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

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

Method of adhering bone to a rigid substrate using a graphite fiber reinforced bone cement

A method is described for adhering bone to the surface of a rigid substrate such as a metal or resin prosthesis using an improved surgical bone cement. The bone cement has mechanical properties more nearly matched to those of animal bone and thermal curing characteristics which result in less traumatization of body tissues and comprises a dispersion of short high modulus graphite fibers within a bonder composition including polymer dissolved in reactive monomer such as polymethylmethacrylate dissolved in methylmethacrylate monomer