IMath Seminar (Feb 18): Dr. Akambadath K. Nandakumaran
You are all invited to a seminar featuring:
Dr. Akambadath K. Nandakumaran, Department of Mathematics, Indian Institute of Science (hosted by the DE Group)
Talk:Mathematics of Micro-structures: Multi-scale Analysis and Theory of Homogenization
This is an in-person event and it will be held on Tuesday, February 18, 2025, 2:30 PM at the Conference room.
Abstract:
Micro-structures and hence multi scales arise in many physical and industrial problems. Many industrial constructions include very complicated structures. Homogenization is a branch of mathematics where we try to understand microscopic structures via a macroscopic medium. This study is basically developed from material science in the creation of composite materials though the present application is much far and wide. It has applications in composite media, porous domains, laminar structures, domains with rapidly oscillating boundaries, to name a few. The PDE problems posed on such complicated domains lead to a type of asymptotic analysis known as homogenization. It is a process of understanding the microscopic behavior of an in-homogeneous medium via a homogenized medium. Though the physical applications are pretty much old, the mathematical theory is quite recent especially after the development of modern functional analysis. There are various methods developed in the last 50 years to understand the mathematical homogenization theory and some of them are: Asymptotic Expansion, Energy Method, Compensated Compactness, Two-scale and multi-scale convergence, Gamma Convergence, Bloch Wave Analysis , Method of Unfolding etc.
We present a very general talk to address the wider audience from different disciplines and try to minimize the
mathematical difficulties involved. At the same time, we indicate the complications and the importance of studying it
mathematically. We introduce multi-scale convergence and method of unfolding, and our main aim is to present
various results established from my group.