287 research outputs found
Rank-(n – 1) convexity and quasiconvexity for divergence free fields
No description supplie
Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors
We show that any pair of real symmetric tensors \BGve and \BGm can be
realized as the effective electric permittivity and effective magnetic
permeability of a metamaterial at a given fixed frequency. The construction
starts with two extremely low loss metamaterials, with arbitrarily small
microstructure, whose existence is ensured by the work of Bouchitt{\'e} and
Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a
permittivity tensor with exactly one negative eigenvalue, and a positive
permeability tensor, and the other having a positive permittivity tensor, and a
permeability tensor having exactly one negative eigenvalue. To achieve the
desired effective properties these materials are laminated together in a
hierarchical multiple rank laminate structure, with widely separated length
scales, and varying directions of lamination, but with the largest length scale
still much shorter than the wavelengths and attenuation lengths in the
macroscopic effective medium.Comment: 12 pages, no figure
Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations
The Navier--Stokes equations are commonly used to model and to simulate flow
phenomena. We introduce the basic equations and discuss the standard methods
for the spatial and temporal discretization. We analyse the semi-discrete
equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index
and quantify the numerical difficulties in the fully discrete schemes, that are
induced by the strangeness of the system. By analyzing the Kronecker index of
the difference-algebraic equations, that represent commonly and successfully
used time stepping schemes for the Navier--Stokes equations, we show that those
time-integration schemes factually remove the strangeness. The theoretical
considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909,
https://doi.org/10.5281/zenodo.99890
Recommended from our members
Hop investigations
Published January 1913. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalo
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The arsenates of lead
Published May 1915. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalo
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Sulfur as a fertilizer for alfalfa in southern Oregon
Published July 1919. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalo
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The soils of Jackson County
Published January 1920. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalo
About curvature, conformal metrics and warped products
We consider the curvature of a family of warped products of two
pseduo-Riemannian manifolds and furnished with metrics of
the form and, in particular, of the type , where are smooth
functions and is a real parameter. We obtain suitable expressions for the
Ricci tensor and scalar curvature of such products that allow us to establish
results about the existence of Einstein or constant scalar curvature structures
in these categories. If is Riemannian, the latter question involves
nonlinear elliptic partial differential equations with concave-convex
nonlinearities and singular partial differential equations of the
Lichnerowicz-York type among others.Comment: 32 pages, 3 figure
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