41,940 research outputs found
Compactly Supported Shearlets are Optimally Sparse
Cartoon-like images, i.e., C^2 functions which are smooth apart from a C^2
discontinuity curve, have by now become a standard model for measuring sparse
(non-linear) approximation properties of directional representation systems. It
was already shown that curvelets, contourlets, as well as shearlets do exhibit
(almost) optimally sparse approximation within this model. However, all those
results are only applicable to band-limited generators, whereas, in particular,
spatially compactly supported generators are of uttermost importance for
applications.
In this paper, we now present the first complete proof of (almost) optimally
sparse approximations of cartoon-like images by using a particular class of
directional representation systems, which indeed consists of compactly
supported elements. This class will be chosen as a subset of shearlet frames --
not necessarily required to be tight -- with shearlet generators having compact
support and satisfying some weak moment conditions
Dense matter equation of state and neutron star properties from nuclear theory and experiment
The equation of state of dense matter determines the structure of neutron
stars, their typical radii, and maximum masses. Recent improvements in
theoretical modeling of nuclear forces from the low-energy effective field
theory of QCD has led to tighter constraints on the equation of state of
neutron-rich matter at and somewhat above the densities of atomic nuclei, while
the equation of state and composition of matter at high densities remains
largely uncertain and open to a multitude of theoretical speculations. In the
present work we review the latest advances in microscopic modeling of the
nuclear equation of state and demonstrate how to consistently include also
empirical nuclear data into a Bayesian posterior probability distribution for
the model parameters. Derived bulk neutron star properties such as radii,
moments of inertia, and tidal deformabilities are computed, and we discuss as
well the limitations of our modeling.Comment: 9 pages, 5 figures. To appear in the AIP Proceedings of the
Xiamen-CUSTIPEN Workshop on the EOS of Dense Neutron-Rich Matter in the Era
of Gravitational Wave Astronomy, Jan. 3-7, Xiamen, Chin
Proton pairing in neutron stars from chiral effective field theory
We study the proton pairing gap in beta-equilibrated neutron star
matter within the framework of chiral effective field theory. We focus on the
role of three-body forces, which strongly modify the effective proton-proton
spin-singlet interaction in dense matter. We find that three-body forces
generically reduce both the size of the pairing gap and the maximum density at
which proton pairing may occur. The pairing gap is computed within BCS theory,
and model uncertainties are estimated by varying the nuclear potential and the
choice of single-particle spectrum in the gap equation. We find that a
second-order perturbative treatment of the single-particle spectrum suppresses
the proton pairing gap relative to the use of a free spectrum. We
estimate the critical temperature for the onset of proton superconductivity to
be K, which is consistent with previous
theoretical results in the literature and marginally within the range deduced
from a recent Bayesian analysis of neutron star cooling observations.Comment: 8 pages, 9 figure
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