Fluids Mechanics and Waves Seminar - Spring 2026

Seminars are held Mondays from 2:30 - 3:30 PM in CULM 611 and/or Zoom, unless otherwise noted.

For questions about the seminar schedule, please contact Thi Phong Nguyen.

Zoom Link for talks: https://njit-edu.zoom.us/j/99973535435?pwd=fUENHPxybbpXp2ImpWuXalrO26ErbP.1

*******************************************************************************************************

February 09 (Virtual Talk)

Kunlun Qi, Michigan State University

Fast Fourier spectral method for kinetic equations: from particle to wave

In this talk, I will present our recent progress on developing fast Fourier spectral methods for both classical kinetic equations and wave kinetic equations (WKE).

In the first part, we focus on the Boltzmann equation, a fundamental model bridging many-particle system with macroscopic fluid dynamics. We introduce an efficient spectral formulation that approximates the non-cutoff Boltzmann collision operator and accelerates its computation through fast Fourier transforms (FFT), achieving accuracy and efficiency comparable to the cutoff case. Despite the practical success of the approaches, stability remains a significant challenge due to the lack of positivity and conservation. To address this, we develop a new analysis framework establishing spectral accuracy via a refined $L^2$ estimate of the negative part of the numerical solution. In the second part, we extend the fast spectral methodology to the WKE, the core equation in wave turbulence theory. By reformulating the high-dimensional nonlinear wave kinetic operator into a spherical integral — mirroring the structure of the Boltzmann operator — we reveal a double-convolution structure in Fourier space. This structure enables an efficient FFT-based evaluation of the wave interaction integral. Throughout the talk, I will demonstrate the accuracy, efficiency, and robustness of the proposed methods through a variety of 2D and 3D numerical experiments, and I will highlight several interesting phenomena and conjectures that emerge from these simulations.

Homepage: https://kunlun-qi.github.io/

*******************************************************************************************************

February 23 (Virtual Talk)

Govanni Granados, University of North Carolina (UNC)-Chapel Hill

Recovering elastic subdomains with strain-gradient elastic interfaces from force measurements

In this talk, we introduce a new inverse problem for two-dimensional antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body that contains an inclusion separated by a thin interface endowed with higher-order surface energy. We show that the Dirichlet-to-Neumann map, which encodes displacement-stress measurements on the exterior boundary, uniquely recovers the mechanical parameters, as well as the shape of the inclusion. To address the inverse shape problem, we adapt the Factorization Method to handle the complications arising from a higher-order boundary operator and its nontrivial null space. Numerical examples will be presented in the unit circle.

Homepage: https://sites.google.com/view/govannigranadosmath/home

*******************************************************************************************************