Nonlinear communication channels with capacity above the linear Shannon limit.

We prove that, under certain conditions, the capacity of an optical communication channel with in-line, nonlinear filtering (regeneration) elements can be higher than the Shannon capacity for the corresponding linear Gaussian white noise channel.

Non-Gaussianity in single-particle tracking: use of kurtosis to learn the characteristics of a cage-type potential.

Nonlinear interaction of membrane proteins with cytoskeleton and membrane leads to non-Gaussian structure of their displacement probability distribution. We propose a statistical analysis technique for learning the characteristics of the nonlinear potential from the time dependence of the cumulants of the displacement distribution. The efficiency of the approach is demonstrated on the analysis of the kurtosis of the displacement distribution of the particle traveling on a membrane in a cage-type potential. Results of numerical simulations are supported by analytical predictions. We show that the approach allows robust identification of some characteristics of the potential for the much lower temporal resolution compared with the mean-square displacement analysis and we demonstrate robustness to experimental errors in determining the particle positions.

Nonlinear repolarization in optical fibers: polarization attraction with copropagating beams.

We propose a type of lossless nonlinear polarizer, novel to our knowledge, a device that transforms any input state of polarization (SOP) of a signal beam into one and the same well-defined SOP toward the output, and perform this without any polarization-dependent losses. At the polarizer output end, the signal SOP appears to be locked to the input pump SOP. The polarizer is based on the nonlinear Kerr interaction of copropagating signal and pump beams in a telecom or randomly birefringent optical fiber.

Convective instability and mass transport of diffusion layers in a Hele-Shaw geometry.

We consider experimentally the instability and mass transport of flow in a Hele-Shaw geometry. In an initially stable configuration, a lighter fluid (water) is located over a heavier fluid (propylene glycol). The fluids mix via diffusion with some regions of the resulting mixture being heavier than either pure fluid. Density-driven convection occurs with downward penetrating dense fingers that transport mass much more effectively than diffusion alone. We investigate the initial instability and the quasisteady state. The convective time and velocity scales, finger width, wave number selection, and normalized mass transport are determined for 6000

Asymmetric disconnection of an underwater air bubble: persistent neck vibrations evolve into a smooth contact.

The disconnection of an underwater bubble illustrates how slight initial asymmetries can prevent the formation of a finite-time singularity. Creating a singularity by focusing a finite amount of energy dynamically into a vanishingly small amount of material requires that the initial condition be perfectly symmetric. In reality, imperfections are always present. We show a slight azimuthal asymmetry in the initial shape of the bubble neck excites vibrations that persist over time. As a result, the focusing singularity is generically preempted by a smooth contact.