14,834 research outputs found
Comment on "Perfect imaging with positive refraction in three dimensions"
Leonhard and Philbin [Phys. Rev. A 81, 011804(R) (2010)] have recently
constructed a mathematical proof that the Maxwell's fish-eye lens provides
perfect imaging of electromagnetic waves without negative refraction. In this
comment, we argue that the unlimited resolution is an artifact of having
introduced an unphysical drain at the position of the geometrical image. The
correct solution gives focusing consistent with the standard diffraction limit
Dodecahedral topology fails to explain quadrupole-octupole alignment
The CMB quadrupole and octupole, as well as being weaker than expected, align
suspiciously well with each other. Non-trivial spatial topology can explain the
weakness. Might it also explain the alignment? The answer, at least in the case
of the Poincare dodecahedral space, is a resounding no.Comment: 5 pages, 1 figur
The von Karman equations, the stress function, and elastic ridges in high dimensions
The elastic energy functional of a thin elastic rod or sheet is generalized
to the case of an M-dimensional manifold in N-dimensional space. We derive
potentials for the stress field and curvatures and find the generalized von
Karman equations for a manifold in elastic equilibrium. We perform a scaling
analysis of an M-1 dimensional ridge in an M = N-1 dimensional manifold. A
ridge of linear size X in a manifold with thickness h << X has a width w ~
h^{1/3}X^{2/3} and a total energy E ~ h^{M} (X/h)^{M-5/3}. We also prove that
the total bending energy of the ridge is exactly five times the total
stretching energy. These results match those of A. Lobkovsky [Phys. Rev. E 53,
3750 (1996)] for the case of a bent plate in three dimensions.Comment: corrected references, 27 pages, RevTeX + epsf, 2 figures, Submitted
to J. Math. Phy
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