Addressing student models of energy loss in quantum tunnelling

We report on a multi-year, multi-institution study to investigate student reasoning about energy in the context of quantum tunnelling. We use ungraded surveys, graded examination questions, individual clinical interviews, and multiple-choice exams to build a picture of the types of responses that students typically give. We find that two descriptions of tunnelling through a square barrier are particularly common. Students often state that tunnelling particles lose energy while tunnelling. When sketching wave functions, students also show a shift in the axis of oscillation, as if the height of the axis of oscillation indicated the energy of the particle. We find inconsistencies between students' conceptual, mathematical, and graphical models of quantum tunnelling. As part of a curriculum in quantum physics, we have developed instructional materials to help students develop a more robust and less inconsistent picture of tunnelling, and present data suggesting that we have succeeded in doing so.Comment: Originally submitted to the European Journal of Physics on 2005 Feb 10. Pages: 14. References: 11. Figures: 9. Tables: 1. Resubmitted May 18 with revisions that include an appendix with the curriculum materials discussed in the paper (4 page small group UW-style tutorial

The role of sign in students' modeling of scalar equations

We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students in a sophomore level mechanics class at some point wrote Newton's Second Law as F = -ma; they were using this form to ensure that the sign of the force pointed in a direction consistent with the chosen coordinate system while assuming that some variables have only positive value. We use one student's detailed explanation to suggest that students' issues with variables are context-dependent, and that much of their reasoning is useful for productive instruction.Comment: 5 pages, 1 figure, to be published in The Physics Teache

Understanding and Affecting Student Reasoning About Sound Waves

Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of resources, i.e. grouped building blocks of thinking that are commonly used in many different settings. Students in our university physics classes often used sets of resources that were different from the ones we wish them to use. By designing curriculum materials that ask students to think about the physics from a different view, we bring about improvement in student understanding of sound waves. Our curriculum modifications are specific to our own classes, but our description of student learning is more generally useful for teachers. We describe how students can use multiple sets of resources in their thinking, and raise questions that should be considered by both instructors and researchers.Comment: 23 pages, 4 figures, 3 tables, 28 references, 7 notes. Accepted for publication in the International Journal of Science Educatio

A distributed algorithm to find k-dominating sets

We consider a connected undirected graph $G(n,m)$ with $n$ nodes and $m$ edges. A $k$-dominating set $D$ in $G$ is a set of nodes having the property that every node in $G$ is at most $k$ edges away from at least one node in $D$. Finding a $k$-dominating set of minimum size is NP-hard. We give a new synchronous distributed algorithm to find a $k$-dominating set in $G$ of size no greater than $\lfloor n/(k+1)\rfloor$. Our algorithm requires $O(k\log^*n)$ time and $O(m\log k+n\log k\log^*n)$ messages to run. It has the same time complexity as the best currently known algorithm, but improves on that algorithm's message complexity and is, in addition, conceptually simpler.Comment: To appear in Discrete Applied Mathematic

Using resource graphs to represent conceptual change

We introduce resource graphs, a representation of linked ideas used when reasoning about specific contexts in physics. Our model is consistent with previous descriptions of resources and coordination classes. It can represent mesoscopic scales that are neither knowledge-in-pieces or large-scale concepts. We use resource graphs to describe several forms of conceptual change: incremental, cascade, wholesale, and dual construction. For each, we give evidence from the physics education research literature to show examples of each form of conceptual change. Where possible, we compare our representation to models used by other researchers. Building on our representation, we introduce a new form of conceptual change, differentiation, and suggest several experimental studies that would help understand the differences between reform-based curricula.Comment: 27 pages, 14 figures, no tables. Submitted for publication to the Physical Review Special Topics Physics Education Research on March 8, 200

Kerncraft: A Tool for Analytic Performance Modeling of Loop Kernels

Achieving optimal program performance requires deep insight into the interaction between hardware and software. For software developers without an in-depth background in computer architecture, understanding and fully utilizing modern architectures is close to impossible. Analytic loop performance modeling is a useful way to understand the relevant bottlenecks of code execution based on simple machine models. The Roofline Model and the Execution-Cache-Memory (ECM) model are proven approaches to performance modeling of loop nests. In comparison to the Roofline model, the ECM model can also describes the single-core performance and saturation behavior on a multicore chip. We give an introduction to the Roofline and ECM models, and to stencil performance modeling using layer conditions (LC). We then present Kerncraft, a tool that can automatically construct Roofline and ECM models for loop nests by performing the required code, data transfer, and LC analysis. The layer condition analysis allows to predict optimal spatial blocking factors for loop nests. Together with the models it enables an ab-initio estimate of the potential benefits of loop blocking optimizations and of useful block sizes. In cases where LC analysis is not easily possible, Kerncraft supports a cache simulator as a fallback option. Using a 25-point long-range stencil we demonstrate the usefulness and predictive power of the Kerncraft tool.Comment: 22 pages, 5 figure

Continuous transition between decagonal quasicrystal and approximant by formation and ordering of out-of-phase domains

The transformation between a quasicrystal and an orthorhombic approximant is studied at the nominal composition Al72.7Ni8.3Co19 by electron diffraction and high-resolution transmission electron microscopy. A series of transition states indicating a continuous transformation is monitored. First, the material transforms to a single-oriented one-dimensional quasicrystal. In the course of this process out-of-phase domains are formed. The approximant results from ordering of these domains to a periodic structure

An assessment of the histidine-loading (Figlu) test in infancy

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Device calibration impacts security of quantum key distribution

Characterizing the physical channel and calibrating the cryptosystem hardware are prerequisites for establishing a quantum channel for quantum key distribution (QKD). Moreover, an inappropriately implemented calibration routine can open a fatal security loophole. We propose and experimentally demonstrate a method to induce a large temporal detector efficiency mismatch in a commercial QKD system by deceiving a channel length calibration routine. We then devise an optimal and realistic strategy using faked states to break the security of the cryptosystem. A fix for this loophole is also suggested.Comment: 4 pages + 1 page of supplementary information. Considerable modification of Eve's attack strategy and QBER minimization technique. All figures have also been improve