Direct, stigmatic, imaging with curved surfaces

We study the possibilities of direct (using one intersection with each light ray) stigmatic imaging with a curved surface that can change ray directions in an arbitrary way. By purely geometric arguments we show that the only possible case of such imaging is the trivial one where the image of any point is identical to the point itself and the surface does not perform any change of the ray direction at all. We also discuss an example of a curved surface which performs indirect stigmatic imaging after twice intersecting each light ray

Wave-scattering from a gently curved surface

We study wave scattering from a gently curved surface. We show that the recursive relations, implied by shift invariance, among the coefficients of the perturbative series for the scattering amplitude allow to perform an infinite resummation of the perturbative series to all orders in the amplitude of the corrugation. The resummed series provides a derivative expansion of the scattering amplitude in powers of derivatives of the height profile, which is expected to become exact in the limit of quasi-specular scattering. We discuss the relation of our results with the so-called small-slope approximation introduced some time ago by Voronovich.Comment: 5 pages, accepted for publication in Phys. Lett.

Nonexistence of classical diamagnetism and nonequilibrium fluctuation theorems for charged particles on a curved surface

We show that the classical Langevin dynamics for a charged particle on a closed curved surface in a time-independent magnetic field leads to the canonical distribution in the long time limit. Thus the Bohr-van Leeuwen theorem holds even for a finite system without any boundary and the average magnetic moment is zero. This is contrary to the recent claim by Kumar and Kumar (EPL, {\bf 86} (2009) 17001), obtained from numerical analysis of Langevin dynamics, that a classical charged particle on the surface of a sphere in the presence of a magnetic field has a nonzero average diamagnetic moment. We extend our analysis to a many-particle system on a curved surface and show that the nonequilibrium fluctuation theorems also hold in this geometry.Comment: 6 pages; typos correcte

Flexible honeycomb structure can bend to fit compound curves

For flexibility in forming a curved surface, a honeycomb configuration using multiple pleats has proved superior to the usual core structures. The partial pleats formed in individual cell walls permit movements to and from the central axis without tearing