A Prehistory of n-Categorical Physics

This paper traces the growing role of categories and n-categories in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts which manifest themselves in Feynman diagrams, spin networks, string theory, loop quantum gravity, and topological quantum field theory. Our chronology ends around 2000, with just a taste of later developments such as open-closed topological string theory, the categorification of quantum groups, Khovanov homology, and Lurie's work on the classification of topological quantum field theories.Comment: 129 pages, 8 eps figure

Scale-up of electrospray atomization using linear arrays of Taylor cones

Linear arrays of Taylor cones were established on capillary electrode tubes opposite a slotted flat plate counterelectrode to investigate the feasibility of increasing the liquid throughput rate in electrospray atomizers. It was found that individual Taylor cones could be established on each capillary over a wide range of the capillary radius to spacing ratio R/S. The onset potential Vs required to establish the cones varied directly with R/S, but the liquid flow rate per cone and current per cone were nearly independent of R/S for a given overpotential ratio P=V/Vs. Only six working capillaries were used, but the results per cone are applicable to larger arrays of cones since end effects were minimized

A comparison of integrated testlet and constructed-response question formats

Constructed-response (CR) questions are a mainstay of introductory physics textbooks and exams. However, because of time, cost, and scoring reliability constraints associated with this format, CR questions are being increasingly replaced by multiple-choice (MC) questions in formal exams. The integrated testlet (IT) is a recently-developed question structure designed to provide a proxy of the pedagogical advantages of CR questions while procedurally functioning as set of MC questions. ITs utilize an answer-until-correct response format that provides immediate confirmatory or corrective feedback, and they thus allow not only for the granting of partial credit in cases of initially incorrect reasoning, but furthermore the ability to build cumulative question structures. Here, we report on a study that directly compares the functionality of ITs and CR questions in introductory physics exams. To do this, CR questions were converted to concept-equivalent ITs, and both sets of questions were deployed in midterm and final exams. We find that both question types provide adequate discrimination between stronger and weaker students, with CR questions discriminating slightly better than the ITs. Meanwhile, an analysis of inter-rater scoring of the CR questions raises serious concerns about the reliability of the granting of partial credit when this traditional assessment technique is used in a realistic (but non optimized) setting. Furthermore, we show evidence that partial credit is granted in a valid manner in the ITs. Thus, together with consideration of the vastly reduced costs of administering IT-based examinations compared to CR-based examinations, our findings indicate that ITs are viable replacements for CR questions in formal examinations where it is desirable to both assess concept integration and to reward partial knowledge, while efficiently scoring examinations.Comment: 14 pages, 3 figures, with appendix. Accepted for publication in PRST-PER (August 2014

Numerical Simulations of Turbulent Molecular Clouds Regulated by Reprocessed Radiation Feedback from Nascent Super Star Clusters

Radiation feedback from young star clusters embedded in giant molecular clouds (GMCs) is believed to be important to the control of star formation. For the most massive and dense clouds, including those in which super star clusters (SSCs) are born, pressure from reprocessed radiation exerted on dust grains may disperse a significant portion of the cloud mass back into the interstellar medium (ISM). Using our radiaton hydrodynamics (RHD) code, Hyperion, we conduct a series of numerical simulations to test this idea. Our models follow the evolution of self-gravitating, strongly turbulent clouds in which collapsing regions are replaced by radiating sink particles representing stellar clusters. We evaluate the dependence of the star formation efficiency (SFE) on the size and mass of the cloud and $\kappa$, the opacity of the gas to infrared (IR) radiation. We find that the single most important parameter determining the evolutionary outcome is $\kappa$, with $\kappa \gtrsim 15 \text{ cm}^2 \text{ g}^{-1}$ needed to disrupt clouds. For $\kappa = 20-40 \text{ cm}^2 \text{ g}^{-1}$, the resulting SFE=50-70% is similar to empirical estimates for some SSC-forming clouds. The opacities required for GMC disruption likely apply only in dust-enriched environments. We find that the subgrid model approach of boosting the direct radiation force $L/c$ by a "trapping factor" equal to a cloud's mean IR optical depth can overestimate the true radiation force by factors of $\sim 4-5$. We conclude that feedback from reprocessed IR radiation alone is unlikely to significantly reduce star formation within GMCs unless their dust abundances or cluster light-to-mass ratios are enhanced.Comment: 19 pages, 18 figures, accepted for publication in Ap

Student Mastery of Engineering with Design Review

Traditional structural engineering pedagogy has consisted of students preparing for class by reading a textbook, followed by a professor giving a lecture, followed by students doing individual homework. Students received feedback in terms of a grade from the professor, and, ideally, the student filed the graded work and possibly reviewed it again before an exam. Following the exam, the professor moved to the next topic and essentially ended any further contact time with the material, resulting in students quickly dumping a good percentage of what was learned. To make matters worse, most faculty would agree that undergraduate students often skip the reading prior to class, and studies have shown that almost half of all students do not pay attention to material presented during a lecture. Thus, it is critical for engineering educators to improve the stagnant method of traditional teaching and learning. Small mistakes in the engineering profession can lead to death or millions of dollars in repair. For the fall 2018 semester, in the Design of Steel and Wood Structures at the United States Military Academy at West Point, Civil Engineering students participated in a cooperative learning technique aimed at improving student learning. These same students tried a different version of this technique in Structural Analysis the prior semester.[1] Prior to submitting individual homework to the instructor for grade, students paired up with a peer within their class hour and checked each other’s work using an instructor provided “Design Review Sheet.” When a student found a mistake, or disagreed with the methodology used by their Design Review partner, the student annotated this on their sheet. The expectation was that when disagreements were discovered between students, they would discuss with each other where the error or misunderstanding existed and subsequently corrected the error prior to submission for grade. This not only required students to explain the work they completed, but it also provided additional contact time with the material. With respect to Engineering Teaching and Learning, Design Review provides the essential cooperative learning characteristic of positive interdependence because individual student learning increases as review partners improved in their Design Review. As a student incentive to complete a thorough review, the quality of review counted for 10% of each assignment. Efforts this iteration were in response to some of the student suggestions following a previous iteration.[1] This iteration, in lieu of students turning in their work in pairs to receive one grade, each student would turn in their individual work and Design Review sheet. This was done to hold all students accountable for the work they completed. In addition, the instructor provided Design Review sheet was modified for clarity and the requirement to write a memorandum summarizing the results of each Design Review was eliminated. This cooperative learning technique was used on six of seven homework assignments during the term and on seven of nine homework assignments in their pre-requisite course. Student feedback was collected from both Likert Scale questions and open-ended questions. This paper will make the case that this pedagogy benefits Engineering Teaching and Learning by: (1) getting engineering students in the practice of what engineers in practice already do (check each other’s work), (2) increasing student learning of course learning objectives through repetition and through observing how others solve problems and present their work, and (3) improving the ability of future engineers to communicate their work clearly and effectively.Cockrell School of Engineerin

A terminal molybdenum carbide prepared by methylidyne deprotonation

The carbide anion [CMo{N(R)Ar}_3]– [R = C(CD_3)_2CH_3, Ar = C_6H_3Me_2-3,5], is obtained by deprotonation of the corresponding methylidyne compound, [HCMo{N(R)Ar}_3], and is characterized by X-ray diffraction as its {K(benzo-15-crown-5)_2}+ salt, thereby providing precedent for the carbon atom as a terminal substituent in transition-metal chemistry