Speaker: Joshua McGinnis, Drexel University
Title: “Rigorous justification for macroscopic waves in a two-dimensional lattice with random masses”

Abstract: The talk will discuss an almost sure approximation of solutions for the lattice differential equation mü = ∆u by an effective wave equation. Here, m (the masses) are i.i.d. random variables that are contained in some positive interval, and ∆ is a discrete Laplace operator. In particular, the talk will present the most important arguments in achieving a rigorous proof for the approximation in the case of a two-dimensional square lattice. The argument hinges upon classical results regarding sub-Gaussian random variables. The two-dimensional case will be contrasted with the one-dimensional case, and the role of dimensionality in the approximation will be discussed.

The Analysis and Applied Mathematics (AAM) Seminar is intended for Kennesaw State faculty working in the various areas of analysis and applied mathematics to get together to discuss their current work or related questions. Seminars often involve advanced mathematical knowledge. However, the seminars are open to anyone who is interested in attending.

This seminar will be held virtually.