Modeling Thermal Fluctuations: Phase Mixing and Percolation

We consider the nonequilibrium dynamics of a a real scalar field in a degenerate double-well potential. The system is prepared in the lowest free energy state in one of the wells and the dynamics is driven by the coupling of the field to a thermal bath. Using a simple analytical model, based on the subcritical bubbles method, we compute the fraction of the total volume which fluctuates to the opposite phase as a function of the parameters of the potential. Furthermore, we show how complete phase mixing, {\em i.e.} symmetry restoration, is related to percolation, which is dynamically driven by domain instability. Our method describes quantitatively recent results obtained by numerical simulations, and is applicable to systems in the Ising universality class.Comment: Latex, 7 pages, 2 postscript figures, submitted to PRL. Also available at http://fnas08.fnal.gov

Calculation of the emergent spectrum and observation of primordial black holes

We calculate the emergent spectrum of microscopic black holes, which emit copious amounts of thermal ``Hawking'' radiation, taking into account the proposition that (contrary to previous models) emitted quarks and gluons do not directly fragment into hadrons, but rather interact and form a photosphere and decrease in energy before fragmenting. The resulting spectrum emits copious amount of photons at energies around 100MeV. We find that the limit on the average universal density of black holes is not significantly affected by the photosphere. However we also find that gamma ray satellites such as EGRET and GLAST are well suited to look for nearby black holes out to a distance on the order of 0.3 parsecs, and conclude that if black holes are clustered locally as much as luminous matter, they may be directly detectable.Comment: 10 pages, Latex, submitted to PR

Searching for stellar mass black holes in the solar neighborhood

We propose a strategy for searching for isolated stellar mass black holes in the solar neighborhood with the Sloan Digital Sky Survey. Due to spherical accretion of the inter-stellar medium and the ambient magnetic field, an isolated black hole is expected to emit a blended, thermal synchrotron spectrum with a roughly flat peak from the optical down to the far infra-red. We find that the Sloan Survey will be able to detect isolated black holes, in the considered mass range of 1--100$M_{\odot}$, out to a few hundred parsecs, depending on the local conditions of the ISM. We also find that the black holes are photmetrically distinguishable from field stars and they have a photometry similar to QSOs. They can be further singled out from QSO searches because they have a featureless spectrum with no emission lines. The Sloan Survey will likely find hundreds of objects that meet these criteria, and to further reduce the number of candidates, we suggest other selection criteria such as infra-red searches and proper motion measurements. Estimates indicate that dozens of black holes may exist out to a few hundred parsecs. If no black hole candidates are found in this survey, important limits can be placed on the local density of black holes and the halo fraction in black holes, especially for masses greater than about $20 M_{\odot}$.Comment: Latex, 7 pages, 3 postscript figures, submitted to ApJ Letters. Also available at http://fnas08.fnal.gov

Evolution of grades and social comparison concern within an introductory physics course

This study investigates the evolution and associations between exam grades and social comparison concern (SCC) among students in an introductory calculus-based physics course. We begin with a descriptive characterization of midterm and final exam scores as well as pre-post SCC scores, including the concurrent evolution of these scores during the course. We hypothesize a feedback loop in which changes in SCC scores are mediated by exam grades, and changes in exam scores are mediated by SCC scores. We employ a structural equation model to determine whether the data are consistent with these hypotheses. Results indicate that there were significant within-student changes in the relative grade standing from exam to exam and that changes in SCC scores depended on both the pre-SCC scores and scores on the first midterm exam. Further, we find evidence that exam scores partially mediate the association between pre- and post-SCC scores, and in turn, post-SCC scores partially mediate associations between midterm and final exam scores, though the mediation effects are somewhat small, comprising 5%–10% of the total effects between exam scores and SCC. We also find that while SCC scores are somewhat correlated with exam scores, they are only very weakly correlated with nonexam grade components, consistent with the idea that exam scores (rather than nonexam scores) are driving changes in SCC and vice versa. Overall, the results provide empirical, correlational evidence to motivate further experimental investigation into a hypothesized dynamic and iterative feedback loop in which student concern about ability or performance compared to others (SCC) can either negatively or positively interfere with student performance on exams

