41 research outputs found
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, 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 .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%Â 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
Observed hierarchy of student proficiency with period, frequency, and angular frequency
In the context of a generic harmonic oscillator, we investigated students’ accuracy in determining the period, frequency, and angular frequency from mathematical and graphical representations. In a series of studies including interviews, free response tests, and multiple choice tests developed in an iterative process, we assessed students in both algebra-based and calculus-based, traditionally instructed university-level introductory physics courses. Using the results, we categorized nine skills necessary for proficiency in determining period, frequency, and angular frequency. Overall results reveal that, postinstruction, proficiency is quite low: only about 20%–40% of students mastered most of the nine skills. Next, we used a semiquantitative, intuitive method to investigate the hierarchical structure of the nine skills. We also employed the more formal item tree analysis method to verify this structure and found that the skills form a multilevel, nonlinear hierarchy, with mastery of some skills being prerequisite for mastery in other skills. Finally, we implemented a targeted, 30-min group-work activity to improve proficiency in these skills and found a 1 standard deviation gain in accuracy. Overall, the results suggest that many students currently lack these essential skills, targeted practice may lead to required mastery, and that the observed hierarchical structure in the skills suggests that instruction should especially attend to the skills lower in the hierarchy