Fluids Mechanics and Waves Seminar - Fall 2025

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

Zoom Link for talks: https://njit-edu.zoom.us/j/94900620988?pwd=4nzLPpUHCMK0ZU6REylbdsvGxa2Ys1.1

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September 08 (Online Talk)

Thu Le, University of Wisconsin-Madison

Fast and Stable Methods for Inverse Scattering: Integrating Sampling, Deep Learning, and Experimental Validation

We consider inverse scattering problems that aim to reconstruct the geometry of unknown objects from boundary measurements of scattered data at a fixed frequency. These problems have applications in radar and nondestructive testing, and are challenging to solve due to their nonlinear and ill-posed nature. In this talk, I will discuss two fast approaches that integrate sampling methods with deep learning and experimental validation. First, for acoustic scattering governed by the Helmholtz equation under limited data from a single incident wave, we combine a sampling-type technique with a deep neural network.  The sampling image initializes the network, then a U-Net enhances the result. Fast computation and prior information from the sampling step help accelerate training. This combined approach significantly improves reconstruction quality. Next, we study a modified sampling method for electromagnetic waves governed by Maxwell’s equations. We provide theoretical justification and apply it to invert unprocessed 3D experimental data from the Fresnel Institute. Although the theory assumes full-aperture data, the method performs well on sparse, limited-aperture data without preprocessing. This shows that the method is practical, easy to implement, and remains accurate and robust to noise. This is joint work with Dinh-Liem Nguyen, Hayden Schmidt, Vu Nguyen, and Trung Truong.

Homepage: https://people.math.wisc.edu/~tle38/

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September 22 (Online Talk)

Mingtao Xia, University of Houston

A novel Wasserstein-distance method for reconstructing stochastic differential equations from time-series data

In this talk, I will introduce two novel Wasserstein-distance-based uncertainty quantification methods I developed for aiming at quantifying intrinsic fluctuations and extrinsic noise with applications in reconstructing noisy single-cell molecular dynamics. The methods I shall discuss include: i) a time-decoupled squared Wasserstein-2 method for efficient training of neural stochastic differential equations as surrogate models for approximating stochastic processes that capture intrinsic fluctuations of intracellular protein and mRNA counts over time and ii) a local squared Wasserstein-2 method for reconstructing uncertain models with latent variables or uncertain parameters, which aim to quantify heterogeneities among cells.

Homepage: https://sites.google.com/nyu.edu/mingtao-xia/home

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October 6

Pierre Amenoagbadji, Columbia University

Wave propagation in junctions of periodic half-spaces

Periodic media appear naturally in many areas of physics, and have drawn particular interest especially with the advent of photonic crystals. Understanding how waves propagate in such media is essential for the design of practical applications.

This talk focuses on the analysis and numerical solution of PDE models for time-harmonic wave propagation at interfaces between two-dimensional periodic half-spaces. While most existing approaches assume periodicity of the medium along the interface, we investigate the more delicate case where this assumption no longer holds. Our analysis relies on the crucial observation that the medium has a quasiperiodic structure along the interface, meaning it can be viewed as a slice of a three-dimensional periodic medium. This enables us to seek solutions to our PDE as restrictions of solutions to an augmented elliptically degenerate PDE set in three dimensions, where periodicity along the interface is recovered.

Based on joint work with Sonia Fliss and Patrick Joly, I will first show how this so-called lifting approach can be used to numerically solve the time-harmonic wave equation in junctions of periodic half-spaces. I will then present ongoing work with Michael Weinstein, where the lifting approach is used to define and study edge states in honeycomb structures perturbed along irrational edges.

Homepage: https://pierreamenoagbadji.github.io

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October 20

Solomon Quinn, Flatiron Institute

Integral formulation of Dirac singular waveguide

This talk concerns a boundary integral formulation for the two-dimensional massive Dirac equation. The mass term is assumed to jump across a one-dimensional interface, which models a transition between two insulating materials. This jump induces surface waves that propagate outward along the interface but decay exponentially in the transverse direction. After providing a derivation of our integral equation, we establish that it has a unique solution for almost all choices of parameters using holomorphic perturbation theory. We then implement a fast numerical method for solving our boundary integral equation and present several numerical examples of solutions and scattering effects.

Homepage: https://www.simonsfoundation.org/people/solomon-quinn/

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November 03 (Online Talk)

Marcella Bonazzoli, Inria and Institut Polytechnique de Paris

Seismic imaging of a dam-rock interface using Full Waveform Inversion

In this talk we are interested in reconstructing the interface between the concrete structure of a hydroelectric gravity dam and the underlying rock, using Full Waveform Inversion. Indeed, it appears that the roughness of the dam-rock interface has an effect on the sliding stability of gravity dams.

We minimize a regularized misfit cost functional by computing its shape derivative and iteratively updating the interface shape by the gradient descent method. At each iteration, we simulate time-harmonic elasto-acoustic wave propagation models, coupling linear elasticity in the solid medium with acoustics in the reservoir. Numerical results using realistic noisy synthetic data demonstrate the method ability to accurately reconstruct the dam-rock interface, even with a limited number of measurements.

Homepage: https://mbonazzo.gitlabpages.inria.fr

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November 24

Kangbo Li, Rensselaer Polytechnic Institute (RPI)

A Galerkin Discretization of Bloch Waves

In a periodic supercell, the position of a particle is not represented by the position operator. As a result, subsequent observables are evaluated by adapting standard quantum operators before correcting for the errors due to finite particle numbers. In this paper, we show that the infinite particle limit can be taken through analytic means, thus avoiding the supercell and its extensive ramifications in condense matter theory and software.

Homepage: https://kangbo.dev/ 

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December 8 (Online Talk)

Pip Matharu, Max Planck Institute for Mathematics in the Sciences

Unraveling Self-Similar Energy Transfer Dynamics: a Case Study for 1D Burgers System

In this talk I will discuss the problem of constructing initial conditions such that the resulting flow evolution leads to a self-similar energy cascade consistent with Kolmogorov's statistical theory of turbulence. As a first step in this direction, we focus on the one-dimensional viscous Burgers equation as a toy model. Its solutions exhibiting self-similar behavior are found by framing these problems in terms of PDE-constrained optimization. The main physical parameters are the time window over which self-similar behavior is sought (equal to approximately one eddy turnover time), viscosity (inversely proportional to the "Reynolds number"), and an integer parameter characterizing the distance in the Fourier space over which self-similar interactions occur. Local solutions to these nonconvex PDE optimization problems are obtained with a state-of-the-art adjoint-based gradient method. Two distinct families of solutions, termed viscous and inertial, are identified and are distinguished primarily by the behavior of enstrophy which, respectively, uniformly decays and grows in the two cases. The physically meaningful and appropriately self-similar inertial solutions are found only when a sufficiently small viscosity is considered. These flows achieve the self-similar behaviour by a uniform steepening of the wave fronts present in the solutions. The successful application and adaptability of the proposed methodology naturally leads to an encouraging avenue for this approach to be employed to systematically search for self-similar flow evolutions in the context of three-dimensional turbulence.

Homepage: https://pipmath.github.io

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Last updated: November 6, 2025