Variable stars in the globular cluster NGC 3201. I. Multimode SX Phe-type variables

We report on the discovery of eleven multimode SX Phoenicis--type blue stragglers in the field of the southern globular cluster NGC 3201. In these variables both radial and non-radial modes are excited. For three variables the derived period ratio is close to that observed in SX Phoenicis itself, suggesting that these stars are pulsating in the fundamental and the first-overtone radial modes. Using the McNamara (1997) period-luminosity relation we have estimated the apparent distance modulus to NGC 3201 to be 14.08$\pm0.06\pm0.1$mag.Comment: 10 pages, requires mn2e.cls,contact the first author at [email protected] for high-resolution figure

Student understanding of the Boltzmann factor

We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable, nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations on student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions