Nonlinearity in materials science

We discuss the all-important issue of nonlinearity in the physical sciences , with emphasis on its importance in condensed matter physics, where nonlin earity provides a natural mechanism for selective trapping of excitations, such as electrons, at a microscopic scale. This mechanism, term "selftrappi ng", is investigated in a variety of lattices with different geometries and dimensionalities. It is found that its main features are universal and rob ust against perturbations of several kind. These findings would have an imp act on the future design of smart materials with pre-ordained transport pro perties, a much sought-after feature nowadays. We also discuss an applicati on of the selftrapping ideas to the problem of power switching in nonlinear optics, an important issue when considering the design of an all-optical c omputer.