sample of well-defined spirals, we similarly exploit the dispersion in colour to analyse the relative histories of bulge and disc stars, in order to resolve the current controversy regarding the ages of galactic bulges. Dust and metallicity gradients are ruled out as major contributors to the colour dispersions we observe in these systems. The median ages of bulge stars are found to be signicantly older than those in galactic discs, and exhibit markedly different star-formation histories. This result is inconsistent with a secular growth of bulges from disc instabilities, but consistent with gradual disc formation by accretion of gas onto bulges, as predicted by hierarchical theories. We extend our technique in order to discuss the star formation history of the entire Bouwens et al sample in the context of earlier studies concerned with global star formation histories.Comment: 8 colour postscript figures plus LaTeX source; submitted to MNRAS. Uses the mnras.sty LaTeX style fil

Evidence for Evolving Spheroidals in the Hubble Deep Fields North and South

We investigate the dispersion in the internal colours of faint spheroidals in the HDFs North and South. We find that a remarkably large fraction ~30% of the morphologically classified spheroidals with I<24 mag show strong variations in internal colour, which we take as evidence for recent episodes of star-formation. In most cases these colour variations manifest themselves via the presence of blue cores, an effect of opposite sign to that expected from metallicity gradients. Examining similarly-selected ellipticals in five rich clusters with 0.37<z<0.83 we find a significant lower dispersion in their internal colours. This suggests that the colour inhomogeneities have a strong environmental dependence being weakest in dense environments where spheroidal formation was presumably accelerated at early times. We use the trends defined by the cluster sample to define an empirical model based on a high-redshift of formation and estimate that at z~1 about half the field spheroidals must be undergoing recent episodes of star-formation. Using spectral synthesis models, we construct the time dependence of the density of star-formation. Although the samples are currently small, we find evidence for an increase in $\rho_{SFR}$ between z=0 to z=1. We discuss the implications of this rise in the context of that observed in the similar rise in the abundance of galaxies with irregular morphology. Regardless of whether there is a connection our results provide strong evidence for the continued formation of field spheroidals over 0<z<1.Comment: 13 pages, 11 figures. To appear in MNRAS in response to referee's Report. Figures and paper also available at http://www.ast.cam.ac.uk/~fmenante/HDFs

Generic local distinguishability and completely entangled subspaces

A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all subspaces with dimension less than or equal to S are completely entangled, and then use this fact to prove that n random pure quantum states are unambiguously locally distinguishable if and only if n does not exceed D-S. This condition holds for almost all sets of states of all multipartite systems, and reveals something surprising. The criterion is identical for separable and for nonseparable states: entanglement makes no difference.Comment: 12 page

Comparing the Evolution of the Galaxy Disk Sizes with CDM Models: The Hubble Deep Field

The intrinsic sizes of the field galaxies with I<26 in the Hubble and ESO-NTT Deep Fields are shown as a function of their redshifts and absolute magnitudes using photometric redshifts derived from the multicolor catalogs and are compared with the CDM predictions. Extending to lower luminosities and to higher z our previous analysis performed on the NTT field alone, we find that the distribution of the galaxy disk sizes at different cosmic epochs is within the range predicted by typical CDM models. However, the observed size distribution of faint (M_B>-19) galaxies is skewed with respect to the CDM predictions and an excess of small-size disks (R_d<2 kpc) is already present at z~ 0.5. The excess persists up to z~3 and involves brighter galaxies . Such an excess may be reduced if luminosity-dependent effects, like starburst activity in interacting galaxies, are included in the physical mechanisms governing the star formation history in CDM models.Comment: 9 pages, 3 figures, ApJ Letters in pres

A Complexity-Brightness Correlation in Gamma Ray Bursts

We observe strong correlations between the temporal properties of gamma ray bursts (GRBs) and their apparent peak brightness. The strongest effect (with a significance level of 10^{-6}) is the difference between the brightness distributions of simple bursts (dominated by a single smooth pulse) and complex bursts (consisting of overlapping pulses). The latter has a break at a peak flux of 1.5 ph/cm^2/s, while the distribution of simple bursts is smooth down to the BATSE threshold. We also observe brightness dependent variations in the shape of the average peak aligned time profile (ATP) of GRBs. The decaying slope of the ATP shows time dilation when comparing bright and dim bursts while the rising slope hardly changes. Both slopes of the ATP are deformed for weak bursts as compared to strong bursts. The interpretation of these effects is simple: a complex burst where a number of independent pulses overlap in time appears intrinsically stronger than a simple burst. Then the BATSE sample of complex bursts covers larger redshifts where some cosmological factor causes the break in the peak brightness distribution. This break could correspond to the peak in the star formation rate that was recently shown to occur at a redshift of z~1.5.Comment: 13 pages; 11 figures; replaced with the published versio