Seminar Schedule – Spring 2019

Thursday, April 11, 2019
Time: 3:30pm
Place: ASE 1.126

Wave Propagation in Lattices and Structured Media

Basant Sharma, Indian Institute of Technology, Kanpur

The topic of this talk arises in applications of current interest such as manufacturing materials with desired properties, signature left on the wave propagation features by certain defects, etc. Although this subject is classical there is a growing interest associated with the development of, so called, meta materials, In these applications, in general, a question arises about the transport of mechanical energy, its guidance, and the conversion/interchange between different modes.Although the applications typically involve three dimensional structures, often it is possible to reduce the study to two-dimensional and quasi-one-dimensional models. Further, for simplicity of mathematical analysis, the attention will be restricted to out-of-plane motion only. I will discuss three different problems:surface localized waves in lattice waveguides with honeycomb structure, energy transmission in bifurcated square lattice waveguides, and wave guidance via a (mode-III) crack in triangular lattice. From the point of view of mathematical tools, the first and second topic involve an application of elementary linear algebra and Chebyshev polynomials, while the second and third topic also involve Wiener-Hopf technique. If time permits, I will discuss wave propagation across an array of defects on square lattice.

Short Biography:

Basant Lal Sharma received his Bachelors of Technology in Mechanical Engineering from the Indian Institute of Technology Bombay, Powai, Mumbai, India in 1999. In 2004 he received a Ph.D. in Mechanics (P.Rosakis) from the Cornell University, Ithaca, NY, USA. After post-doctoral positions at Cornell University (S.H. Strogatz) and École Polytechnique, Palaiseau, Paris, France (L. Truskinovsky), he joined the Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India in January 2007 as a Faculty member. He is interestedin studying physical phenomena that occur due to the presence of small length scales, for example, the structure and dynamics of defects in crystal. Since summer 2011, he has been interested in discrete scattering theory.

For further information, please contact Dr. Rui Huang at ruihuang@mail.utexas.edu or (512) 471-7558.