Computation across the curriculum: What skills are needed?

Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most undergraduate programs, students have little formal opportunity to engage with computation and, thus, are left to their own to develop their computational expertise. As part of a larger project to study how computation is incorporated in some undergraduate physics programs (and how it might be incorporated further), we convened a mini-conference and conducted a series of interviews with industry professionals, academic faculty, and employed bachelor's graduates who make use of computation in their everyday work. We present preliminary results that speak to how participants developed the requisite skills to do professional computational work and what skills they perceive are necessary to conduct such work.Comment: 4 pages; accepted to 2015 Physics Education Research Conference Proceeding

Classical particle scattering for power-law two-body potentials

We present a rigorous study of the classical scattering for anytwo-body inter-particle potential of the form $v(r)=g/r^\gamma$, with\gamma\textgreater{}0, for repulsive (g\textgreater{}0) and attractive (g\textless{}0)interactions. We give a derivation of the complete power series of thedeflection angle in terms of the impact factor for the weak scatteringregime (large impact factors) as well as the asymptotic expressionsfor the hard scattering regime (small impact factors). We see a verydifferent qualitative and quantitative behavior depending whether theinteraction is repulsive or attractive. In the latter case, thefamilies of trajectories depend also strongly on the value of$\gamma$. We also study carefully the modifications of the resultswhen a regularization is introduced in the potential at small scales.We check and illustrate all the results with the exact integration ofthe equations of motion.Comment: 23 pages, 17 figure

Rubric Design for Separating the Roles of Open-Ended Assessments

End-of-course assessments play important roles in the ongoing attempt to improve instruction in physics courses. Comparison of students' performance on assessments before and after instruction gives a measure of student learning. In addition, analysis of students' answers to assessment items provides insight into students' difficulties with specific concepts and practices. While open-ended assessments scored with detailed rubrics provide useful information about student reasoning to researchers, end users need to score students' responses so that they may obtain meaningful feedback on their instruction. One solution that satisfies end users and researchers is a grading rubric that separates scoring student work and uncovering student difficulties. We have constructed a separable rubric for the Colorado Classical Mechanics/Math Methods Instrument that has been used by untrained graders to score the assessment reliably, and by researchers to unpack common student difficulties. Here we present rubric development, measures of inter-rater reliability, and some uncovered student difficulties.Comment: 4 pages, PERC 2014 Proceeding

Assessing Student Learning in Middle-Division Classical Mechanics/Math Methods

Reliable and validated assessments of introductory physics have been instrumental in driving curricular and pedagogical reforms that lead to improved student learning. As part of an effort to systematically improve our sophomore-level Classical Mechanics and Math Methods course (CM 1) at CU Boulder, we are developing a tool to assess student learning of CM 1 concepts in the upper-division. The Colorado Classical Mechanics/Math Methods Instrument (CCMI) builds on faculty-consensus learning goals and systematic observations of student difficulties. The result is a 9-question open-ended post-test that probes student learning in the first half of a two-semester classical mechanics / math methods sequence. In this paper, we describe the design and development of this instrument, its validation, and measurements made in classes at CU Boulder.Comment: 4 pages, 3 figures, 1 table; submitted to 2013 Proceedings of the Physics Education Research Conferenc

Methods for Analyzing Pathways through a Physics Major

Physics Education Research frequently investigates what students studying physics do on small time scales (e.g. single courses, observations within single courses), or post-education time scales (e.g., what jobs do physics majors get?) but there is little research into how students get from the beginning to the end of a physics degree. Our work attempts to visualize students paths through the physics major, and quantitatively describe the students who take physics courses, receive physics degrees, and change degree paths into and out of the physics program at Michigan State University.Comment: submitted to Physics Education Research Conference Proceedings 201

Blowup formulae in Donaldson-Witten theory and integrable hierarchies

We investigate blowup formulae in Donaldson-Witten theory with gauge group SU(N), using the theory of hyperelliptic Kleinian functions. We find that the blowup function is a hyperelliptic sigma-function and we describe an explicit procedure to expand it in terms of the Casimirs of the gauge group up to arbitrary order. As a corollary, we obtain a new expression for the contact terms and we show that the correlation functions involving the exceptional divisor are governed by the KdV hierarchy. We also show that, for manifolds of simple type, the blowup function becomes a tau-function for a multisoliton solution.Comment: 34 pages, harvmac, typos corrected, final versio

Superconducting Circuits for Quantum Simulation of Dynamical Gauge Fields

We describe a superconducting-circuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a one-dimensional U(1) quantum-link model, where superconducting qubits play the role of matter fields on the lattice sites and the gauge fields are represented by two coupled microwave resonators on each link between neighboring sites. A detailed analysis of a minimal experimental protocol for probing the physics related to string breaking effects shows that despite the presence of decoherence in these systems, distinctive phenomena from condensed-matter and high-energy physics can be visualized with state-of-the-art technology in small superconducting-circuit arrays

Magnetic Susceptibility of the Kagome Antiferromagnet ZnCu3(OH)6Cl2

We analyze the experimental data for the magnetic susceptibility of the material ZnCu3(OH)6Cl2 in terms of the Kagome Lattice Heisenberg model (KLHM), discussing possible role of impurity spins, dilution, exchange anisotropy, and both out-of-plane and in-plane Dzyaloshinsky-Moriya (DM) anisotropies, with explicit theoretical calculations using the Numerical Linked Cluster (NLC) method and exact diagonalization (ED). The high-temperature experimental data are well described by the pure Heisenberg model with J=170 K. We show that the sudden upturn in the susceptibility around T=75 K is due to DM interactions. We also observe that at intermediate temperatures, below T=J, our calculated susceptibility for KLHM fits well with a power law T^{-0.25}.Comment: 4 pages, 5 figures, published versio