Abstract

I plan to discuss the researches and ideas associated with wave scattering in discrete models. Some of these are counterparts of few problems in the classical theory of wave scattering and hence appear as their discretized versions. I will present an overview, mostly of my work and a few collaborators, in the context of questions raised over last decade, as well as few bits from last century, within the perspective of understanding the dynamical behavior of crystalline materials of varied structure and dimensions. Briefly the modern avatars of old questions will be addressed while the talk features some challenging and new open problems in the so called ‘discrete scattering’ and its limiting cases. As we understand via the evolving technological scenario, the emerging paradigm of nanoscale structures, metamaterials, and structured media, as well as the concomitant coupling between multi-physics and multiple-scales, motivates a part of the development of existing theories and tools for single- and multiple-scattering problems. Keywords: complex analysis, Wiener-Hopf technique, bifurcating waveguides, localized waves, crack, nearest-neighbour interaction.