Combinatorial Aspects of the Splitting Number

We define the strong splitting number, prove that it equals s when exists, and put some restrictions on the possibility that s is a singular carcinal

Model sensitivity in the effect of Antarctic sea ice and stratification on atmospheric pCO2

Several recent papers have demonstrated a decrease in atmospheric pCO(2) resulting from barriers to communication between the deep sea and the atmosphere in the Southern Ocean. Stephens and Keeling [2000] decreased pCO(2) by increasing Antarctic sea ice in a seven-box model of the world ocean, and Toggweiler [1999] showed a similar response to Southern Ocean stratification. In box models the pCO(2) of the atmosphere is controlled by the region of the surface ocean that fills the deep sea [Archer et al., 2000a]. By severing the Southern Ocean link between the deep sea and the atmosphere, atmospheric pCO(2) in these models is controlled elsewhere and typically declines, although the models range widely in their responses. "Continuum models,'' such as three-dimensional (3-D) and 2-D general circulation models, control pCO(2) in a more distributed way and do not exhibit box model sensitivity to high-latitude sea ice or presumably stratification. There is still uncertainty about the high-latitude sensitivity of the real ocean. Until these model sensitivities can be resolved, glacial pCO(2) hypotheses and interpretations based on Southern Ocean barrier mechanisms (see above mentioned references plus Elderfield and Rickaby [2000], Francois et al. [1998], Gildor and Tziperman [2001], Sigman and Boyle [2000], and Watson et al. [2000]) are walking on thin ice

Highly-resolved 2D HYDRA simulations of Double-Shell Ignition Designs

Double-shell (DS) targets (Amendt, P. A. et al., 2002) offer a complementary approach to the cryogenic baseline design (Lindl, J. et al., 2004) for achieving ignition on the National Ignition Facility (NIF). Among the expected benefits are the ease of room temperature preparation and fielding, the potential for lower laser backscatter and the reduced need for careful shock timing. These benefits are offset, however, by demanding fabrication tolerances, e.g., shell concentricity and shell surface smoothness. In particular, the latter is of paramount importance since DS targets are susceptible to the growth of interface perturbations from impulsive and time-dependent accelerations. Previous work (Milovich, J. L. et al., 2004) has indicated that the growth of perturbations on the outer surface of the inner shell is potentially disruptive. To control this instability new designs have been proposed requiring bimetallic inner shells and material-matching mid-Z nanoporous foam. The challenges in manufacturing such exotic foams have led to a further evaluation of the densities and pore sizes needed to reduce the seeding of perturbations on the outer surface of the inner shell, thereby guiding the ongoing material science research efforts. Highly-resolved 2D simulations of porous foams have been performed to establish an upper limit on the allowable pore sizes for instability growth. Simulations indicate that foams with higher densities than previously thought are now possible. Moreover, while at the present time we are only able to simulate foams with average pore sizes larger than 1 micron (due to computational limitations), we can conclude that these pore sizes are potentially problematic. Furthermore, the effect of low-order hohlraum radiation asymmetries on the growth of intrinsic surface perturbations is also addressed. Highly-resolved 2D simulations indicate that the transverse flows that are set up by these low-order mode features (which can excite Kelvin-Helmholtz instabilities) are not large enough to offset the overall robustness of our current design

Advances in the simulation of toroidal gyro Landau fluid model turbulence

The gyro-Landau fluid (GLF) model equations for toroidal geometry have been recently applied to the study ion temperature gradient (ITG) mode turbulence using the 3D nonlinear ballooning mode representation (BMR). The present paper extends this work by treating some unresolved issues conceming ITG turbulence with adiabatic electrons. Although eddies are highly elongated in the radial direction long time radial correlation lengths are short and comparable to poloidal lengths. Although transport at vanishing shear is not particularly large, transport at reverse global shear, is significantly less. Electrostatic transport at moderate shear is not much effected by inclusion of local shear and average favorable curvature. Transport is suppressed when critical E{times}B rotational shear is comparable to the maximum linear growth rate with only a weak dependence on magnetic shear. Self consistent turbulent transport of toroidal momentum can result in a transport bifurcation at suffciently large r/(Rq). However the main thrust of the new formulation in the paper deals with advances in the development of finite beta GLF models with trapped electron and BMR numerical methods for treating the fast parallel field motion of the untrapped electrons

Simulations of implosions with a 3D, parallel, unstructured-grid, radiation-hydrodynamics code

An unstructured-grid, radiation-hydrodynamics code is used to simulate implosions. Although most of the problems are spherically symmetric, they are run on 3D, unstructured grids in order to test the code�s ability to maintain spherical symmetry of the converging waves. Three problems, of increasing complexity, are presented. In the first, a cold, spherical, ideal gas bubble is imploded by an enclosing high pressure source. For the second, we add non-linear heat conduction and drive the implosion with twelve laser beams centered on the vertices of an icosahedron. In the third problem, a NIF capsule is driven with a Planckian radiation source

Assessing the Prospects for Achieving Double-Shell Ignition on the National Ignition Facility Using Vacuum Hohlraums

