Do nonlinear waves in random media follow nonlinear diffusion equations?

Probably yes, since we find a striking similarity in the spatio-temporal evolution of nonlinear diffusion equations and wave packet spreading in generic nonlinear disordered lattices, including self-similarity and scaling.Comment: 6 pages, 4 figure

Nonlinear Lattice Waves in Random Potentials

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field. We will discuss recent advances in the dynamics of nonlinear lattice waves in random potentials. In the absence of nonlinear terms in the wave equations, Anderson localization is leading to a halt of wave packet spreading. Nonlinearity couples localized eigenstates and, potentially, enables spreading and destruction of Anderson localization due to nonintegrability, chaos and decoherence. The spreading process is characterized by universal subdiffusive laws due to nonlinear diffusion. We review extensive computational studies for one- and two-dimensional systems with tunable nonlinearity power. We also briefly discuss extensions to other cases where the linear wave equation features localization: Aubry-Andre localization with quasiperiodic potentials, Wannier-Stark localization with dc fields, and dynamical localization in momentum space with kicked rotors.Comment: 45 pages, 19 figure

Quasiperiodic driving of Anderson localized waves in one dimension

We consider a quantum particle in a one-dimensional disordered lattice with Anderson localization in the presence of multifrequency perturbations of the onsite energies. Using the Floquet representation, we transform the eigenvalue problem into a Wannier-Stark basis. Each frequency component contributes either to a single channel or a multichannel connectivity along the lattice, depending on the control parameters. The single-channel regime is essentially equivalent to the undriven case. The multichannel driving increases substantially the localization length for slow driving, showing two different scaling regimes of weak and strong driving, yet the localization length stays finite for a finite number of frequency components. ©2016 American Physical Society1331sciescopu

Lipolytic enzymes and hydrolytic rancidity

Lipolysis, the enzymic hydrolysis of milk lipids to free fatty acids and partial glycerides, is a constant concern to the dairy industry because of the detrimental effcts it can have on the flvor and other properties of milk and milk products. However, free fatty acids also contribute to the desirable flavor of milk and milk products when present at low concentrations and, in some cheeses, when present at high concentrations. The enzymes responsible for the detrimental effects of lipolysis are of two main types: those indigenous to milk, and those of microbial origin. The major indigenous milk enzyme is lipoprotein lipase. It is active on the fat in natural milk fat globules only after their disruption by physical treatments or if certain blood serum lipoproteins are present. The major microbial lipases are produced by psychrotrophic bacteria. Many of these enzymes are heat stable and are particularly significant in stored products. Human milk differs from cows' milk in that it contains two lipases, a lipoprotein lipase and a bile salt-stimulated lipase. The ability of the latter to cause considerable hydrolysis of ingested milk lipids has important nutritional implications