31,050 research outputs found
Gisin's Theorem for Arbitrary Dimensional Multipartite States
We present a set of Bell inequalities which are sufficient and necessary for
separability of general pure multipartite quantum states in arbitrary
dimensions. The relations between Bell inequalities and distillability are also
studied. We show that any quantum states that violate one of these Bell
inequalities are distillable.Comment: 5 page
Sensitivity of Coronal Loop Sausage Mode Frequencies and Decay Rates to Radial and Longitudinal Density Inhomogeneities: A Spectral Approach
Fast sausage modes in solar magnetic coronal loops are only fully contained
in unrealistically short dense loops. Otherwise they are leaky, losing energy
to their surrounds as outgoing waves. This causes any oscillation to decay
exponentially in time. Simultaneous observations of both period and decay rate
therefore reveal the eigenfrequency of the observed mode, and potentially
insight into the tubes' nonuniform internal structure. In this article, a
global spectral description of the oscillations is presented that results in an
implicit matrix eigenvalue equation where the eigenvalues are associated
predominantly with the diagonal terms of the matrix. The off-diagonal terms
vanish identically if the tube is uniform. A linearized perturbation approach,
applied with respect to a uniform reference model, is developed that makes the
eigenvalues explicit. The implicit eigenvalue problem is easily solved
numerically though, and it is shown that knowledge of the real and imaginary
parts of the eigenfrequency is sufficient to determine the width and density
contrast of a boundary layer over which the tubes' enhanced internal densities
drop to ambient values. Linearized density kernels are developed that show
sensitivity only to the extreme outside of the loops for radial fundamental
modes, especially for small density enhancements, with no sensitivity to the
core. Higher radial harmonics do show some internal sensitivity, but these will
be more difficult to observe. Only kink modes are sensitive to the tube
centres. {Variation in internal and external Alfv\'en speed along the loop is
shown to have little effect on the fundamental dimensionless eigenfrequency,
though the associated eigenfunction becomes more compact at the loop apex as
stratification increases, or may even displace from the apex.Comment: Accepted J. Phys. A: Math. Theor. (Oct 31 2017). 20 pages, 12 figure
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Joining the CCS Club! Insights from a Northwest European CO2 Pipeline Project
The large-scale diffusion of Carbon Capture and Storage (CCS) imposes the construction of a sizeable CO2 pipeline infrastructure. This paper analyzes the conditions for a widespread adoption of CCS by a group of emitters that can be connected to a common pipeline system. It details a quantitative framework capable of assessing how the tariff structure and the regulatory constraints imposed on the pipeline operator impact the overall cost of CO2 abatement via CCS. This modeling framework is applied to the case of a real European CO2 pipeline project. We find that the obligation to use cross-subsidy-free pipeline tariffs has a minor impact on the minimum CO2 price required to adopt the
CCS. In contrast, the obligation to charge non-discriminatory prices can either impede the adoption of CCS or significantly raises that price. Besides, we compared two alternative regulatory frameworks for CCS pipelines: a common European organization as opposed to a collection of national regulations. The results indicate that the institutional scope of that regulation has a limited impact on the adoption of CCS compared to the detailed design of the tariff structure imposed to pipeline operators
Factorization of Multivariate Positive Laurent Polynomials
Recently Dritschel proves that any positive multivariate Laurent polynomial
can be factorized into a sum of square magnitudes of polynomials. We first give
another proof of the Dritschel theorem. Our proof is based on the univariate
matrix Fejer-Riesz theorem. Then we discuss a computational method to find
approximates of polynomial matrix factorization. Some numerical examples will
be shown. Finally we discuss how to compute nonnegative Laurent polynomial
factorizations in the multivariate setting
Strategic implications of critical fixities under continuous technological change
Includes bibliographical references (p. 27-28)
Lookahead Strategies for Sequential Monte Carlo
Based on the principles of importance sampling and resampling, sequential
Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with
complex stochastic dynamic systems. Many of these systems possess strong
memory, with which future information can help sharpen the inference about the
current state. By providing theoretical justification of several existing
algorithms and introducing several new ones, we study systematically how to
construct efficient SMC algorithms to take advantage of the "future"
information without creating a substantially high computational burden. The
main idea is to allow for lookahead in the Monte Carlo process so that future
information can be utilized in weighting and generating Monte Carlo samples, or
resampling from samples of the current state.Comment: Published in at http://dx.doi.org/10.1214/12-STS401 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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