The goal of demonstrating ignition on the National Ignition Facility (NIF) has motivated a revisit of double-shell (DS) targets as a complementary path to the cryogenic baseline approach. Expected benefits of DS ignition targets include non-cryogenic deuterium-tritium (DT) fuel preparation, minimal hohlraum-plasma mediated laser backscatter, low threshold ignition temperatures ({approx} 4 keV) for relaxed hohlraum x-ray flux asymmetry tolerances, and minimal (two-) shock timing requirements. On the other hand, DS ignition presents several formidable challenges, encompassing room-temperature containment of high-pressure DT ({approx} 790 atm) in the inner shell, strict concentricity requirements on the two shells (< 3 {micro}m), development of nano-porous (<100 nm) low-density (<100 mg/cc) metallic foams for structural support of the inner shell and hydrodynamic instability mitigation, and effective control of hydrodynamic instabilities on the high-Atwood number interface between the DT fuel and the high-Z inner shell. Recent progress in DS ignition designs and required materials-science advances at the nanoscale are described herein. Two new ignition designs that use rugby-shaped vacuum hohlraums are presented which utilize either 1 MJ or 2 MJ of laser energy at 3{omega}. The capability of the NIF to generate the requested reverse-ramp pulse shape for DS ignition is expected to be comparable to the planned high-contrast ({approx}100) pulse-shape at 1.8 MJ for the baseline cryogenic target. Nano-crystalline, high-strength, Au-Cu alloy inner shells are under development using electrochemical deposition over a glass mandrel, exhibiting tensile strengths well in excess of 790 atm. Novel, low-density (85 mg/cc) copper foams have recently been demonstrated using 10 mg/cc SiO{sub 2} nano-porous aerogels with suspended Cu particles. A prototype demonstration of an ignition DS is planned for 2008, incorporating the needed novel nano-materials science developments and the required fabrication tolerances for a realistic ignition attempt after 2010

Structural and magnetic properties of nanostructured composites (SrFe<inf>12</inf>O<inf>19</inf>)<inf>x</inf>(CaCu<inf>3</inf>Ti<inf>4</inf>O<inf>12</inf>)<inf>1-x</inf>

© 2017 Elsevier B.V. (SrFe 12 O 19 ) x (CaCu 3 Ti 4 O 12 ) 1-x (x = 0.01, 0.03, 0.07, 0.1) composites were synthesized using a solid state method, while the pre-synthesized strontium hexaferrite SrFe 12 O 19 (SFO) was added to the stoichiometric amount of CaO, CuO and TiO oxides to form the CaCu 3 Ti 4 O 12 (CCTO) structure around SFO microinclusions. The structural and microstructural properties of obtained composites were studied by X-ray diffraction, scanning electron microscopy and transmission electron microscopy techniques. The magnetic properties were studied by electron spin resonance and magnetometry methods. Based on all experimental data we can conclude, that SFO x CCTO 1-x nanostructured composites were formed only for concentrations x = 0.03 and x = 0.07, where SFO nanoinclusions are inside CCTO matrix, that leads to the strong mutual influence of the magnetic properties of both component

Fabrication of Double Shell Targets with a Glass Inner Capsule Supported by SiO2 Aerogel for Shots on the Omega Laser in 2006

Indirectly driven double shell implosions are being investigated as a possible noncryogenic path to ignition on the National Ignition Facility. Lawrence Livermore National Laboratory has made several technological advances that have produced double shell targets that represent a significant improvement to previously fielded targets. The inner capsule is supported inside the ablator shell by SiO{sub 2} aerogel with a nominal density of 50 mg/cm{sup 3}. The aerogel is cast around the inner capsule and then machined concentric to it. The seamless sphere of aerogel containing the embedded capsule is then assembled between the two halves of the ablator shell. The concentricity between the two shells has been improved to less than 1.5 {micro}m. The ablator shell consists of two hemispherical shells that mate at a step joint that incorporates a gap with a nominal thickness of 0.1 {micro}m. Using a new flexure-based tool holder that precisely positions the diamond cutting tool on the diamond turning machine, step discontinuities on the inner surface of the ablator of less than 0.5 {micro}m have been achieved. New methods have been used to comprehensively characterize each of the targets using high-resolution x-ray imaging systems

Very-high-growth-factor Planar Ablative Rayleigh Taylor Experiments

The Rayleigh-Taylor (RT) instability is an important factor in bounding the performance envelope of ignition targets. This paper describes an experiment for ablative RT instability that for the first time achieves growth factors close to those expected to occur in ignition targets at the National Ignition Facility (NIF). The large growth allows small seed perturbations to be detected and can be used to place an upper bound on perturbation growth at the ablation front resulting from microstructure in the preferred Be ablator. The experiments were performed on the Omega laser using a halfraum 1.2 mm long by 2 mm diameter with a 75% laser entrance hole. The halfraum was filled with {approx} 1 atm of neopentane to delay gold plasma from closing the diagnostic line of sight down the axis of the halfraum. The ablator was mounted at the base of the halfraum, and was accelerated by a two stepped X-ray pulse consisting of an early time section {approx} 100 eV to emulate the NIF foot followed by an approximately constant {approx} 150 eV drive sustained over an additional 5-7ns. It is this long pulse duration and late time observation that distinguishes the present work from previous experiments, and is responsible for the large growth that is achieved. The growth of a 2D sinusoidal perturbation machined on the drive side of the ablator was measured using face-on radiography. The diagnostic view remained open until {approx} 11 ns with maximum growth factors measured to be {approx} 200. The trajectory of the ablator was measured using streaked backlit radiography. The design and analysis of the experiments is described, and implications for experiments on ignition target ablators are discussed