Solutions to the reconstruction problem in asymptotic safety

Starting from a full renormalised trajectory for the effective average action (a.k.a. infrared cutoff Legendre effective action) $\Gamma_k$, we explicitly reconstruct corresponding bare actions, formulated in one of two ways. The first step is to construct the corresponding Wilsonian effective action $S^k$ through a tree-level expansion in terms of the vertices provided by $\Gamma_k$. It forms a perfect bare action giving the same renormalised trajectory. A bare action with some ultraviolet cutoff scale $\Lambda$ and infrared cutoff $k$ necessarily produces an effective average action $\Gamma^\Lambda_k$ that depends on both cutoffs, but if the already computed $S^\Lambda$ is used, we show how $\Gamma^\Lambda_k$ can also be computed from $\Gamma_k$ by a tree-level expansion, and that $\Gamma^\Lambda_k\to\Gamma_k$ as $\Lambda\to\infty$. Along the way we show that Legendre effective actions with different UV cutoff profiles, but which correspond to the same Wilsonian effective action, are related through tree-level expansions. All these expansions follow from Legendre transform relationships that can be derived from the original one between $\Gamma^\Lambda_k$ and $S^k$.Comment: 32 page

The effect of extreme temperatures on the elastic properties and fracture behavior of graphite/polyimide composites

The influence of elevated and cryogenic temperatures on the elastic moduli and fracture strengths of several C6000/PMR-15 and C6000/NR-15082 laminates was measured. Tests were conducted at -157 C, 24 C, and 316 C (-250 F, 75 F, and 600 F). Both notched and unnotched laminates were tested. The average stress failure criterion was used to predict the fracture strength of quasi-isotropic notched laminates

A simulator study of the supersonic transport in the air traffic control system

Real time environment and control simulation of supersonic transport in air traffic control syste

Swashplate feedback control for tilt-rotor aircraft

Changes in angle of attack in system were sensed indirectly by gages which responded to strains induced in wing structure. Output signals were amplified, filtered, and used to activate swashplate actuators. System provided significant reduction in blade loads and desirable changes in hub forces and moments

Ion yields and erosion rates for Si1−xGex(0x1) ultralow energy O2+ secondary ion mass spectrometry in the energy range of 0.25–1 keV

We report the SIMS parameters required for the quantitative analysis of Si1−xGex across the range of 0 ≤ x ≤ 1 when using low energy O2+ primary ions at normal incidence. These include the silicon and germanium secondary ion yield [i.e., the measured ion signal (ions/s)] and erosion rate [i.e., the speed at which the material sputters (nm/min)] as a function of x. We show that the ratio Rx of erosion rates, Si1−xGex/Si, at a given x is almost independent of beam energy, implying that the properties of the altered layer are dominated by the interaction of oxygen with silicon. Rx shows an exponential dependence on x. Unsurprisingly, the silicon and germanium secondary ion yields are found to depart somewhat from proportionality to (1−x) and x, respectively, although an approximate linear relationship could be used for quantification across around 30% of the range of x (i.e., a reference material containing Ge fraction x would give reasonably accurate quantification across the range of ±0.15x). Direct comparison of the useful (ion) yields [i.e., the ratio of ion yield to the total number of atoms sputtered for a particular species (ions/atom)] and the sputter yields [i.e., the total number of atoms sputtered per incident primary ion (atoms/ions)] reveals a moderate matrix effect where the former decrease monotonically with increasing x except at the lowest beam energy investigated (250 eV). Here, the useful yield of Ge is found to be invariant with x. At 250 eV, the germanium ion and sputter yields are proportional to x for all x