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Title: A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance

Authors:
; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1348014
Grant/Contract Number:
SC0008271
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 316; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-06 15:26:41; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English

Citation Formats

Bao, Yuanxun, Kaye, Jason, and Peskin, Charles S. A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance. United States: N. p., 2016. Web. doi:10.1016/j.jcp.2016.04.024.
Bao, Yuanxun, Kaye, Jason, & Peskin, Charles S. A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance. United States. doi:10.1016/j.jcp.2016.04.024.
Bao, Yuanxun, Kaye, Jason, and Peskin, Charles S. Fri . "A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance". United States. doi:10.1016/j.jcp.2016.04.024.
@article{osti_1348014,
title = {A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance},
author = {Bao, Yuanxun and Kaye, Jason and Peskin, Charles S.},
abstractNote = {},
doi = {10.1016/j.jcp.2016.04.024},
journal = {Journal of Computational Physics},
number = C,
volume = 316,
place = {United States},
year = {Fri Jul 01 00:00:00 EDT 2016},
month = {Fri Jul 01 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.jcp.2016.04.024

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  • Highlights: {yields} A radial basis function based smoothing technique is introduced. {yields} It is more general and easier to implement compared to other techniques. {yields} With this technique, a combined immersed boundary and spectral method is developed. {yields} It is shown that the proposed method works better in terms of reducing the non-physical Gibbs oscillation. - Abstract: It is known that, when the immersed boundary method (IBM) is implemented within spectral-like methods, the Gibbs oscillation seriously deteriorates the calculation of derivatives near the body surface. In this paper, a radial basis function (RBF) based smoothing technique is proposed with themore » intention of eliminating or efficiently reducing the Gibbs oscillation without affecting the flow field outside the body. Based on this technique, a combined IBM/spectral scheme is developed to solve the incompressible Navier-Stokes equations. Numerical simulations of flow through a periodic lattice of cylinders of various cross sections are performed. The results demonstrate that the proposed methodology is able to give accurate and nearly oscillation-free numerical solutions of incompressible viscous flows.« less
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  • We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequalitymore » constraint [G. Adesso and F. Illuminati, New J. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/W states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the W states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ/W states are shown to be maximally robust against losses and thermal noise.« less
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