Mediating relationship of differential products in understanding integration in introductory physics

In the context of introductory physics, we study student conceptual understanding of differentials, differential products, and integrals and possible pathways to understanding these quantities. We developed a multiple choice conceptual assessment employing a variety of physical contexts probing physical understanding of these three quantities and administered the instrument to over 1000 students in first and second semester introductory physics courses. Using a regression-based mediation analysis with conceptual understanding of integration as the dependent variable, we found evidence consistent with a simple mediation model: the relationship between differentials scores and integral scores may be mediated by the understanding of differential products. The indirect effect (a quantifiable metric of mediation) was estimated as ab=0.29, 95% CI [0.25, 0.33] for N=1102 Physics 1 students, and ab=0.27, 95% CI [0.14, 0.48] for N=65 Physics 2 students. We also find evidence that the physical context of the questions can be an important factor. These results imply that for introductory physics courses, instructional emphasis first on differentials then on differential products in a variety of contexts may in turn promote better integral understanding

Evolution of response time and accuracy on online mastery practice assignments for introductory physics students

We have investigated the temporal patterns of algebra (N=606) and calculus (N=507) introductory physics students practicing multiple basic physics topics several times throughout the semester using an online mastery homework application called science, technology, engineering, and mathematics (STEM) fluency aimed at improving basic physics skills. For all skill practice categories, we observed an increase in measures of student accuracy, such as a decrease in the number of questions attempted to reach mastery, and a decrease in response time per question, resulting in an overall decrease in the total time spent on the assignments. The findings in this study show that there are several factors that impact a student’s performance and evolution on the mastery assignments throughout the semester. For example, using linear mixed modeling, we report that students with lower math preparation for the physics class start with lower accuracy and slower response times on the mastery assignments than students with higher math preparation. However, by the end of the semester, the less prepared students reach similar performance levels to their more prepared classmates on the mastery assignments. This suggests that STEM fluency is a useful tool for instructors to implement to refresh student’s basic math skills. Additionally, gender and procrastination habits impact the effectiveness and progression of the student’s response time and accuracy on the STEM fluency assignments throughout the semester. We find that women initially answer more questions in the same amount of time as men before reaching mastery. As the semester progresses and students practice the categories more, this performance gap diminishes between males and females. In addition, we find that students who procrastinate (those who wait until the final few hours to complete the assignments) are spending more time on the assignments despite answering a similar number of questions as compared to students who do not procrastinate. We also find that student mindset (growth vs fixed mindset) was not related to a student’s progress on the online mastery assignments. Finally, we find that STEM fluency practice improves performance beyond the effects of other components of instruction, such as lectures, group-work recitations, and homework assignments

Factors affecting learning of vector math from computer-based practice: Feedback complexity and prior knowledge

In experiments including over 450 university-level students, we studied the effectiveness and time efficiency of several levels of feedback complexity in simple, computer-based training utilizing static question sequences. The learning domain was simple vector math, an essential skill in introductory physics. In a unique full factorial design, we studied the relative effects of “knowledge of correct response” feedback and “elaborated feedback” (i.e., a general explanation) both separately and together. A number of other factors were analyzed, including training time, physics course grade, prior knowledge of vector math, and student beliefs about both their proficiency in and the importance of vector math. We hypothesize a simple model predicting how the effectiveness of feedback depends on prior knowledge, and the results confirm this knowledge-by-treatment interaction. Most notably, elaborated feedback is the most effective feedback, especially for students with low prior knowledge and low course grade. In contrast, knowledge of correct response feedback was less effective for low-performing students, and including both kinds of feedback did not significantly improve performance compared to elaborated feedback alone. Further, while elaborated feedback resulted in higher scores, the learning rate was at best only marginally higher because the training time was slightly longer. Training time data revealed that students spent significantly more time on the elaborated feedback after answering a training question incorrectly. Finally, we found that training improved student self-reported proficiency and that belief in the importance of the learned domain improved the effectiveness of training. Overall, we found that computer based training with static question sequences and immediate elaborated feedback in the form of simple and general explanations can be an effective way to improve student performance on a physics essential skill, especially for less prepared and low-performing students