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. 

Department of Mathematical Sciences

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 

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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/ 

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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 

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March 09

Ricardo Barros, Loughborough University, UK

Mode-1 and mode-2 internal solitary waves in a three-layer fluid

There are infinitely many propagation modes in a continuously density-stratified fluid. In the ocean, more than 90% of the kinetic energy associated with internal solitary waves (ISWs) resides in the first two baroclinic modes (mode-1 and mode-2). To investigate the main characteristics and complex behaviour of these waves, we consider stratifications featuring a double pycnocline which, when sufficiently sharp, can be effectively approximated by a three-layer fluid system. Within this reduced framework, we provide a comprehensive classification of mode-1 ISWs and reveal the existence of mode-2 ISWs characterised by multi-humped profiles. Our findings are validated through comparison with solutions of the fully nonlinear Euler theory.

Homepage: https://www.lboro.ac.uk/departments/maths/staff/ricardo-barros/ 

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March 11 (Special Addition)

Alex Doak, University of Bath, UK

Free-surface flows past a point vortex

In this talk, I will present a numerical method for computing free-surface flows in which a point vortex lies inside the domain. We start by revisiting the gravity-free case, where an analytic solution was derived by Gurevich and extended by Shaw. We then demonstrate how to modify the method to include gravity. Finally, we extend the result to include multiple point vortices.

Homepage: https://researchportal.bath.ac.uk/en/persons/alex-doak/ 

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March 23

Giuseppe Pucci, CNR-Nanotec at the University of Calabria, Italy

Wave-driven active systems at fluid interfaces

Active systems consist of self-driven units that convert energy from their environment into motion or mechanical forces. Their study has motivated efforts to extend statistical mechanics to nonequilibrium systems. Most work to date has focused on two limiting regimes: overdamped systems, such as bacteria and colloids, whose interactions are mediated by viscous flows that decay monotonically with distance, and inertial systems, such as flocks of birds or schools of fish, characterized by complex spatiotemporal interactions.

In this talk, I will review recent work on wave-driven active systems at vibrating fluid interfaces, which operate in an intermediate regime where both viscosity and inertia play important roles. In these systems, interactions are mediated by surface waves and are therefore spatiotemporally oscillatory, leading to collective behaviors that differ qualitatively from those observed in more conventional active matter.

I will first present hydrodynamic spin lattices, an active system composed of droplets that orbit in submerged wells while interacting through the waves they generate on a vibrating bath [1]. The resulting wave-mediated coupling gives rise to emergent collective states with striking analogies to magnetic ordering in electronic systems.

In the second part of the talk, I will introduce recent work on capillary surfers [2,3] and capillary spinners [4], asymmetric solid particles that propel or rotate at a vibrating fluid interface through asymmetric wave generation. Their propulsion speed and interactions can be tuned through particle geometry, fluid properties, and vibration parameters. Surfers interact through their mutual capillary wavefield and exhibit multiple bound states characterized by discrete equilibrium spacings, while spinners display synchronization phenomena arising from wave-mediated coupling.

These systems provide a tunable platform for exploring active matter with oscillatory long-range interactions at intermediate Reynolds numbers.

[1] Sáenz et al. Nature 596, 58 (2021).
[2] Ho et al. Phys. Rev. Fluids 8, L112001 (2023).
[3] Oza et al. Phys. Rev. Fluids 8, 114001 (2023).
[4] Barotta et al. Phys. Rev. E 111, 035105 (2025).

Homepage: https://www.gpucci.net/ 

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April 06

Uyen Le, Texas A&M University - Corpus Christi

Existence and Stability of Periodic Waves in the Fractional Korteweg de Vries Equation

The fractional Korteweg–de Vries (fKdV) equation models the unidirectional propagation of weakly nonlinear dispersive waves of long-wavelength. The existence of periodic waves in the fKdV equation has been studied using fixed point, perturbative, and variational methods. From the point of view of variational method, the periodic waves are characterized as constrained minimizers of the energy functional subject to fixed mass and momentum. In this talk, we are going to discuss two results regarding the existence and stability of the periodic waves of the fKdV equation. First, we are going to show the existence of positive periodic solution by proving that the Green’s function for the linear operator in the fKdV equation is strictly positive. Second, in the context of variational method, we are going to propose an alternative framework in which the periodic waves are constrained minimizers of the quadratic form of energy subject to fixed cubic part of energy and the zero mean. This new characterization allows us to fully unfold the region of existence of the periodic waves and to establish a sharp stability criteria based on the monotonicity of the map from the wave speed to the wave momentum.

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April 07 (Special Addition)

Pouria Behnoudfar, University of Wisconsin-Madison

Bridging idealized and operational models: an explainable AI framework for Earth system emulators

Computational models are indispensable for understanding complex dynamical systems. High-fidelity operational models offer rich resolution and comprehensive state descriptions but often suffer from persistent biases, particularly in extreme events and long-term statistics. At the other end of the spectrum, coarse-grained idealized models isolate fundamental processes and can be precisely calibrated to excel in characterizing specific dynamical and statistical features. However, different models remain siloed by disciplinary boundaries. In this talk, we present an explainable AI framework that bridges the model hierarchy through a reconfigured latent data assimilation technique, uniquely suited to exploit the sparse output from the idealized models. The resulting bridging model inherits the high resolution and comprehensive variables of operational models while achieving global accuracy enhancements through targeted improvements from idealized models. Crucially, the mechanism of AI provides a clear rationale for these advancements, moving beyond black-box correction to physically insightful understanding in a computationally efficient framework that enables effective physics-assisted digital twins and uncertainty quantification. We demonstrate its power by significantly correcting biases in CMIP6 simulations of El Niño spatiotemporal patterns, leveraging statistically accurate idealized models.

Homepage: https://scholar.google.com/citations?user=Imuw5CMAAAAJ&hl=fa 

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April 20

Xin Guan, Imperial College London

Title/Abstract Forthcoming

Homepage: https://scholar.google.com/citations?user=N0ISMdYAAAAJ&hl=en 

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May 04

Matteo Polimeno, NJIT

Title/Abstract Forthcoming

Homepage: https://scholar.google.com/citations?user=Pna2K9wAAAAJ&hl=it 

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Last edited: April 1, 2026