Super rogue wave generation in the linear regime.

Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate super rogue waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of ordinary rogue waves. Here we show, experimentally and theoretically, that optical super rogue waves emerge in the simple case of linear light diffraction in one transverse dimension. The underlying physics is a long-range correlation on the random initial phases of the light waves. When subgroups of random phases appear recurrently along the spatial phase distribution, a more ordered phase structure greatly increases the probability of constructive interference to generate super rogue events (non-Gaussian statistics with superlong tails). Our results consist in a significant advance in the understanding of extreme waves formation by linear superposition of random waves, with applications in a large variety of wave systems.

The propagator (retarded Green function) formalism as a new calculation method to predict the time evolution of bands in capillary electrophoresis and microchannels.

Capillary electrophoresis (CE) and microchannel (MC) techniques are important tools in chemical and biological sciences, mainly in the study of genomes, transcriptomes, proteomes, metabolomes, and organic as well as inorganic ions. The speed of DNA sequencing increased significantly during the last decade with the use of capillary electrophoresis (CE). The time evolution of the bands' spatial profile inside capillaries and channels is of paramount importance, since the main goal of these techniques is to maximize resolution (the ratio between the spacing of the peaks and their mean standard deviations). In the present work, the propagator (retarded Green function) formalism is applied to solve a few problems which are typical for CE and MC. We also apply this mathematical method to the problem of velocity gradients along the capillary, i.e., the time evolution of the bands is analyzed when they enter regions where they migrate with different velocities.