Upper-division Student Understanding of Coulomb's Law: Difficulties with Continuous Charge Distributions

Utilizing the integral expression of Coulomb's Law to determine the electric potential from a continuous charge distribution is a canonical exercise in Electricity and Magnetism (E&M). In this study, we use both think-aloud interviews and responses to traditional exam questions to investigate student difficulties with this topic at the upper-division level. Leveraging a theoretical framework for the use of mathematics in physics, we discuss how students activate, construct, execute and reflect on the integral form of Coulomb's Law when solving problems with continuous charge distributions. We present evidence that junior-level E&M students have difficulty mapping physical systems onto the mathematical expression for the Coulomb potential. Common challenges include difficulty expressing the difference vector in appropriate coordinates as well as determining expressions for the differential charge element and limits of integration for a specific charge distribution. We discuss possible implications of these findings for future research directions and instructional strategies.Comment: 5 pages, 1 figure, 2 tables, accepted to 2012 PERC Proceeding

ACER: A Framework on the Use of Mathematics in Upper-division Physics

At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics, electromagnetism, and quantum mechanics. Unsurprisingly, a number of difficulties are related to students' use of mathematical tools (e.g., approximation methods). Previous work has documented a number of challenges that students must overcome to use mathematical tools fluently in introductory physics (e.g., mapping meaning onto mathematical symbols). We have developed a theoretical framework to facilitate connecting students' difficulties to challenges with specific mathematical and physical concepts. In this paper, we motivate the need for this framework and demonstrate its utility for both researchers and course instructors by applying it to frame results from interview data on students' use of Taylor approximations.Comment: 10 pages, 1 figures, 2 tables, accepted to the 2012 PERC Proceeding

Assessing Learning Outcomes in Middle-Division Classical Mechanics: The Colorado Classical Mechanics/Math Methods Instrument

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 have developed 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 and elsewhere.Comment: 11 pages, 6 figures, 1 tabl

Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called "Particle Linear Theory" (PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects -- in the linear regime -- of N-body simulations for which initial conditions have been set-up using these different lattices.Comment: 9 pages, 4 figures and 4 tables. Minor corrections to match published versio

Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.Comment: Published versio

An eGovernment Platform for Improving Communication among Municipalities and Citizens in the North of Chile

Government and its further development has been increasingly associated with the use of IT and communication. This interconnection is also happening in developing countries such as Chile. This study is designed to assess the e-government infrastructure and the use of IT and communication among some municipalities in Chile in order to implement a platform that allows government to government (G2G), government to employees and government to citizens (G2C) communication. The proposed platform will allow these municipalities to share information about citizens and corporations in the region. This study is conducted in second region of Chile and considered eight municipal governments. The findings suggest that while all the municipalities are highly interested in e-government initiatives, their infrastructure are different and in a very early stage of development. Thus, the study suggested e-government platform highly flexible to incorporate the differences in infrastructure among the municipalities, as secure as possible to allows government interactions, and implemented using an Application Service Provider (ASP) solution. As a result a distributed system using a Java system (J2EE) was the technology chosen e implemented for the ARM2 e-government platform

Energy and Cost Analysis of Cellular Networks Under Co-Channel Interference

In this paper we carry out an energy efficiency and economic cost analysis of different cellular network designs. Our system model considers the co-channel interference, different amounts of available bandwidths and also the reuse of frequencies. The energy efficiency analysis employs a realistic power consumption model, while the economic analysis focus on infrastructure, spectrum licenses, and energy costs. Our results show that from an economic point of view the bandwidth cost and the number of employed base stations can be the most relevant factors to be balanced, while from an energy efficiency analysis it is more interesting to employ larger bandwidths and to balance the reuse of frequencies and the number of base stations. Moreover, although the system design under these two different points of view can be rather different, we also look into scenarios when the most energy efficient system design may also lead to the best economic option

Radio Detection of SN 1986E in NGC 4302

Radio observations of SN 1986E have shown a clear detection of emission at 6 cm wavelength about 8 months after optical discovery. Combined with a number of new upper limits and a study of the possible models, it appears that SN 1986E was probably a fairly normal Type IIL supernova, somewhat similar to SN 1980K, with radio emission at roughly expected levels. This detection continues the correlation between radio detection and late time optical emission.Comment: 14 pages, LaTeX (AASTeX), 2 PostScript figures, to appear in ApJ (Letters