879 research outputs found
Violator Spaces: Structure and Algorithms
Sharir and Welzl introduced an abstract framework for optimization problems,
called LP-type problems or also generalized linear programming problems, which
proved useful in algorithm design. We define a new, and as we believe, simpler
and more natural framework: violator spaces, which constitute a proper
generalization of LP-type problems. We show that Clarkson's randomized
algorithms for low-dimensional linear programming work in the context of
violator spaces. For example, in this way we obtain the fastest known algorithm
for the P-matrix generalized linear complementarity problem with a constant
number of blocks. We also give two new characterizations of LP-type problems:
they are equivalent to acyclic violator spaces, as well as to concrete LP-type
problems (informally, the constraints in a concrete LP-type problem are subsets
of a linearly ordered ground set, and the value of a set of constraints is the
minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006;
author spelling fixe
Extreme alpha-clustering in the 18O nucleus
The structure of the 18O nucleus at excitation energies above the alpha decay
threshold was studied using 14C+alpha resonance elastic scattering. A number of
states with large alpha reduced widths have been observed, indicating that the
alpha-cluster degree of freedom plays an important role in this N not equal Z
nucleus. However, the alpha-cluster structure of this nucleus is very different
from the relatively simple pattern of strong alpha-cluster quasi-rotational
bands in the neighboring 16O and 20Ne nuclei. A 0+ state with an alpha reduced
width exceeding the single particle limit was identified at an excitation
energy of 9.9+/-0.3 MeV. We discuss evidence that states of this kind are
common in light nuclei and give possible explanations of this feature.Comment: 4 pages, 2 figures, 1 table. Resubmission with minor changes for
clarity, including removal of one figur
Octupole strength in the neutron-rich calcium isotopes
Low-lying excited states of the neutron-rich calcium isotopes Ca
have been studied via -ray spectroscopy following inverse-kinematics
proton scattering on a liquid hydrogen target using the GRETINA -ray
tracking array. The energies and strengths of the octupole states in these
isotopes are remarkably constant, indicating that these states are dominated by
proton excitations.Comment: 15 pages, 3 figure
Population of bound excited states in intermediate-energy fragmentation reactions
Fragmentation reactions with intermediate-energy heavy-ion beams exhibit a
wide range of reaction mechanisms, ranging from direct reactions to statistical
processes. We examine this transition by measuring the relative population of
excited states in several sd-shell nuclei produced by fragmentation with the
number of removed nucleons ranging from two to sixteen. The two-nucleon removal
is consistent with a non-dissipative process whereas the removal of more than
five nucleons appears to be mainly statistical.Comment: 5 pages, 6 figure
Fermi's golden rule and exponential decay as a RG fixed point
We discuss the decay of unstable states into a quasicontinuum using models of
the effective Hamiltonian type. The goal is to show that exponential decay and
the golden rule are exact in a suitable scaling limit, and that there is an
associated renormalization group (RG) with these properties as a fixed point.
The method is inspired by a limit theorem for infinitely divisible
distributions in probability theory, where there is a RG with a Cauchy
distribution, i.e. a Lorentz line shape, as a fixed point. Our method of
solving for the spectrum is well known; it does not involve a perturbation
expansion in the interaction, and needs no assumption of a weak interaction. We
use random matrices for the interaction, and show that the ensemble
fluctuations vanish in the scaling limit. Thus the limit is the same for every
model in the ensemble with probability one.Comment: 20 pages, 1 figur
Spectroscopy of Ti and the systematic behavior of low energy octupole states in Ca and Ti isotopes
Excited states of the nucleus Ti have been studied, via both
inverse-kinematics proton scattering and one-neutron knockout from Ti by
a liquid hydrogen target, using the GRETINA -ray tracking array.
Inelastic proton-scattering cross sections and deformation lengths have been
determined. A low-lying octupole state has been tentatively identified in
Ti for the first time. A comparison of results on low-energy
octupole states in the neutron-rich Ca and Ti isotopes with the results of
Random Phase Approximation calculations demonstrates that the observed
systematic behavior of these states is unexpected.Comment: 7 pages, 8 figure
Spectroscopy of Ti and the systematic behavior of low energy octupole states in Ca and Ti isotopes
Excited states of the nucleus Ti have been studied, via both
inverse-kinematics proton scattering and one-neutron knockout from Ti by
a liquid hydrogen target, using the GRETINA -ray tracking array.
Inelastic proton-scattering cross sections and deformation lengths have been
determined. A low-lying octupole state has been tentatively identified in
Ti for the first time. A comparison of results on low-energy
octupole states in the neutron-rich Ca and Ti isotopes with the results of
Random Phase Approximation calculations demonstrates that the observed
systematic behavior of these states is unexpected.Comment: 7 pages, 8 figure
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