737 research outputs found
A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories
We present a general method for the analysis of the stability of static,
spherically symmetric solutions to spherically symmetric perturbations in an
arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves
fixing the gauge and solving the linearized gravitational field equations to
eliminate the metric perturbation variable in terms of the matter variables. In
a wide class of cases--which include f(R) gravity, the Einstein-aether theory
of Jacobson and Mattingly, and Bekenstein's TeVeS theory--the remaining
perturbation equations for the matter fields are second order in time. We show
how the symplectic current arising from the original Lagrangian gives rise to a
symmetric bilinear form on the variables of the reduced theory. If this
bilinear form is positive definite, it provides an inner product that puts the
equations of motion of the reduced theory into a self-adjoint form. A
variational principle can then be written down immediately, from which
stability can be tested readily. We illustrate our method in the case of
Einstein's equation with perfect fluid matter, thereby re-deriving, in a
systematic manner, Chandrasekhar's variational principle for radial
oscillations of spherically symmetric stars. In a subsequent paper, we will
apply our analysis to f(R) gravity, the Einstein-aether theory, and
Bekenstein's TeVeS theory.Comment: 13 pages; submitted to Phys. Rev. D. v2: changed formatting, added
conclusion, corrected sign convention
Assessing the Quality of Regulatory Impact Analyses
This study provides the most comprehensive evaluation of the quality of recent economic analyses that agencies conduct before finalizing major regulations. We construct a new dataset that includes analyses of forty-eight major health, safety, and environmental regulations from mid-1996 to mid-1999. This dataset provides detailed information on a variety of issues, including an agency's treatment of benefits, costs, net benefits, discounting, and uncertainty. We use this dataset to assess the quality of recent economic analyses and to determine the extent to which they are consistent with President Clinton's Executive Order 12866 and the benefit-cost guidelines issued by the Office of Management and Budget (OMB). We find that economic analyses prepared by regulatory agencies typically do not provide enough information to make decisions that will maximize the efficiency or effectiveness of a rule. Agencies quantified net benefits for only 29 percent of the rules. Agencies failed to discuss alternatives in 27 percent of the rules and quantified costs and benefits of alternatives in only 31 percent of the rules. Our findings strongly suggest that agencies generally failed to comply with the executive order and adhere to the OMB guidelines. We offer specific suggestions for improving the quality of analysis and the transparency of the regulatory process, including writing clear executive summaries, making analyses available on the Internet, providing more careful consideration of alternatives to a regulation, and estimating net benefits of a regulation when data on costs and benefits are provided.
Assessing Regulatory Impact Analyses: The Failure of Agencies to Comply With Executive Order 12,866
None.Environment, Health and Safety, Regulatory Reform
Coyote, Canis latrans, Predation on a Bison, Bison bison, Calf in Yellowstone National Park
We observed a single adult male Coyote (Canis latrans) kill a Bison (Bison bison) calf in Yellowstone National Park. The predation is, to our knowledge, the only direct and complete observation of a lone Coyote capturing and killing a Bison calf. The bison calf had unsuccessfully attempted to ford a river with a group and subsequently become stranded alone in the territory of a six-year-old alpha male Coyote
Quantum phases of atomic boson-fermion mixtures in optical lattices
The zero-temperature phase diagram of a binary mixture of bosonic and
fermionic atoms in an one-dimensional optical lattice is studied in the
framework of the Bose-Fermi-Hubbard model. By exact numerical solution of the
associated eigenvalue problems, ground state observables and the response to an
external phase twist are evaluated. The stiffnesses under phase variations
provide measures for the boson superfluid fraction and the fermionic Drude
weight. Several distinct quantum phases are identified as function of the
strength of the repulsive boson-boson and the boson-fermion interaction.
Besides the bosonic Mott-insulator phase, two other insulating phases are
found, where both the bosonic superfluid fraction and the fermionic Drude
weight vanish simultaneously. One of these double-insulator phases exhibits a
crystalline diagonal long-range order, while the other is characterized by
spatial separation of the two species.Comment: 4 pages, 3 figures, using REVTEX
Ultracold Bosonic Atoms in Disordered Optical Superlattices
The influence of disorder on ultracold atomic Bose gases in quasiperiodic
optical lattices is discussed in the framework of the one-dimensional
Bose-Hubbard model. It is shown that simple periodic modulations of the well
depths generate a rich phase diagram consisting of superfluid, Mott insulator,
Bose-glass and Anderson localized phases. The detailed evolution of mean
occupation numbers and number fluctuations as function of modulation amplitude
and interaction strength is discussed. Finally, the signatures of the different
phases, especially of the Bose-glass phase, in matter-wave interference
experiments are investigated.Comment: 4 pages, 4 figures, using REVTEX
A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
In general relativity, the notion of mass and other conserved quantities at
spatial infinity can be defined in a natural way via the Hamiltonian framework:
Each conserved quantity is associated with an asymptotic symmetry and the value
of the conserved quantity is defined to be the value of the Hamiltonian which
generates the canonical transformation on phase space corresponding to this
symmetry. However, such an approach cannot be employed to define `conserved
quantities' in a situation where symplectic current can be radiated away (such
as occurs at null infinity in general relativity) because there does not, in
general, exist a Hamiltonian which generates the given asymptotic symmetry.
(This fact is closely related to the fact that the desired `conserved
quantities' are not, in general, conserved!) In this paper we give a
prescription for defining `conserved quantities' by proposing a modification of
the equation that must be satisfied by a Hamiltonian. Our prescription is a
very general one, and is applicable to a very general class of asymptotic
conditions in arbitrary diffeomorphism covariant theories of gravity derivable
from a Lagrangian, although we have not investigated existence and uniqueness
issues in the most general contexts. In the case of general relativity with the
standard asymptotic conditions at null infinity, our prescription agrees with
the one proposed by Dray and Streubel from entirely different considerations.Comment: 39 pages, no figure
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