21,547 research outputs found
A Prehistory of n-Categorical Physics
This paper traces the growing role of categories and n-categories in physics,
starting with groups and their role in relativity, and leading up to more
sophisticated concepts which manifest themselves in Feynman diagrams, spin
networks, string theory, loop quantum gravity, and topological quantum field
theory. Our chronology ends around 2000, with just a taste of later
developments such as open-closed topological string theory, the
categorification of quantum groups, Khovanov homology, and Lurie's work on the
classification of topological quantum field theories.Comment: 129 pages, 8 eps figure
Helioseismology challenges models of solar convection
Convection is the mechanism by which energy is transported through the
outermost 30% of the Sun. Solar turbulent convection is notoriously difficult
to model across the entire convection zone where the density spans many orders
of magnitude. In this issue of PNAS, Hanasoge et al. (2012) employ recent
helioseismic observations to derive stringent empirical constraints on the
amplitude of large-scale convective velocities in the solar interior. They
report an upper limit that is far smaller than predicted by a popular
hydrodynamic numerical simulation.Comment: Printed in the Proceedings of the National Academy of Sciences (2
pages, 1 figure). Available at
http://www.pnas.org/cgi/doi/10.1073/pnas.120887510
A Two-moment Radiation Hydrodynamics Module in Athena Using a Time-explicit Godunov Method
We describe a module for the Athena code that solves the gray equations of
radiation hydrodynamics (RHD), based on the first two moments of the radiative
transfer equation. We use a combination of explicit Godunov methods to advance
the gas and radiation variables including the non-stiff source terms, and a
local implicit method to integrate the stiff source terms. We adopt the M1
closure relation and include all leading source terms. We employ the reduced
speed of light approximation (RSLA) with subcycling of the radiation variables
in order to reduce computational costs. Our code is dimensionally unsplit in
one, two, and three space dimensions and is parallelized using MPI. The
streaming and diffusion limits are well-described by the M1 closure model, and
our implementation shows excellent behavior for a problem with a concentrated
radiation source containing both regimes simultaneously. Our operator-split
method is ideally suited for problems with a slowly varying radiation field and
dynamical gas flows, in which the effect of the RSLA is minimal. We present an
analysis of the dispersion relation of RHD linear waves highlighting the
conditions of applicability for the RSLA. To demonstrate the accuracy of our
method, we utilize a suite of radiation and RHD tests covering a broad range of
regimes, including RHD waves, shocks, and equilibria, which show second-order
convergence in most cases. As an application, we investigate radiation-driven
ejection of a dusty, optically thick shell in the interstellar medium (ISM).
Finally, we compare the timing of our method with other well-known iterative
schemes for the RHD equations. Our code implementation, Hyperion, is suitable
for a wide variety of astrophysical applications and will be made freely
available on the Web.Comment: 30 pages, 29 figures, accepted for publication in ApJ
A comparison of integrated testlet and constructed-response question formats
Constructed-response (CR) questions are a mainstay of introductory physics
textbooks and exams. However, because of time, cost, and scoring reliability
constraints associated with this format, CR questions are being increasingly
replaced by multiple-choice (MC) questions in formal exams. The integrated
testlet (IT) is a recently-developed question structure designed to provide a
proxy of the pedagogical advantages of CR questions while procedurally
functioning as set of MC questions. ITs utilize an answer-until-correct
response format that provides immediate confirmatory or corrective feedback,
and they thus allow not only for the granting of partial credit in cases of
initially incorrect reasoning, but furthermore the ability to build cumulative
question structures. Here, we report on a study that directly compares the
functionality of ITs and CR questions in introductory physics exams. To do
this, CR questions were converted to concept-equivalent ITs, and both sets of
questions were deployed in midterm and final exams. We find that both question
types provide adequate discrimination between stronger and weaker students,
with CR questions discriminating slightly better than the ITs. Meanwhile, an
analysis of inter-rater scoring of the CR questions raises serious concerns
about the reliability of the granting of partial credit when this traditional
assessment technique is used in a realistic (but non optimized) setting.
Furthermore, we show evidence that partial credit is granted in a valid manner
in the ITs. Thus, together with consideration of the vastly reduced costs of
administering IT-based examinations compared to CR-based examinations, our
findings indicate that ITs are viable replacements for CR questions in formal
examinations where it is desirable to both assess concept integration and to
reward partial knowledge, while efficiently scoring examinations.Comment: 14 pages, 3 figures, with appendix. Accepted for publication in
PRST-PER (August 2014
Numerical Simulations of Turbulent Molecular Clouds Regulated by Reprocessed Radiation Feedback from Nascent Super Star Clusters
Radiation feedback from young star clusters embedded in giant molecular
clouds (GMCs) is believed to be important to the control of star formation. For
the most massive and dense clouds, including those in which super star clusters
(SSCs) are born, pressure from reprocessed radiation exerted on dust grains may
disperse a significant portion of the cloud mass back into the interstellar
medium (ISM). Using our radiaton hydrodynamics (RHD) code, Hyperion, we conduct
a series of numerical simulations to test this idea. Our models follow the
evolution of self-gravitating, strongly turbulent clouds in which collapsing
regions are replaced by radiating sink particles representing stellar clusters.
We evaluate the dependence of the star formation efficiency (SFE) on the size
and mass of the cloud and , the opacity of the gas to infrared (IR)
radiation. We find that the single most important parameter determining the
evolutionary outcome is , with needed to disrupt clouds. For , the resulting SFE=50-70% is similar to empirical estimates for some
SSC-forming clouds. The opacities required for GMC disruption likely apply only
in dust-enriched environments. We find that the subgrid model approach of
boosting the direct radiation force by a "trapping factor" equal to a
cloud's mean IR optical depth can overestimate the true radiation force by
factors of . We conclude that feedback from reprocessed IR radiation
alone is unlikely to significantly reduce star formation within GMCs unless
their dust abundances or cluster light-to-mass ratios are enhanced.Comment: 19 pages, 18 figures, accepted for publication in Ap
Scale-up of electrospray atomization using linear arrays of Taylor cones
Linear arrays of Taylor cones were established on capillary electrode tubes opposite a slotted flat plate counterelectrode to investigate the feasibility of increasing the liquid throughput rate in electrospray atomizers. It was found that individual Taylor cones could be established on each capillary over a wide range of the capillary radius to spacing ratio R/S. The onset potential Vs required to establish the cones varied directly with R/S, but the liquid flow rate per cone and current per cone were nearly independent of R/S for a given overpotential ratio P=V/Vs. Only six working capillaries were used, but the results per cone are applicable to larger arrays of cones since end effects were minimized
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