Harmonic sets and the harmonic prime number theorem

We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2

Toxicity of materials in fire situations: Laboratory data obtained at the University of San Francisco

Approximately 300 materials were evaluated using a specific set of test conditions. Materials tested included wood, fibers, fabrics and synthetic polymers. Data obtained using 10 different sets of test conditions are presented

Aeroheating Measurements of BOLT Aerodynamic Fairings and Transition Module

The Air Force Office of Scientific Research (AFOSR) has sponsored the Boundary Layer Transition (BOLT) Experiments to investigate hypersonic boundary layer transition on a low-curvature, concave surface with swept leading edges. This paper presents aeroheating measurements on a subscale model of the BOLT Flight Geometry, aerodynamic fairings, and Transition Module (TSM) in the NASA Langley 20-Inch Mach 6 Air Tunnel. The purpose of the test was to investigate and identify any areas of localized heating on the TSM for inclusion in the BOLT Critical Design Review (CDR). Surface heating distributions were measured using global phosphor thermography, and data were obtained for a range of model attitudes and free stream Reynolds numbers. Measurements showed low heating on the fairings and TSM. Additional analysis was completed after the CDR to compare heating on the TSM for the nominal BOLT vehicle reentry angle-of-attack with heating on the TSM for possible reentry angle-of-attack excursions. The results of this analysis were used in conjunction with thermal analyses from Johns Hopkins Applied Physics Lab (JHU/APL) and the Air Force Research Laboratory (AFRL) to assess the need for thermal protection on the flight vehicle TSM

Optimising sward structure and herbage yield for the performance of dairy cows at pasture.

End of Project ReportsThe basic unit of intake is the bite. The total daily intake of grazed grass is determined by the number of bites taken and the weight of the average bite. In this project the focus was on sward structure (architecture) and its effects on bite volume and weight. There were two objectives. The first was to determine the plant growth mechanism responsible for variations in sward structure. The investigation was carried out at The Queen’s University in Belfast and involved microscopic study of leaves from plants grown under controlled conditions. The second objective, to determine how bite volume and mass was affected by differences in sward structure was a field study using fistulated cows and was done at Moorepark.EU Structural Funds (EAGGF

Active Carbon and Oxygen Shell Burning Hydrodynamics

We have simulated 2.5$\times10^3$ s of the late evolution of a $23 \rm M_\odot$ star with full hydrodynamic behavior. We present the first simulations of a multiple-shell burning epoch, including the concurrent evolution and interaction of an oxygen and carbon burning shell. In addition, we have evolved a 3D model of the oxygen burning shell to sufficiently long times (300 s) to begin to assess the adequacy of the 2D approximation. We summarize striking new results: (1) strong interactions occur between active carbon and oxygen burning shells, (2) hydrodynamic wave motions in nonconvective regions, generated at the convective-radiative boundaries, are energetically important in both 2D and 3D with important consequences for compositional mixing, and (3) a spectrum of mixed p- and g-modes are unambiguously identified with corresponding adiabatic waves in these computational domains. We find that 2D convective motions are exaggerated relative to 3D because of vortex instability in 3D. We discuss the implications for supernova progenitor evolution and symmetry breaking in core collapse.Comment: 5 pages, 4 figures in emulateapj format. Accepted for publication in ApJ Letters. High resolution figure version available at http://spinach.as.arizona.ed

Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I

We analyze the issue of anomaly-free representations of the constraint algebra in Loop Quantum Gravity (LQG) in the context of a diffeomorphism-invariant gauge theory in three spacetime dimensions. We construct a Hamiltonian constraint operator whose commutator matches with a quantization of the classical Poisson bracket involving structure functions. Our quantization scheme is based on a geometric interpretation of the Hamiltonian constraint as a generator of phase space-dependent diffeomorphisms. The resulting Hamiltonian constraint at finite triangulation has a conceptual similarity with the "mu-bar"-scheme in loop quantum cosmology and highly intricate action on the spin-network states of the theory. We construct a subspace of non-normalizable states (distributions) on which the continuum Hamiltonian constraint is defined which leads to an anomaly-free representation of the Poisson bracket of two Hamiltonian constraints in loop quantized framework.Comment: 60 pages, 6 figure