2,107 research outputs found
On Equivalence of Critical Collapse of Non-Abelian Fields
We continue our study of the gravitational collapse of spherically symmetric
skyrmions. For certain families of initial data, we find the discretely
self-similar Type II critical transition characterized by the mass scaling
exponent and the echoing period . We
argue that the coincidence of these critical exponents with those found
previously in the Einstein-Yang-Mills model is not accidental but, in fact, the
two models belong to the same universality class.Comment: 7 pages, REVTex, 2 figures included, accepted for publication in
Physical Review
Universality and properties of neutron star type I critical collapses
We study the neutron star axisymmetric critical solution previously found in
the numerical studies of neutron star mergers. Using neutron star-like initial
data and performing similar merger simulations, we demonstrate that the
solution is indeed a semi-attractor on the threshold plane separating the basin
of a neutron star and the basin of a black hole in the solution space of the
Einstein equations. In order to explore the extent of the attraction basin of
the neutron star semiattractor, we construct initial data phase spaces for
these neutron star-like initial data. From these phase spaces, we also observe
several interesting dynamical scenarios where the merged object is supported
from prompt collapse. The properties of the critical index of the solution, in
particular, its dependence on conserved quantities, are then studied. From the
study, it is found that a family of neutron star semi-attractors exist that can
be classified by both their rest masses and ADM masses.Comment: 13 pages, 12 figures, 1 new reference adde
Scale invariance and critical gravitational collapse
We examine ways to write the Choptuik critical solution as the evolution of
scale invariant variables. It is shown that a system of scale invariant
variables proposed by one of the authors does not evolve periodically in the
Choptuik critical solution. We find a different system, based on maximal
slicing. This system does evolve periodically, and may generalize to the case
of axisymmetry or of no symmetry at all.Comment: 7 pages, 3 figures, Revtex, discussion modified to clarify
presentatio
Late-time evolution of nonlinear gravitational collapse
We study numerically the fully nonlinear gravitational collapse of a
self-gravitating, minimally-coupled, massless scalar field in spherical
symmetry. Our numerical code is based on double-null coordinates and on free
evolution of the metric functions: The evolution equations are integrated
numerically, whereas the constraint equations are only monitored. The numerical
code is stable (unlike recent claims) and second-order accurate. We use this
code to study the late-time asymptotic behavior at fixed (outside the black
hole), along the event horizon, and along future null infinity. In all three
asymptotic regions we find that, after the decay of the quasi-normal modes, the
perturbations are dominated by inverse power-law tails. The corresponding power
indices agree with the integer values predicted by linearized theory. We also
study the case of a charged black hole nonlinearly perturbed by a (neutral)
self-gravitating scalar field, and find the same type of behavior---i.e.,
quasi-normal modes followed by inverse power-law tails, with the same indices
as in the uncharged case.Comment: 14 pages, standard LaTeX, 18 Encapsulated PostScript figures. A new
convergence test and a determination of QN ringing were added, in addition to
correction of typos and update of reference
The naked singularity in the global structure of critical collapse spacetimes
We examine the global structure of scalar field critical collapse spacetimes
using a characteristic double-null code. It can integrate past the horizon
without any coordinate problems, due to the careful choice of constraint
equations used in the evolution. The limiting sequence of sub- and
supercritical spacetimes presents an apparent paradox in the expected Penrose
diagrams, which we address in this paper. We argue that the limiting spacetime
converges pointwise to a unique limit for all r>0, but not uniformly. The r=0
line is different in the two limits. We interpret that the two different
Penrose diagrams differ by a discontinuous gauge transformation. We conclude
that the limiting spacetime possesses a singular event, with a future removable
naked singularity.Comment: RevTeX 4; 6 pages, 7 figure
Microgrids and Resilience to Climate-Driven Impacts on Public Health
âResilienceâ has burst into the lexicons of several policy areas in recent years, owing in no small part to climate changeâs amplification of extreme events that severely disrupt the operation of natural, social, and engineered systems. Fostering resilience means anticipating severe disruptions and planning, investing, and designing so that such disruptions, which are certain to occur, are made shallower in depth and shorter in duration. Thus a resilient system or community can continue functioning despite disruptive events, return more swiftly to routine function following disruption, and incorporate new information so as to improve operations in extremis and speed future restorations.
