74,563 research outputs found
Hybrid Spectral Difference/Embedded Finite Volume Method for Conservation Laws
A novel hybrid spectral difference/embedded finite volume method is
introduced in order to apply a discontinuous high-order method for large scale
engineering applications involving discontinuities in the flows with complex
geometries. In the proposed hybrid approach, the finite volume (FV) element,
consisting of structured FV subcells, is embedded in the base hexahedral
element containing discontinuity, and an FV based high-order shock-capturing
scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is
captured at the resolution of FV subcells within an embedded FV element. In the
smooth flow region, the SD element is used in the base hexahedral element.
Then, the governing equations are solved by the SD method. The SD method is
chosen for its low numerical dissipation and computational efficiency
preserving high-order accurate solutions. The coupling between the SD element
and the FV element is achieved by the globally conserved mortar method. In this
paper, the 5th-order WENO scheme with the characteristic decomposition is
employed as the shock-capturing scheme in the embedded FV element, and the
5th-order SD method is used in the smooth flow field.
The order of accuracy study and various 1D and 2D test cases are carried out,
which involve the discontinuities and vortex flows. Overall, it is shown that
the proposed hybrid method results in comparable or better simulation results
compared with the standalone WENO scheme when the same number of solution DOF
is considered in both SD and FV elements.Comment: 27 pages, 17 figures, 2 tables, Accepted for publication in the
Journal of Computational Physics, April 201
Zigzag Filamentary Theory of Broken Symmetry of Neutron and Infrared Vibronic Spectra of YBa2Cu3O(6+x)
Filamentary high-temperature superconductivity (HTSC) theory differs
fundamentally from continuous HTSC theories because it emphasizes
self-organized, discrete dopant networks and does not make the effective medium
approximation (EMA). Analysis of neutron and infrared (especially with c-axis
polarization) vibrational spectra, primarily for YBa2Cu3O(6+x), within the
filamentary framework, shows that the observed vibronic anomalies near 400 cm-1
(50 meV) are associated with curvilinear filamentary paths. these paths pass
through cuprate chains and planes, as well as resonant tunneling centers in the
BaO layers. The analysis and the data confirm earlier filamentary structural
models containing ferroelastic domains of 3-4 nm in the CuO2 planes; it is
these nanodomains that are responsible for the discrete glassy nature of both
electronic and vibronic properties. Chemical trends in vibronic energies and
oscillator strengths, both for neutron and photon scattering, that were
anomalous in continuum models, are readily explained by the filamentary model.Comment: 45 pages, 17 figures, PD
Perfect Regular Equilibrium
We propose a revised version of the perfect Bayesian equilibrium in general multi-period games with observed actions. In finite games, perfect Bayesian equilibria are weakly consistent and subgame perfect Nash equilibria. In general games that allow a continuum of types and strategies, however, perfect Bayesian equilibria might not satisfy these criteria of rational solution concepts. To solve this problem, we revise the definition of the perfect Bayesian equilibrium by replacing Bayes' rule with a regular conditional probability. We call this revised solution concept a perfect regular equilibrium. Perfect regular equilibria are always weakly consistent and subgame perfect Nash equilibria in general games. In addition, perfect regular equilibria are equivalent to simplified perfect Bayesian equilibria in finite games. Therefore, the perfect regular equilibrium is an extended and simple version of the perfect Bayesian equilibrium in general multi-period games with observed actions
PCA consistency in high dimension, low sample size context
Principal Component Analysis (PCA) is an important tool of dimension
reduction especially when the dimension (or the number of variables) is very
high. Asymptotic studies where the sample size is fixed, and the dimension
grows [i.e., High Dimension, Low Sample Size (HDLSS)] are becoming increasingly
relevant. We investigate the asymptotic behavior of the Principal Component
(PC) directions. HDLSS asymptotics are used to study consistency, strong
inconsistency and subspace consistency. We show that if the first few
eigenvalues of a population covariance matrix are large enough compared to the
others, then the corresponding estimated PC directions are consistent or
converge to the appropriate subspace (subspace consistency) and most other PC
directions are strongly inconsistent. Broad sets of sufficient conditions for
each of these cases are specified and the main theorem gives a catalogue of
possible combinations. In preparation for these results, we show that the
geometric representation of HDLSS data holds under general conditions, which
includes a -mixing condition and a broad range of sphericity measures of
the covariance matrix.Comment: Published in at http://dx.doi.org/10.1214/09-AOS709 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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