295 research outputs found
Stokes waves with vorticity
The existence of periodic waves propagating downstream on the surface of a
two-dimensional infinitely deep water under gravity is established for a
general class of vorticities. When reformulated as an elliptic boundary value
problem in a fixed semi-infinite strip with a parameter, the operator
describing the problem is nonlinear and non-Fredholm. A global connected set of
nontrivial solutions is obtained via singular theory of bifurcation. Each
solution on the continuum has a symmetric and monotone wave profile. The proof
uses a generalized degree theory, global bifurcation theory and Wyburn's lemma
in topology, combined with the Schauder theory for elliptic problems and the
maximum principle
Shielding at a distance due to anomalous resonance in superlens with eccentric core
A cylindrical plasmonic structure with a concentric core exhibits an
anomalous localized resonance which results in cloaking effects. Here we show
that, if the structure has an eccentric core, a new kind of shielding effect
can happen. In contrast to the conventional shielding device, our proposed
structure can block the effect of external electrical sources even on a region
which is not enclosed by any conducting materials. In fact, the shielded region
is located at a distance from the device. We analytically investigate this
phenomenon by using the m\"{o}bius transformation via which an eccentric
annulus is transformed into a concentric one. We also present several numerical
examples.Comment: 11 pages, 6 figure
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