214 research outputs found
The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends
A simple sufficient condition on curved end of a straight cylinder is found
that provides a localization of the principal eigenfunction of the mixed
boundary value for the Laplace operator with the Dirichlet conditions on the
lateral side. Namely, the eigenfunction concentrates in the vicinity of the
ends and decays exponentially in the interior. Similar effects are observed in
the Dirichlet and Neumann problems, too.Comment: 25 pages, 10 figure
Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods
We consider Dirichlet Laplacian in a thin curved three-dimensional rod. The
rod is finite. Its cross-section is constant and small, and rotates along the
reference curve in an arbitrary way. We find a two-parametric set of the
eigenvalues of such operator and construct their complete asymptotic
expansions. We show that this two-parametric set contains any prescribed number
of the first eigenvalues of the considered operator. We obtain the complete
asymptotic expansions for the eigenfunctions associated with these first
eigenvalues
Annual research briefs, 1993
The 1993 annual progress reports of the Research Fellow and students of the Center for Turbulence Research are included. The first group of reports are directed towards the theory and application of active control in turbulent flows including the development of a systematic mathematical procedure based on the Navier Stokes equations for flow control. The second group of reports are concerned with the prediction of turbulent flows. The remaining articles are devoted to turbulent reacting flows, turbulence physics, experiments, and simulations
Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions
We investigate a time harmonic acoustic scattering problem by a penetrable
inclusion with compact support embedded in the free space. We consider cases
where an observer can produce incident plane waves and measure the far field
pattern of the resulting scattered field only in a finite set of directions. In
this context, we say that a wavenumber is a non-scattering wavenumber if the
associated relative scattering matrix has a non trivial kernel. Under certain
assumptions on the physical coefficients of the inclusion, we show that the
non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a
second step, for a given real wavenumber and a given domain D, we present a
constructive technique to prove that there exist inclusions supported in D for
which the corresponding relative scattering matrix is null. These inclusions
have the important property to be impossible to detect from far field
measurements. The approach leads to a numerical algorithm which is described at
the end of the paper and which allows to provide examples of (approximated)
invisible inclusions.Comment: 20 pages, 7 figure
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