49,929 research outputs found
Fermi-Surface Reconstruction in the Periodic Anderson Model
We study ground state properties of periodic Anderson model in a
two-dimensional square lattice with variational Monte Carlo method. It is shown
that there are two different types of quantum phase transition: a conventional
antiferromagnetic transition and a Fermi-surface reconstruction which
accompanies a change of topology of the Fermi surface. The former is induced by
a simple back-folding of the Fermi surface while the latter is induced by
localization of electrons. The mechanism of these transitions and the
relation to the recent experiments on Fermi surface are discussed in detail.Comment: 8 pages, 7 figures, submitted to Journal of the Physical Society of
Japa
Robust Phase Unwrapping by Convex Optimization
The 2-D phase unwrapping problem aims at retrieving a "phase" image from its
modulo observations. Many applications, such as interferometry or
synthetic aperture radar imaging, are concerned by this problem since they
proceed by recording complex or modulated data from which a "wrapped" phase is
extracted. Although 1-D phase unwrapping is trivial, a challenge remains in
higher dimensions to overcome two common problems: noise and discontinuities in
the true phase image. In contrast to state-of-the-art techniques, this work
aims at simultaneously unwrap and denoise the phase image. We propose a robust
convex optimization approach that enforces data fidelity constraints expressed
in the corrupted phase derivative domain while promoting a sparse phase prior.
The resulting optimization problem is solved by the Chambolle-Pock primal-dual
scheme. We show that under different observation noise levels, our approach
compares favorably to those that perform the unwrapping and denoising in two
separate steps.Comment: 6 pages, 4 figures, submitted in ICIP1
Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes
This is the continuation of the paper "central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction" by the same authors. The hierarchical reconstruction introduced therein is applied to central schemes on overlapping cells and to nite volume schemes on non-staggered grids. This takes a new nite volume approach for approximating non-smooth solutions. A critical step for high order nite volume schemes is to reconstruct a nonoscillatory
high degree polynomial approximation in each cell out of nearby cell averages. In the paper this procedure is accomplished in two steps: first to reconstruct a high degree polynomial in each cell by using e.g., a central reconstruction, which is easy to do despite the fact that the reconstructed
polynomial could be oscillatory; then to apply the hierarchical reconstruction to remove the spurious oscillations while maintaining the high resolution. All numerical computations for systems of conservation laws are performed without characteristic decomposition. In particular, we demonstrate that this new approach can generate essentially non-oscillatory solutions even for 5th order schemes without
characteristic decomposition.The research of Y. Liu was supported in part by NSF grant DMS-0511815. The research of C.-W. Shu was supported in part by the Chinese Academy of Sciences while this author was visiting the University of Science
and Technology of China (grant 2004-1-8) and the Institute of Computational Mathematics and Scienti c/Engineering Computing. Additional support was provided by ARO grant W911NF-04-1-0291 and NSF grant DMS-0510345. The research of E. Tadmor was supported in part by NSF grant 04-07704 and ONR grant N00014-91-J-1076. The research of M. Zhang was supported in part by the Chinese Academy of Sciences grant 2004-1-8
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
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