564 research outputs found
Explicit Integration of Extremely-Stiff Reaction Networks: Quasi-Steady-State Methods
A preceding paper demonstrated that explicit asymptotic methods generally
work much better for extremely stiff reaction networks than has previously been
shown in the literature. There we showed that for systems well removed from
equilibrium explicit asymptotic methods can rival standard implicit codes in
speed and accuracy for solving extremely stiff differential equations. In this
paper we continue the investigation of systems well removed from equilibrium by
examining quasi-steady-state (QSS) methods as an alternative to asymptotic
methods. We show that for systems well removed from equilibrium, QSS methods
also can compete with, or even exceed, standard implicit methods in speed, even
for extremely stiff networks, and in many cases give somewhat better
integration speed than for asymptotic methods. As for asymptotic methods, we
will find that QSS methods give correct results, but with non-competitive
integration speed as equilibrium is approached. Thus, we shall find that both
asymptotic and QSS methods must be supplemented with partial equilibrium
methods as equilibrium is approached to remain competitive with implicit
methods.Comment: Updated reference
Solution of the Nuclear Shell Model by Symmetry-Dictated Truncation
The dynamical symmetries of the Fermion Dynamical Symmetry Model are used as
a principle of truncation for the spherical shell model. Utilizing the usual
principle of energy-dictated truncation to select a valence space, and
symmetry-dictated truncation to select a collective subspace of that valence
space, we are able to reduce the full shell model space to one of manageable
dimensions with modern supercomputers, even for the heaviest nuclei. The
resulting shell model then consists of diagonalizing an effective Hamiltonian
within the restricted subspace. This theory is not confined to any symmetry
limits, and represents a full solution of the original shell model if the
appropriate effective interaction of the truncated space can be determined. As
a first step in constructing that interaction, we present an empirical
determination of its matrix elements for the collective subspace with no broken
pairs in a representative set of nuclei with . We demonstrate
that this effective interaction can be parameterized in terms of a few
quantities varying slowly with particle number, and is capable of describing a
broad range of low-energy observables for these nuclei. Finally we give a brief
discussion of extending these methods to include a single broken collective
pair.Comment: invited paper for J. Phys. G, 57 pages, Latex, 18 figures a macro are
available under request at [email protected]
SU(3) Richardson-Gaudin models: three level systems
We present the exact solution of the Richardson-Gaudin models associated with
the SU(3) Lie algebra. The derivation is based on a Gaudin algebra valid for
any simple Lie algebra in the rational, trigonometric and hyperbolic cases. For
the rational case additional cubic integrals of motion are obtained, whose
number is added to that of the quadratic ones to match, as required from the
integrability condition, the number of quantum degrees of freedom of the model.
We discuss different SU(3) physical representations and elucidate the meaning
of the parameters entering in the formalism. By considering a bosonic mapping
limit of one of the SU(3) copies, we derive new integrable models for three
level systems interacting with two bosons. These models include a generalized
Tavis-Cummings model for three level atoms interacting with two modes of the
quantized electric field.Comment: Revised version. To appear in Jour. Phys. A: Math. and Theo
The QCD Membrane
In this paper we study spatially quenched, SU(N) Yang-Mills theory in the
large-N limit. The resulting reduced action shows the same formal look as the
Banks-Fischler-Shenker-Susskind M-theory action. The Weyl-Wigner-Moyal symbol
of this matrix model is the Moyal deformation of a p(=2)-brane action. Thus,
the large-N limit of the spatially quenched SU(N) Yang-Mills is seen to
describe a dynamical membrane. By assuming spherical symmetry we compute the
mass spectrum of this object in the WKB approximation.Comment: 14 pages, LaTeX, non figures; accepted for publication in
Class.Quant. Gra
One- and two-proton transfer reactions with vibrational Nuclei
We extend a semiclassical model of transfer reactions to the case in which
one of the collision partners is a vibrational nucleus. The model is applied to
one- and two-proton stripping reactions in the 37Cl + 98Mo system, for which a
rapid transition from normal to anomalous slope in the two proton transfer
reaction at energies around the Coulomb barrier is experimentally observed.
This behavior is satisfactorily reproduced by the present extension of the
model.Comment: LaTeX, 10 pages, 1 figure (PostScript
A Unified Description of Cuprate and Iron Arsenide Superconductors
We propose a unified description of cuprate and iron-based superconductivity.
Consistency with magnetic structure inferred from neutron scattering implies
significant constraints on the symmetry of the pairing gap for the iron-based
superconductors. We find that this unification requires the orbital pairing
formfactors for the iron arsenides to differ fundamentally from those for
cuprates at the microscopic level.Comment: 12 pages, 10 figures, 2 table
The Interplay Between Protoneutron Star Convection and Neutrino Transport in Core Collapse Supernovae
We couple two-dimensional hydrodynamics to realistic one-dimensional
multigroup flux-limited diffusion neutrino transport to investigate
protoneutron star convection in core collapse supernovae, and more
specifically, the interplay between its development and neutrino transport, for
both 15 and 25 solar mass models. In the presence of neutrino transport,
protoneutron star convection velocities are too small relative to bulk inflow
velocities to result in any significant convective transport of entropy and
leptons. A simple analytical model supports our numerical results, indicating
that the inclusion of neutrino transport reduces the entropy-driven
(lepton-driven) convection growth rates and asymptotic velocities by a factor
of 3 (50) at the neutrinosphere and a factor 250 (1000) at a density of 10^{12}
g/cm^{3}, for both our 15 and 25 solar mass models. Moreover, when transport is
included, the initial postbounce entropy gradient is smoothed out by neutrino
diffusion, whereas the initial lepton gradient is maintained by electron
capture and neutrino escape near the neutrinosphere. Despite the maintenance of
the lepton gradient, protoneutron star convection does not develop over the 100
ms duration typical of all our simulations, except in the instance where
``low-test'' initial conditions are used, which are generated by core collapse
and bounce simulations that neglect neutrino-electron scattering and ion-ion
screening corrections to neutrino- nucleus elastic scattering.Comment: 61 pages, 31 figures; accepted for publication in The Astrophysical
Journa
- …