Elastic scattering of traveling phonons by discrete breathers as a time-periodic scatterer in the one-dimensional discrete nonlinear Schrödinger model: Exact analysis.

Discrete nonlinear Schrödinger model is a nonlinear lattice model used to investigate different nonlinear phenomena arising in many physical contexts. In this work we used this model to observe linear traveling phonon scattering by time-periodic discrete breathers in the piecewise smooth (PWS) version of nonlinearity. In one-dimensional system the single-channel scattering is found to be elastic (with the incoming and outgoing fluxes of energy being equal to each other).

A theoretical interpretation of length-biomass allometry of predominantly bidimensional seaweeds.

Experimental studies on bidimensional seaweeds revealed a scaling exponent of 0.472 for their length-biomass allometry. This was significantly higher than the value 0.

Traveling kinks in discrete media: exact solution in a piecewise linear model.

We present an exact integral representation of a traveling kink solution in a reaction-diffusion equation with a piecewise linear reaction function, complementing existence proofs and numerical observations of such solutions in discrete excitable media. The kink speed is determined through a matching condition, and is worked out explicitly in two limiting situations: the pinning limit, and the opposite limit of infinitely fast kink. Results on the pinning limit agree with those in a recent paper by Fath [Physica D 116, 176 (1998)].