A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

We present a numerical comparison study of planar Richtmyer-Meshkov instability with the intention of exposing the role of the equation of state. Results for Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship (Jeanloz, J. Geophys. Res. 94, 5873, 1989; McQueen et al., High Velocity Impact Phenomena (1970), pp. 294–417; Menikoff and Plohr, Rev. Mod. Phys. 61(1), 75 1989) are compared to those from perfect gases under nondimensionally matched initial conditions at room temperature and pressure. The study was performed using Caltech’s Adaptive Mesh Refinement, Object-oriented C++ (AMROC) (Deiterding, Adaptive Mesh Refinement: Theory and Applications (2005), Vol. 41, pp. 361–372; Deiterding, “Parallel adaptive simulation of multi-dimensional detonation structures,” Ph.D. thesis (Brandenburgische Technische Universität Cottbus, September 2003)) framework with a low-dissipation, hybrid, center-difference, limiter patch solver (Ward and Pullin, J. Comput. Phys. 229, 2999 (2010)). Results for single and triple mode planar Richtmyer-Meshkov instability when a reflected shock wave occurs are first examined for mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state. The single mode case is examined for incident shock Mach numbers of 1.5 and 2.5. The planar triple mode case is studied using a single incident Mach number of 2.5 with initial corrugation wavenumbers related by k_1 = k_2+k_3. Comparison is then drawn to Richtmyer-Meshkov instability in perfect gases with matched nondimensional pressure jump across the incident shock, post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by Richtmyer’s linear growth time constant prediction. Differences in start-up time and growth rate oscillations are observed across equations of state. Growth rate oscillation frequency is seen to correlate directly to the oscillation frequency for the transmitted and reflected shocks. For the single mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction. Additionally, we examine single mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. The formation of incipient weak waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected

Star Formation in the Circumnuclear Environment of NGC1068

We present near-infrared emission line images of the circumnuclear ring in NGC1068. We have measured the Br_gamma fluxes in a number of star forming complexes and derived extinctions for each of these by comparison with H_alpha. We investigate the star forming histories of these regions and find that a short burst of star formation occured co-evally throughout the ring within the last 30-40 Myr, and perhaps as recently as 4-7 Myr ago. The 1-0 S(1) flux and S(1)/Br_gamma ratios indicate that as well as fluorescence, shock excited H_2 emission contributes to the total flux. There is excess H_2 flux to the North-West where the ionisation cone crosses the ring, and we have shown it is possible that the non-stellar continuum from the Seyfert nucleus which produces the high excitation lines could also be causing fluorescence at the edges of molecular clouds in the ring. The nuclear 1-0 S(1) is more extended than previously realised but only along the bar's major axis, and we consider mechanisms for its excitation.Comment: 10 pages, 4 figures, LaTeX (mn.sty & psfig.sty). Accepted for publication in MNRA

ROSAT observations of the dwarf starforming galaxy Holmerg II (UGC 4305)

We present ROSAT PSPC and HRI observations of the dwarf irregular galaxy Holmberg II (UGC4305). This is one of the most luminous dwarf galaxies (Lx~ 10^{40} erg s^{-1} cm^{-2}) detected in the ROSAT All-Sky Survey. The X-ray emission comes from a single unresolved point source, coincident with a large HII region which emits intense radio emission. The source is variable on both year and day timescales, clearly favouring accretion into a compact object rather than a supernova remnant or a superbubble interpretation for the origin of the X-ray emission. However, its X-ray spectrum is well-fit by a a Raymond-Smith spectrum with kT~0.8 keV, lower than the temperature of X-ray binaries in nearby spiral galaxies.Comment: Accepted for publication in MNRA

On the Running of the Cosmological Constant in Quantum General Relativity

We present arguments that show what the running of the cosmological constant means when quantum general relativity is formulated following the prescription developed by Feynman.Comment: 5 page

The twistor geometry of three-qubit entanglement

A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states can be represented by the points of the Klein quadric ${\cal Q}$ a space known from twistor theory. It is shown that three-qubit invariants are vanishing on special subspaces of ${\cal Q}$. An invariant vanishing for the $GHZ$ class is proposed. A geometric interpretation of the canonical decomposition and the inequality for distributed entanglement is also given.Comment: 4 pages RevTeX

The Trials of Apuleius: An Ironic Legal History

\ua9 The Author(s) 2024.This article is an exercise in what might be termed ‘ironic’ legal history. The first part explores the idea of ‘ironic’ history, which aligns the insights of literary ‘ironism’ with those of micro and ‘anecdotal’ history and ‘new’ historicism. It will focus more particularly on the work of Richard Rorty, Carlo Ginzburg and Stephen Greenblatt. The second part of the article will present a ‘case-study’ in ironic legal history; revisiting the second-century trial of the Roman orator and writer Apuleius. Apuleius wrote two notably different accounts of the same experience, one pretending to fact, the other to fiction. To read these accounts is to engage in an exercise in ironic legal history

Resummed Quantum Gravity

We present the current status of the a new approach to quantum general relativity based on the exact resummation of its perturbative series as that series was formulated by Feynman. We show that the resummed theory is UV finite and we present some phenomenological applications as well.Comment: 4 pages, 1 figure; presented at ICHEP0

The effect of perennial grass species on forage growth and quality, etiolated growth, animal performance and economics

A series of experiments were conducted during 2005 and 2006 to evaluate five perennial grass species for forage yield and quality, steer performance and grazing capacity, animal intake, plant energy reserves and economic return under grazed conditions. In 1999, two 0.8 ha replicates each of ‘Paddock’ meadow bromegrass (Bromus ripariusRehm.), ‘Carlton’ smooth bromegrass (Bromus inermisLeyss.) and ‘AC Knowles’ hybrid bromegrass (B. riparius x B. inermis) were seeded. In 2003, two 0.8 ha replicates each of ‘AC Goliath’ crested wheatgrass (Agropyron cristatum (L.) Gaertn.), hybrid bromegrass, and ‘Courtenay’ tall fescue (Festuca arundinacea Schreb.) were seeded. A long established stand of crested wheatgrass acted as the control pasture. For 2003 established pastures, AC Goliath crested wheatgrass (7515 kg ha-1) had greater (