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On an elementary analysis and some applications of scattering theory involving edges in a discrete framework

Prof Basant Lal Sharma IIT Kanpur
Speaker
Prof Basant Lal Sharma IIT Kanpur
When Dec 24, 2018
from 03:00 PM to 04:00 PM
Where LH 006
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Abstract: In the presence of various length scales, the wave propagation problem, as well as those involving other kinds of dynamical phenomena (elastic waves, lattice waves or phonons, electronic transport, etc), starts to reveal new effects due to interplay between wave dispersion and structural features.

The present talk concerns an exposure to the analysis of discrete scattering effects in certain simple structures. As a prototype example of diffraction phenomenon, which is frequently present in above mentioned context, a discrete analogue of Sommerfeld diffraction by a half plane has been recently analysed for three different lattic structures: square, triangular, and hexagonal. The two simple cases that have been recently studied correspond to semi-infinite row with discrete Neumann condition and discrete Dirichlet condition. Both kinds of half-row `defects’ have been analyzed in infinite lattices as well as in waveguides using Fourier analysis.

The talk will give a flavour of the mathematical formulation and the mathematical techniques which are useful to derive some physically relevant entities; for the infinite lattice, an example of the latter is far-field approximation and for the waveguides, the reflectance and transmittance. The talk will also include some open problems associated with these newly emerging developments as well as some reflections on the ongoing work.

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