Patterns in dissipative systems with weakly broken continuous symmetry.

Patterns in dissipative systems with weakly broken symmetry are studied based upon the simplest canonical equation (generalized Nikolaevskiy model). A generic cubic dispersion equation governing stability of steady spatially periodic patterns is derived and analyzed. A domain of stable states in the space of the problem parameters (stability balloon) is obtained.

Light scattering by a finite obstacle and fano resonances.

The conditions for observing Fano resonances at elastic light scattering by a single finite-size obstacle are discussed. General arguments are illustrated by consideration of the scattering by a small (relative to the incident light wavelength) spherical obstacle based upon the exact Mie solution of the diffraction problem. The most attention is paid to recently discovered anomalous scattering.

Anomalous light scattering by small particles.

Light scattering by a small spherical particle with a low dissipation rate is discussed based upon the Mie theory. It is shown that if close to the plasmon (polariton) resonance frequencies the radiative damping prevails over dissipative losses, sharp giant resonances with very unusual properties may be observed. In particular, the resonance extinction cross section increases with an increase in the order of the resonance (dipole, quadrupole, etc.