Developing an Action Concept Inventory

We report on progress towards the development of an Action Concept Inventory (ACI), a test that measures student understanding of action principles in introductory mechanics and optics. The ACI also covers key concepts of many-paths quantum mechanics, from which classical action physics arises. We used a multi-stage iterative development cycle for incorporating expert and student feedback into successive revisions of the ACI. The student feedback, including think-aloud interviews, enabled us to identify their misconceptions about action physics.Comment: 6 pages. This paper started out as arXiv:1507.06075v1, then split into arXiv:1507.06075v2 and this paper as a result of feedback from referees and an editor. arXiv:1507.06075v2 presents the case for teaching action physics, while this paper presents an evaluation too

Flexibility effects on tooth contact location in spiral bevel gear transmissions

An analytical method to predict the shift of the contact ellipse between the meshing teeth in a spiral bevel gear set is presented in this report. The contact ellipse shift of interest is the motion of the nominal tooth contact location on each tooth from the ideal pitch point to the point of contact between the two teeth considering the elastic motions of the gears and their supporting shafts. This is the shift of the pitch point from the ideal, unloaded position on each tooth to the nominal contact location on the tooth when the gears are fully loaded. It is assumed that the major contributors of this motion are the elastic deflections of the gear shafts, the slopes of the shafts under load and the radial deflections of the four gear shaft bearings. The motions of the two pitch point locations on the pinion and the gear tooth surfaces are calculated in a FORTRAN program which also calculates the size and orientation of the Hertzian contact ellipse on the tooth faces. Based on the curvatures of the two spiral bevel gear teeth and the size of the contact ellipse, the program also predicts the basic dynamic capacity of the tooth pair. A complete numerical example is given to illustrate the use of the program

The optimal design of standard gearsets

A design procedure for sizing standard involute spur gearsets is presented. The procedure is applied to find the optimal design for two examples - an external gear mesh with a ratio of 5:1 and an internal gear mesh with a ratio of 5:1. In the procedure, the gear mesh is designed to minimize the center distance for a given gear ratio, pressure angle, pinion torque, and allowable tooth strengths. From the methodology presented, a design space may be formulated for either external gear contact or for internal contact. The design space includes kinematics considerations of involute interference, tip fouling, and contact ratio. Also included are design constraints based on bending fatigue in the pinion fillet and Hertzian contact pressure in the full load region and at the gear tip where scoring is possible. This design space is two dimensional, giving the gear mesh center distance as a function of diametral pitch and the number of pinion teeth. The constraint equations were identified for kinematic interference, fillet bending fatigue, pitting fatigue, and scoring pressure, which define the optimal design space for a given gear design. The locus of equal size optimum designs was identified as the straight line through the origin which has the least slope in the design region

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with non-opposite momenta. The net effect of this process -- which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion -- is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode-mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.Comment: Final published version, with updated references and minor modification

The optimal design of involute gear teeth with unequal addenda

The design of a gear mesh is treated with the objective of minimizing the gear size for a given gear ratio, pinion torque, pressure angle, and allowable tooth lengths. Tooth strengths considered include scoring, pitting fatigue, and bending fatigue. Kinematic involute interference is avoided. The design variation on standard spur gear teeth called the long and short addendum system, is considered. In this system the mesh center distance and pressure angle are maintained as is the ability to manufacture the teeth with standard tooling. However, the pinion and gear tooth proportions are altered in order to obtain fewer teeth numbers for the same ratio as standard gears without kinematic involute interference. The effect of this nonstandard gearing geometry with on tooth strengths and gear mesh size are studied. For a 2:1 gearing ratio, the optimal nonstandard gear design is compared with the optimal standard gear design

Stability of continuously pumped atom lasers

A multimode model of a continuously pumped atom laser is shown to be unstable below a critical value of the scattering length. Above the critical scattering length, the atom laser reaches a steady state, the stability of which increases with pumping. Below this limit the laser does not reach a steady state. This instability results from the competition between gain and loss for the excited states of the lasing mode. It will determine a fundamental limit for the linewidth of an atom laser beam.Comment: 4 page

Oxalate content of miner’s lettuce irrigated with water or fertilizer solutions

The total, soluble and insoluble oxalate contents of the small, large and cauline leaves and small and large stems of miner’s lettuce (Claytonia perfoliata ) plants which had been irrigated with tap water or a soluble fertilizer were extracted and measured using HPLC chromatography. Overall, all plant parts of miner’s lettuce analyzed contained high levels of total and soluble oxalates; however plants irrigated with fertilizer contained lower levels of oxalates compared with plants irrigated with water. On a dry matter basis, the small leaves contained higher levels of total oxalate when compared to the total oxalate in the large leaves. Soluble oxalate in the leaves of plants irrigated with water ranged from 2.6 to 7.5 mg/100g dry matter (DM) and was significantly higher (P < 0.05) than the leaves of the fertilizer-watered plants, which ranged from 1.8 to 2.8 mg/100g DM. The soluble oxalate in the small and large stems of the fertilizer-watered plants ranged from 1.20 to 1.5 mg/100g DM and was significantly lower (P < 0.05) than the water-treated small and large stems, which ranged from 3.75 to 4.4 mg/100g DM. It is recommended that the leaves of miner’s lettuce should be consumed in moderation