Speaker: Mohsen Zayernouri, Department of Mechanical Engineering, FMATH Group, Michigan State University

Time : 15:00 - 16:00 CET (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

MS Teams : A link shall appear here - one hour before the talk. For best experince, please download the app.

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Non-Maxwellian Distributions, Turbulence-Closure at Particle Kinetics, Fractional Subgrid-Scale Dynamics, Pseudo-Turbulence in Materials

Abstract:  Nature remembers and is abundant with processes that exhibit heavy-tail distributions. The probabilistic consequences of such tails entail informative details, whose proper incorporations can directly contribute to new phenomena discoveries. This can happen via extracting and exploiting intrinsic features from (Lagrangian/Eulerian) data and by means of two-way linkage between the microscopic motions and their collective/continuum dynamics. To this end, we first tackle the only major unsolved problem in classical physics, i.e., Flow/Scalar Turbulence. By performing a novel statistical analysis and introducing a new nonlocal length scale in the inertial-convective subrange which codes intermittency in the jump processes, we derive a new spectral scaling law for the cascade of scalar variance that remarkably aligns with data. Next, we mathematically show that this spectral law in turn leads to a new nonlocal dynamic subgrid-scale (SGS) model for the large-eddy simulation (LES) of scalar turbulence, surpassing the current state-of-the-art and dynamic LES approaches in an unprecedented way. On the numerical analysis side, the k-fold cross-validation of nonlocal convective/advective-diffusive models often introduces a range of solution singularities, rendering the underlying Sobolev spaces’ fractional indices random. We first review some major developments in fractional and tempered fractional Sturm-Liouville eigen-problems, providing tunable basis/test functions with attractive spectral properties. Subsequently, we introduce our notion of “Distributed Sobolev Spaces”, which helps rigorously obtain the corresponding variational formulation for the resulting distributed PDEs. We will next present a variant of Petrov-Galerkin spacetime spectral method for fully distributed advection-diffusion-reaction PDEs along with a uni- fied fast solver with optimal complexity in any (1 + d) dimensions. We finally reveal several new exciting research fronts, where our proposed stochastic multi-scale approach in discovering predictive generalized-order models appear to make a noticeable difference in the context of complex/polymeric and aging materials in energy, defense, and health applications.

Biography:  Dr. Zayernouri is an Associate Professor of Mechanical Engineering at MSU. He obtained his 2nd PhD in Applied Mathematics at Brown University and his 1st PhD in Mechanical Engineering at the University of Utah. His research brings to bear cutting-edge tools from mathematical physics, applied mathematics, and data sciences to develop kinetics-to-hydrodynamics turbulence modeling, memory-dependent stochastic L\'evy processes in turbulent flows, long-range and highly correlated nonlocal transports, supersonic and non-equilibrium condensing flows, in addition to sub-/super-/distributed-order diffusion processes. The main thrust of Dr. Zayernouri's research in his FMATH group is on stochastic fractional-order modeling, spectral (eigen-problems) theories, forward/inverse uncertainty quantification \& qualification, nonlocal numerical analysis, semi-supervised statistical learning employing Lagrangian/Eulerian data, and computational fluid dynamics. 

Dr. Zayernouri has already supervised and graduated 10 PhDs, moreover, he is the recipient of the ARO YIP and AFOSR YIP awards. He recently lead-authored a new book on: ``Spectral and Spectral-Element Methods for Fractional ODEs/PDEs'' by the Cambridge University Press.

Bibliography

[1] Zayernouri, M., Wang, L.-L., Shen, J., & Karniadakis, G. E. (2024). Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations. Cambridge University Press, Cambridge.
[2] Samiee, M., Akhavan-Safaei, A., & Zayernouri, M. (2022). Tempered fractional LES modeling. Journal of Fluid Mechanics, 932, A4.
[3] Seyedi, S. H., Akhavan-Safaei, A., & Zayernouri, M. (2022). Dynamic nonlocal passive scalar subgrid-scale turbulence modeling. Physics of Fluids, 34(10).
[4] Akhavan-Safaei, A., & Zayernouri, M. (2023). Deep Learning of Subgrid-Scale Dynamics in Scalar Turbulence and Generalization to Other Transport Regimes. Journal of Machine Learning for Modeling and Computing.
[5] de Moraes, E. A. B., D’Elia, M., & Zayernouri, M. (2023). Machine learning of non-local micro-structural defect evolutions in crystalline materials. Computer Methods in Applied Mechanics and Engineering, 403, 115743.
[6] Khoshnevis, A., Tzelepis, D. A., Ginzburg, V. V., & Zayernouri, M. (2025). Stochastic Generalized-Order Constitutive Modeling of Viscoelastic Spectra of PolyureaGraphene Nanocomposites. Engineering Reports, 7(9), e70367