Scheme Independence to all Loops

The immense freedom in the construction of Exact Renormalization Groups means that the many non-universal details of the formalism need never be exactly specified, instead satisfying only general constraints. In the context of a manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills, we outline a proof that, to all orders in perturbation theory, all explicit dependence of beta function coefficients on both the seed action and details of the covariantization cancels out. Further, we speculate that, within the infinite number of renormalization schemes implicit within our approach, the perturbative beta function depends only on the universal details of the setup, to all orders.Comment: 18 pages, 8 figures; Proceedings of Renormalization Group 2005, Helsinki, Finland, 30th August - 3 September 2005. v2: Published in jphysa; minor changes / refinements; refs. adde

Modeling an elastic beam with piezoelectric patches by including magnetic effects

Models for piezoelectric beams using Euler-Bernoulli small displacement theory predict the dynamics of slender beams at the low frequency accurately but are insufficient for beams vibrating at high frequencies or beams with low length-to-width aspect ratios. A more thorough model that includes the effects of rotational inertia and shear strain, Mindlin-Timoshenko small displacement theory, is needed to predict the dynamics more accurately for these cases. Moreover, existing models ignore the magnetic effects since the magnetic effects are relatively small. However, it was shown recently \cite{O-M1} that these effects can substantially change the controllability and stabilizability properties of even a single piezoelectric beam. In this paper, we use a variational approach to derive models that include magnetic effects for an elastic beam with two piezoelectric patches actuated by different voltage sources. Both Euler-Bernoulli and Mindlin-Timoshenko small displacement theories are considered. Due to the magnetic effects, the equations are quite different from the standard equations.Comment: 3 figures. 2014 American Control Conference Proceeding

Sensitivity of Nonrenormalizable Trajectories to the Bare Scale

Working in scalar field theory, we consider RG trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space, how the effective action at the effective scale, Lambda, changes as the bare scale (and hence the duration of the flow down to Lambda) is changed. When the effective action satisfies Polchinski's version of the Exact Renormalization Group equation, we prove, directly from the path integral, that the dependence of the effective action on the bare scale, keeping the interaction part of the bare action fixed, is given by an equation of the same form as the Polchinski equation but with a kernel of the opposite sign. We then investigate whether similar equations exist for various generalizations of the Polchinski equation. Using nonperturbative, diagrammatic arguments we find that an action can always be constructed which satisfies the Polchinski-like equation under variation of the bare scale. For the family of flow equations in which the field is renormalized, but the blocking functional is the simplest allowed, this action is essentially identified with the effective action at Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in jphy

Investigation of light source and scattering medium related to vapor-screen flow visualization in a supersonic wind tunnel

Methods for increasing the radiant in light sheets used for vapor screen set-ups were investigated. Both high-pressure mercury arc lamps and lasers were considered. Pulsed operation of the air-cooled 1-kW lamps increased the light output but decreased reliability. An ellipsoidal mirror improved the output of the air-cooled lamps by concentrating the light but increased the complexity of the housing. Water-cooled-4-kW lamps coupled with high-aperture Fresnel lenses provided reasonable improvements over the air-cooled lamps. Fanned laser beams measurements of scattered light versus dew point made in conjunction with successful attempts to control the fluid injection. A number of smoke generators are described and test results comparing smoke and vapor screens are shown. Finally, one test included a periscope system to relay the image to a camera outside the flow

Wind Tunnel Test of Low Boom Equivalent Body at Mach 4

A body of revolution, representing the equivalent area distribution of a low boom aircraft design cruising at 24,384 meters at a Mach number of 4, was tested to determine whether its theoretical sonic boom characteristics could be experimentally verified. Results indicate that the essential features of the ground signature are well predicted

The influence of early questions on learning from text

In this research we explored the use of short-answer questions to improve learning from chapter-like texts (3395 words). Experiment 1 investigated the influence of pre-questions on recall from a text passage when tested a week later; two question sets were counterbalanced within the experimental group. Participants with pre-questions scored higher both overall (d = 3.6, 95%CI [2.4, 4.8]) and on novel questions (d = 2.0 [1.6, 2.4]). In Experiment 2, questions were made available immediately after studying the text either alongside the text, open-book, or closed-book with the opportunity to check answers, or not at all with additional study time. Learning was tested after a week. Although the immediate test scores were substantially higher for open- than closed-book tests, week-delayed performance on the same items was much worse for open-book tests and was moderately improved for closed-book tests. For seen questions, closed-book tests led to better delayed recall than did open-book tests, d = 0.7 [0.02, 1.5]. For novel questions, observed differences were small; ds = .2 [-0.6, 0.9] for both comparisons

Aerodynamic tests and analysis of a turbojet-boosted launch vehicle concept (spacejet) over a Mach number range of 1.50 to 2.86

Results from analytical and experimental studies of the aerodynamic characteristics of a turbojet-boosted launch vehicle concept through a Mach number range of 1.50 to 2.86 are presented. The vehicle consists of a winged orbiter utilizing an area-ruled axisymmetric body and two winged turbojet boosters mounted underneath the orbiter wing. Drag characteristics near zero lift were of prime interest. Force measurements and flow visualization techniques were employed. Estimates from wave drag theory, supersonic lifting surface theory, and impact theory are compared with data and indicate the ability of these theories to adequately predict the aerodynamic characteristics of the vehicle. Despite the existence of multiple wings and bodies in close proximity to each other, no large scale effects of boundary layer separation on drag or lift could be discerned. Total drag levels were, however, sensitive to booster locations

Experimental effects of fuselage camber on longitudinal aerodynamic characteristics of a series of wing-fuselage configurations at a Mach number of 1.41

An experimental investigation was conducted to evaluate a method for the integration of a fighter-type fuselage with a theoretical wing to preserve desirable wing aerodynamic characteristics for efficient maneuvering. The investigation was conducted by using semispan wing fuselage models mounted on a splitter plate. The models were tested through an angle of attack range at a Mach number of 1.41. The wing had a leading edge sweep angle of 50 deg and an aspect ratio of 2.76; the wing camber surface was designed for minimum drag due to lift and was to be self trimming at a lift coefficient of 0.2 and at a Mach number of 1.40. A series of five fuselages of various camber was tested on the wing