Termination Casts: A Flexible Approach to Termination with General Recursion

This paper proposes a type-and-effect system called Teqt, which distinguishes terminating terms and total functions from possibly diverging terms and partial functions, for a lambda calculus with general recursion and equality types. The central idea is to include a primitive type-form "Terminates t", expressing that term t is terminating; and then allow terms t to be coerced from possibly diverging to total, using a proof of Terminates t. We call such coercions termination casts, and show how to implement terminating recursion using them. For the meta-theory of the system, we describe a translation from Teqt to a logical theory of termination for general recursive, simply typed functions. Every typing judgment of Teqt is translated to a theorem expressing the appropriate termination property of the computational part of the Teqt term.Comment: In Proceedings PAR 2010, arXiv:1012.455

A new numerical method for obtaining gluon distribution functions G(x,Q2)=xg(x,Q2)G(x,Q^2)=xg(x,Q^2), from the proton structure function F2γp(x,Q2)F_2^{\gamma p}(x,Q^2)

An exact expression for the leading-order (LO) gluon distribution function $G(x,Q^2)=xg(x,Q^2)$ from the DGLAP evolution equation for the proton structure function $F_2^{\gamma p}(x,Q^2)$ for deep inelastic $\gamma^* p$ scattering has recently been obtained [M. M. Block, L. Durand and D. W. McKay, Phys. Rev. D{\bf 79}, 014031, (2009)] for massless quarks, using Laplace transformation techniques. Here, we develop a fast and accurate numerical inverse Laplace transformation algorithm, required to invert the Laplace transforms needed to evaluate $G(x,Q^2)$, and compare it to the exact solution. We obtain accuracies of less than 1 part in 1000 over the entire $x$ and $Q^2$ spectrum. Since no analytic Laplace inversion is possible for next-to-leading order (NLO) and higher orders, this numerical algorithm will enable one to obtain accurate NLO (and NNLO) gluon distributions, using only experimental measurements of $F_2^{\gamma p}(x,Q^2)$.Comment: 9 pages, 2 figure

Comparing introductory and beyond-introductory students' reasoning about uncertainty

Uncertainty is an important concept in physics laboratory instruction. However, little work has examined how students reason about uncertainty beyond the introductory (intro) level. In this work we aimed to compare intro and beyond-intro students' ideas about uncertainty. We administered a survey to students at 10 different universities with questions probing procedural reasoning about measurement, student-identified sources of uncertainty, and predictive reasoning about data distributions. We found that intro and beyond-intro students answered similarly on questions where intro students already exhibited expert-level reasoning, such as in comparing two data sets with the same mean but different spreads, identifying limitations in an experimental setup, and predicting how a data distribution would change if more data were collected. For other questions, beyond-intro students generally exhibited more expert-like reasoning than intro students, such as when determining whether two sets of data agree, identifying principles of measurement that contribute to spread, and predicting how a data distribution would change if better data were collected. Neither differences in student populations, lab courses taken, nor research experience were able to fully explain the variability between intro and beyond-intro student responses. These results call for further research to better understand how students' ideas about uncertainty develop beyond the intro level.Comment: 19 pages, 12 figure

Context affects student thinking about sources of uncertainty in classical and quantum mechanics

Measurement uncertainty is an important topic in the undergraduate laboratory curriculum. Previous research on student thinking about experimental measurement uncertainty has focused primarily on introductory-level students' procedural reasoning about data collection and interpretation. In this paper, we extended this prior work to study upper-level students' thinking about sources of measurement uncertainty across experimental contexts, with a particular focus on classical and quantum mechanics contexts. We developed a survey to probe students' thinking in the generic question ``What comes to mind when you think about measurement uncertainty in [classical/quantum] mechanics?'' as well as in a range of specific experimental scenarios. We found that students primarily focused on limitations of the experimental setup in classical mechanics and principles of the underlying physics theory in quantum mechanics. Our results suggest that students need careful scaffolding to identify principles in appropriate classical experimental contexts and limitations in appropriate quantum experimental contexts. We recommend that future research probe how instruction in both classical and quantum contexts can help students better understand the range of sources of uncertainty present in classical and quantum experiments.Comment: 15 pages, 8 figure

