Hyperk\"ahler Arnold Conjecture and its Generalizations

We generalize and refine the hyperk\"ahler Arnold conjecture, which was originally established, in the non-degenerate case, for three-dimensional time by Hohloch, Noetzel and Salamon by means of hyperk\"ahler Floer theory. In particular, we prove the conjecture in the case where the time manifold is a multidimensional torus and also establish the degenerate version of the conjecture. Our method relies on Morse theory for generating functions and a finite-dimensional reduction along the lines of the Conley-Zehnder proof of the Arnold conjecture for the torus.Comment: 13 page

Gain-assisted slow to superluminal group velocity manipulation in nano-waveguides

We study the energy propagation in subwavelength waveguides and demonstrate that the mechanism of material gain, previously suggested for loss compensation, is also a powerful tool to manipulate dispersion and propagation characteristics of electromagnetic pulses at the nanoscale. We show theoretically that the group velocity in lossy nano-waveguides can be controlled from slow to superluminal values by the material gain and waveguide geometry and develop an analytical description of the relevant physics. We utilize the developed formalism to show that gain-assisted dispersion management can be used to control the transition between ``photonic-funnel'' and ``photonic-compressor'' regimes in tapered nano-waveguides. The phenomenon of strong modulation of group velocity in subwavelength structures can be realized in waveguides with different geometries, and is present for both volume and surface-modes.Comment: Some changes in the abstract and Fig.1. No results affecte

Boundary hopping and the mobility edge in the Anderson model in three dimensions

It is shown, using high-precision numerical simulations, that the mobility edge of the 3d Anderson model depends on the boundary hopping term t in the infinite size limit. The critical exponent is independent of it. The renormalized localization length at the critical point is also found to depend on t but not on the distribution of on-site energies for box and Lorentzian distributions. Implications of results for the description of the transition in terms of a local order-parameter are discussed

Scattering-free plasmonic optics with anisotropic metamaterials

We develop an approach to utilize anisotropic metamaterials to solve one of the fundamental problems of modern plasmonics -- parasitic scattering of surface waves into free-space modes, opening the road to truly two-dimensional plasmonic optics. We illustrate the developed formalism on examples of plasmonic refractor and plasmonic crystal, and discuss limitations of the developed technique and its possible applications for sensing and imaging structures, high-performance mode couplers, optical cloaking structures, and dynamically reconfigurable electro-plasmonic circuits

Inertia compensation while scanning screw threads on coordinate-measuring machines

Usage of scanning coordinate-measuring machines for inspection of screw threads has become a common practice nowadays. Compared to touch trigger probing, scanning capabilities allow to speed up measuring process while still maintaining high accuracy. However, in some cases accuracy drasticaly depends on the scanning speed. In this paper a compensation method is proposed allowing to reduce the influence of some dynamic effects while scanning screw threads on coordinate-measuring machines