Fluids Mechanics and Waves Seminar - Spring 2025

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

February 27

Jiajie Chen, Courant Institute, New York University

Singularity Formation in Fluids

Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is a long-standing open problem in mathematical fluid mechanics. In this talk, I will begin by providing an overview of this problem and then introduce a framework for stable, nearly self-similar blowup, developed in joint work with Tom Hou (Caltech). Using this framework, we establish singularity formation in the incompressible Euler equations with smooth data and boundary. Additionally, I will briefly present recent results on vorticity blowup in compressible Euler equations and beyond, using the self-similar blowup method.

Homepage: https://jiajiechen94.github.io/

March 10

Svetlana Tlupova, Farmingdale State College, State University of New York

Regularization based methods for evaluating single and double layer surface integrals in Stokes flow

We will give an overview of joint work with J. Thomas Beale on numerical methods for computing the single and double layer integrals on closed surfaces in Stokes flow. The Stokeslet and stresslet kernels are singular when evaluated on the surface and nearly singular when evaluated near the surface, which is the most difficult case to compute accurately. The kernels are first regularized, or smoothed out, using a length scale parameter. In one approach, corrections for the smoothing error are derived analytically using local analysis and added to obtain about third order accuracy. As an alternative approach, an extrapolation strategy is to compute the regularized integral for three choices of the smoothing parameter and solve for the extrapolated value of the integral with about fifth order accuracy. When evaluating the integrals on the surface, as needed when solving integral equations, special smoothing can be used so that high accuracy is obtained without needing corrections or extrapolation.

Homepage: https://www.farmingdale.edu/faculty/?fid=52171

March 24

Xuenan Li, Columbia University

Deformations in Soft Mechanical Metamaterials: Modeling, Analysis, and Applications

Mechanical metamaterials are synthetic materials that exhibit microscale buckling in response to mechanical deformation. These artificial materials are like elastic composites but sometimes more degenerate since they can deform with almost zero elastic energy. We call such deformations with very small elastic energy mechanisms. In this talk, I will focus mainly on a rich example, the Kagome lattice metamaterial, which has many mechanisms that might seem incompatible with having a meaningful macroscopic energy at first sight. I will discuss our model of the Kagome lattice metamaterial, which allows us to obtain a well-defined effective energy, and further discuss the large-scale elastic behavior. Our macroscopic theory reveals that compressive conformal maps are the only deformations that achieve zero effective energy. This is a joint work with Robert V. Kohn.

If time permits, I will also discuss the algebraic singularity in the Kagome lattice metamaterial, which leads to the existence of an infinite number of mechanisms. In fact, such algebraic singularity can be understood by a constrained saddle search perspective, and we provide a numerical algorithm that can find new singular structures. This is a joint work with Miranda Holmes-Cerfon and Christian D. Santangelo.

Homepage: https://xuenanli.github.io/ 

April 7

Shanyin Tong, Columbia University

A policy iteration method for inverse mean field games

Mean-field games (MFGs) model non-cooperative games among large populations of agents and are widely applied in areas such as traffic flow, finance, and epidemic control. Inverse mean-field games address the challenge of inferring environmental factors from observed agent behavior. The coupled forward-backward structure of MFG equations makes solving these problems difficult and adds even greater complexity to their inverse problems. In this talk, I will introduce a policy iteration method for solving inverse MFGs. This method simplifies the problem by decoupling it into solving linear PDEs and linear inverse problems, leading to significant computational efficiency. The approach is flexible, accommodating a variety of numerical methods and machine learning tools. I will also present theoretical results that guarantee the convergence of our proposed method, along with numerical examples demonstrating its accuracy and efficiency.

Homepage: https://www.apam.columbia.edu/shanyin-tong

April 9

Mathieu Sellier, University of Canterbury

Inferring rheological properties from free surface measurements

Viscometric flows refer to a type of flow characterized by simple shear, elongational, or a combination of both, where the stress is proportional to the rate of strain. Rheometers always aim to produce consistently viscometric flow conditions to enable the repeatable and reliable characterisation of fluid samples under well controlled conditions. Unfortunately, many situations occur when the rheological properties of a fluid need to be quantified but viscometric flow conditions cannot be achieved in practice. In the talk, I will present a number of free surface flows which are not viscometric as they do not exhibit a uniform state of strain rate but are “rheometric” nonetheless as the combination of free surface measurements with careful mathematical modelling and numerical simulations still enables the inference of useful rheological information.

Homepage: https://profiles.canterbury.ac.nz/Mathieu-Sellier

April 21

Dinh-Liem Nguyen, Kansas State University

Direct reconstruction methods for inverse source and scattering problems with single-frequency data

Inverse source and scattering problems involve determining an unknown object from indirect measurements associated with the object. These problems, which arise in a variety of applications such as nondestructive testing, radar, medical imaging, and geophysical exploration, have been an active research topic in the mathematics, engineering, and physics communities for several decades. However, they are highly ill-posed and nonlinear, posing significant challenges in developing efficient numerical methods for their solution. In this talk, we will present our recent results in developing sampling-type methods with novel imaging functions for solving inverse source and scattering problems using boundary data at a single frequency. Theoretical justifications and numerical simulations of the proposed method will be discussed. Our approach is non-iterative, computationally efficient, and straightforward to implement. This talk is based on joint work with Isaac Harris, Tran Lan, and Thu Le.

Homepage: https://sites.google.com/site/dinhliemnguyen/home

May 5

Andrew Hofstrand, New York Institute of Technology

Nonlinear Waves in Lattices

Since the famous Fermi-Pasta-Ulam-Tsingou (FPUT) experiment of the 1950’s, the study of nonlinear waves in lattices has played a fundamental role in shaping our broad understanding of nonlinear phenomena. In this talk, we give an overview of recent results on 1.) the stability of traveling wave solutions to a continuum description for a nonlinear variant of the well-known Su-Schrieffer-Heeger (SSH) model and 2.) the construction of time-periodic, spatially localized solutions known as discrete breathers in a honeycomb lattice and their connection to gap solitons near a so-called semi-Dirac point. Part of this work is in collaboration with Huaiyu Li and Michael Weinstein.

Homepage: https://site.nyit.edu/bio/ahofstra

Last edited: April 28, 2025