The t-tbar cross-section at 1.8 and 1.96 TeV: a study of the systematics due to parton densities and scale dependence

We update the theoretical predictions for the t-tbar production cross-section at the Tevatron, taking into account the most recent determinations of systematic uncertainties in the extraction of the proton parton densities.Comment: 12 pages, 1 figure, Late

New perspectives on student reasoning about measurement uncertainty: More or better data

Uncertainty is an important and fundamental concept in physics education. Students are often first exposed to uncertainty in introductory labs, expand their knowledge across lab courses, and then are introduced to quantum mechanical uncertainty in upper-division courses. This study is part of a larger project evaluating student thinking about uncertainty across these contexts. In this research, we investigate advanced physics student thinking about uncertainty by asking them conceptual questions about how a hypothetical distribution of measurements would change if `more' or `better' data were collected in four different experimental scenarios. The scenarios include both classical and quantum experiments, as well as experiments that theoretically result in an expected single value or an expected distribution. This investigation is motivated by our goal of finding insights into students' potential point- and set-like thinking about uncertainty and of shining light on the limitations of those binary paradigms.Comment: 15 pages, 5 figures, accepted to Physical Review Physics Education Researc

Lunar lander conceptual design

This paper is a first look at the problems of building a lunar lander to support a small lunar surface base. A series of trade studies was performed to define the lander. The initial trades concerned choosing number of stages, payload mass, parking orbit altitude, and propellant type. Other important trades and issues included plane change capability, propellant loading and maintenance location, and reusability considerations. Given a rough baseline, the systems were then reviewed. A conceptual design was then produced. The process was carried through only one iteration. Many more iterations are needed. A transportation system using reusable, aerobraked orbital transfer vehicles (OTV's) is assumed. These OTV's are assumed to be based and maintained at a low Earth orbit (LEO) space station, optimized for transportation functions. Single- and two-stage OTV stacks are considered. The OTV's make the translunar injection (TLI), lunar orbit insertion (LOI), and trans-Earth injection (TEI) burns, as well as midcourse and perigee raise maneuvers

The impact of new neutrino DIS and Drell-Yan data on large-x parton distributions

New data sets have recently become available for neutrino and antineutrino deep inelastic scattering on nuclear targets and for inclusive dimuon production in pp pd interactions. These data sets are sensitive to different combinations of parton distribution functions in the large-x region and, therefore, provide different constraints when incorporated into global parton distribution function fits. We compare and contrast the effects of these new data on parton distribution fits, with special emphasis on the effects at large x. The effects of the use of nuclear targets in the neutrino and antineutrino data sets are also investigated.Comment: 24 pages, 13 figure

Weak-scale phenomenology of models with gauge-mediated supersymmetry breaking

We study in some detail the spectral phenomenology of models in which supersymmetry is dynamically broken and transmitted to the supersymmetric partners of the quarks, leptons and gauge bosons, and the Higgs bosons themselves, via the usual gauge interactions. We elucidate the parameter space of what we consider to be the minimal model, and explore the regions which give rise to consistent radiative electroweak symmetry breaking. We include the weak-scale threshold corrections, and show how they considerably reduce the scale dependence of the results. We examine the sensitivity of our results to unknown higher-order messenger-sector corrections. We compute the superpartner spectrum across the entire parameter space, and compare it to that of the minimal supergravity-inspired model. We delineate the regions where the lightest neutralino or tau slepton is the next-to-lightest supersymmetric particle, and compute the lifetime and branching ratios of the NLSP. In contrast to the minimal supergravity-inspired model, we find that the lightest neutralino can have a large Higgsino component, of order 50%. Nevertheless, the neutralino branching fraction to the gravitino and the light Higgs boson remains small, < 10^{-4}, so the observation of such a decay would point to a non-minimal Higgs sector.Comment: 22 pages, 16 figures, published versio