Narrow Results

Nonpotential effects in nonlinear evolution of Marangoni convection patterns are investigated analytically and numerically. Three manifestations of nonpotential effects are considered: (i) spatial modulations of hexagonal patterns; (ii) interaction between a short-scale hexagonal pattern and a long-scale slow deformational (Goldstone) mode; (iii) generation of the mean flow by the free-surface deformation in a large-scale Marangoni convection with poorly conducting boundaries. Nonpotential effects are shown to cause various secondary instabilities leading to skewed hexagonal structures, coexisting u- and d-hexagons, oscillating hexagonal patterns, spatially irregular cellular patterns, etc.

We investigate fixed dopants in the presence of mobile point defects like foreign atoms or vacancies. A mobile defect entering the first Bohr radius R_B of a dopant will modulate the generation-recombination process. The times a defect walks inside or outside R_B are shown to be power-law distributed giving rise to 1 / f^b noise. The predicted Hooge coefficient α_def depends on R_B, on the normalized fluctuations of charge carriers and on the number of charge carriers compared to lattice sites; our model suggests that the magnitude of 1/f noise can be decreased at will by increasing the ionization of dopants.

We investigate fixed dopants in the presence of mobile point defects. A defect entering the first Bohr radius R_B of a dopant will modulate the generation-recombination (g-r) process. The times a defect walks inside and outside of R_B are found to be power-law distributed; correspondingly, the modulated g-r process exhibits 1/f^b noise. The predicted Hooge coefficient depends on R_B, on the normalized fluctuations of charge carriers, the number of lattice sites and on the modulation depth of the g-r process.