As different policy communities apply the concept of resilience to their respective missions, they emphasize different objectives. This article examines how the definitions adopted by the public health and electricity communities can, but do not necessarily, converge in responses to electricity outages so severe that they affect the operation of critical infrastructure, such as wastewater treatment and drinking water facilities, hospitals, and cooling centers. Currently, such outages cause a form of handoff from utilities to their customers: grid power fails and a small constellation of backup generators maintained by atomized campuses, facilities, or individual structures switch on, or fail to switch on, or were never purchased and so leave the location dark and its equipment inoperative. This handoff is operational, but it reflects legal obligationsâand their limits.
Enter the microgrid, a specially designed segment of the electricity distribution gridâs mesh that can either operate seamlessly as part of the wider grid, or as an independent âislandâ that serves some or all of the electricity users within its boundary even when the wider grid fails. Microgrids can, but do not necessarily, mitigate the adverse public health implications of the handoff that accompanies widespread and severe grid failure. To encourage the convergence of public health and electricity policy priorities in decisions about microgrid siting, design, and operation, this article makes several recommendations. Some of these should ideally be taken up at the federal level, but the bulk of the work they recommend should take place at the state-level, and would necessarily be implemented at the state and local levels
To Negotiate a Carbon Tax: A Rough Map of Policy Interactions, Tradeoffs, and Risks
Sooner or later, the federal government will assign a price to carbon dioxide emissions via legislation. The contents of that legislation will reflect negotiated agreementâbuilt on various political tradeoffsâover a host of policy issues, ranging from taxes to energy efficiency standards. These tradeoffs would implicate not only the scope and price assigned by the carbon pricing policy, but also the policies with which it would interact. This paper anticipates that price will take the form of a carbon tax and describes interactions between that tax and various existing and proposed policies relating to climate change, energy, and environmental protection. Specifically, it proposes a typology for those interactions and applies it to characterize particular policies. It also notes how trading off particular policies for a more robust carbon tax could undermine the climate change mitigation goal of such a tax
Scaling of curvature in sub-critical gravitational collapse
We perform numerical simulations of the gravitational collapse of a
spherically symmetric scalar field. For those data that just barely do not form
black holes we find the maximum curvature at the position of the central
observer. We find a scaling relation between this maximum curvature and
distance from the critical solution. The scaling relation is analogous to that
found by Choptuik for black hole mass for those data that do collapse to form
black holes. We also find a periodic wiggle in the scaling exponent.Comment: Revtex, 2 figures, Discussion modified, to appear in Phys. Rev.
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How Much Does the Existing Regulatory Patchwork Reduce U.S. Greenhouse Gas Emissions?
This paper offers an answer to the question, âWhat levels of greenhouse gas (âGHGâ) emissions reduction do the constituent programs in the U.S.âs existing regulatory patchwork achieve?â Its answer represents an attempt to measure the same effect from eight regulatory interventions: EPAâs Prevention of Significant Deterioration program, as it is expected to operate following the Supreme Courtâs UARG v. EPA decision in 2014; EPAâs Clean Power Plan; EPAâs renewable fuel standard; the federal Corporate Average Fuel Economy standards for light, medium, and heavy duty vehicles; the renewable electricity generation Production Tax Credit and Investment Tax Credit; the Regional Greenhouse Gas Initiative, which encompasses 9 states in the mid-Atlantic and Northeast; Californiaâs Global Warming Solutions Act of 2006, Assembly Bill 32; and state renewable portfolio standards. Notably, though it seeks to measure the same effect of diverse policies, this paper does not purport to measure the aggregated net effects of those policies on GHG emissions. Most important among its conclusions are the following. First, federal CAFE standards, the Clean Power Plan, and state renewable portfolio standards will be crucial for achieving emissions reduction goals. Second, the reductions available from the renewable fuel standard are uncertain and highly contentious. And thirdâan important subtextâthe effectiveness (and costeffectiveness) of this patchwork of programs is unwieldy even to measure, much less to ensure
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