Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems

We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time) rather than in configuration space. To illustrate our general ideas, we analyze the one-dimensional (d = 1) Fredrickson-Andersen and East models. Dynamics of such dynamically constrained systems are shown to be isomorphic to the statics of ( d + 1)-dimensional dense mixtures of polydisperse noninterpenetrating domains. The domains coincide with arrested regions in trajectory space.     

Hot dense capsule-implosion cores produced by Z-pinch dynamic Hohlraum radiation

Hot dense capsule implosions driven by Z-pinch x rays have been measured using a approximately 220 eV dynamic Hohlraum to implode 1.7-2.1 mm diameter gas-filled CH capsules. The capsules absorbed up to approximately 20 kJ of x rays. Argon tracer atom spectra were used to measure the T(e) approximately 1 keV electron temperature and the n(e) approximately 1-4 x 10(23) cm(-3) electron density. Spectra from multiple directions provide core symmetry estimates. Computer simulations agree well with the peak emission values of T(e), n(e), and symmetry, indicating reasonable understanding of the Hohlraum and implosion physics.     

Time- and space-resolved spectroscopy of dynamic hohlraum interiors

A dynamic hohlraum is created when an annular z-pinch plasma implodes onto a cylindrical 0.014 g/cc 6-mm-diameter CH₂ foam. The impact launches a radiating shock that propagates toward the axis at 350 μm/ns. The radiation trapped by the tungsten z-pinch plasma forms a 200 eV hohlraum that provides X-rays for indirect drive inertial confinement fusion capsule implosion experiments. We are developing the ability to diagnose the hohlraum interior using emission and absorption spectroscopy of Si atoms added as a tracer to the central portion of the foam. Time- and space-resolved Si spectra are recorded with an elliptical crystal spectrometer viewing the cylindrical hohlraum end-on. A rectangular aperture at the end of the hohlraum restricts the field of view so that the 1D spectrometer resolution corresponds approximately to the hohlraum radial direction. This enables distinguishing between spectra from the unshocked radiation-heated foam and from the shocked foam. Typical spectral lines observed include the Si Lyα with its He-like satellites and the He-like resonance sequence including Heα, Heβ, and Heγ, along with some of their associated Li-like satellites. Work is in progress to infer the hohlraum conditions using collisional–radiative modeling that accounts for the radiation environment and includes both opacity effects and detailed Stark broadening calculations. These 6-mm-scale radiation-heated plasmas might eventually also prove suitable for testing Stark broadening line profile calculations or for opacity measurements.     

Linear Systems of Cubics Singular at General Points of Projective Space

We present an elementary proof that given a general collection of d points in Pⁿ the linear system of cubics singular on each point has the expected codimension except when n=4 and d=7. In that case the cubic is unique. This, together with previous work of the author, gives a proof of the Alexander–Hirschowitz interpolation theorem.     

Flow mechanisms in dense silica-metal oxide-water suspensions

The rheological properties of dense silica in water suspensions (approx. 50% solids by volume) containing additions of metal oxides were examined. Metal oxides used were ferric, zinc and stannic. To prevent settling, testing was performed in a rheometer which was modified to provide for continual stirring of the materials. Relatively small oxide additions had the effect of thickening the mixtures and making them non-Newtonian. Different rate-limiting steps for flow were identified depending on the particular mixture, testing temperature and shear strain rate. Flow could be described using empirical equations which are identical to those often used to describe plastic flow in solid crystalline materials.