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The Stephen H. Davis Lecture

The Stephen H. Davis Lecture honors the retirement of Stephen Davis, Walter P. Murphy Professor of Applied Mathematics and McCormick Institute Professor. Professor Davis’s contributions to fluid mechanics and materials science are well known, and the symposium celebrates his many fundamental and impactful contributions to the field.

2023 Stephen H. Davis Lecture

The 2023 Davis Lecture will be held on Monday, October 23, at 4:00 PM, in Tech LR4 featuring a lecture by Michael D. Graham of the University of Wisconsin-Madison. Register for in-person attendance. The lecture will also be broadcast via Zoom. Register for the webinar.

Michael D. Graham

Steenbock Professor of Engineering and Harvey D. Spangler Professor,
Department of Chemical & Biological Engineering, Department of Mechanical Engineering, University of Wisconsin-Madison

Data, Dynamics, and Manifolds: Machine Learning Approaches for Modeling and Controlling Complex Flows

Fluid flows often exhibit chaotic or turbulent dynamics and require a large number of degrees of freedom for accurate simulation. Nevertheless, because of the fast damping of small scales by viscosity, these flows can in principle be characterized with a much smaller number of dimensions, as their long-time dynamics relax in state space to a finite-dimensional invariant manifold. Classical data-driven methods for dimension reduction approximate this manifold as a flat surface, but for complex systems, this approach is severely limited.  We describe a data-driven reduced order modeling method,  “Data-driven Manifold Dynamics” (DManD), that finds a nonlinear coordinate representation of the manifold using a machine-learning architecture called an autoencoder, then learns an ordinary differential equation for the dynamics on the manifold. Exploitation of symmetries substantially improves performance. We apply DManD to a range of systems including transitional turbulence, where we accurately represent the dynamics with 25 degrees of freedom, as compared to the 105 degrees of freedom of the direct simulation. We then use the model to efficiently train a reinforcement learning control policy that is highly effective in laminarizing the flow. We also introduce an autoencoder architecture that yields an explicit estimate of manifold dimension. DManD can be combined with a clustering algorithm to generate overlapping local representations that are particularly useful for intermittent dynamics.


Michael D. Graham is the Steenbock Professor of Engineering and Harvey D. Spangler Professor of Chemical and Biological Engineering at the University of Wisconsin-Madison. He received his B.S. in Chemical Engineering from the University of Dayton in 1986 and his PhD. from Cornell University in 1992. After postdoctoral appointments at Houston and Princeton, he joined the faculty at Madison in 1994.
Professor Graham’s research interests include the dynamics of complex fluids, blood flow, swimming microorganisms; and nonlinear dynamics in Newtonian and complex fluids. He is author of two textbooks: Microhydrodynamics, Brownian Motion, and Complex Fluids and Modeling and Analysis Principles for Chemical and Biological Engineers (with James B. Rawlings).
Among Professor Graham’s professional distinctions are the François Frenkiel Award (2004) and Stanley Corrsin Award (2015) from the American Physical Society Division of Fluid Dynamics, and a 2018 Vannevar Bush Faculty Fellowship from the US Department of Defense.
Professor Graham has served as an Associate Editor of the Journal of Fluid Mechanics and as Editor-in-Chief of the Journal of Non-Newtonian Fluid Mechanics.  He is Past President of the Society of Rheology.

2022 Stephen H. Davis Lecture

The 2022 Davis Lecture was held on Wednesday, May 25, at 3:00 PM, featuring a lecture by Grae Worster of the University of Cambridge. The lecture was recorded and can be viewed online here.

Grae Worster

Professor of Fluid Dynamics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

The Dynamics of Super-absorbent Hydrogels

Worster's speech, "The Dynamics of Super-absorbent Hydrogels," will outline how he and his colleagues developed a new mathematical approach to model super-absorbent hydrogels, allowing for strongly nonlinear swelling while remaining linear in deviatoric strains, in effect treating hydrogels as instantaneously incompressible and linear elastic materials. Worster will describe this model and illustrate its features by solving simple examples of swelling spheres and transpiration through cylinders, and by analyzing different instabilities that can arise during swelling and drying. Worster will also introduce a hypothesis for a potential role of hydrogels in pumping water up very tall trees.

2021 Stephen H. Davis Lecture

The 2021 Davis Symposium was held on Monday, October 4, at 4:00 PM, featuring a lecture by Harry Swinney of the University of Texas at Austin. The lecture was recorded and can be viewed online here.

Harry Swinney

Professor, Physics, University of Texas, Austin

Crystallization in a periodically perturbed random granular medium

An understanding of crystal formation in a homogeneous disordered state can provide insights into crystallization in a fluid, such as the formation of ice crystals in water, which is still poorly understood. Experiments on packings of spheres over the past half century suggest that under repeated small disturbances, the spheres reach a “Random Close Packed” (RCP) state where the spheres occupy a maximum fraction of the container volume, 0.62-0.66. This talk will describe an experiment and numerical simulations on hard spheres that reveal that randomly packed spheres, after repeated small disturbances, occupy a well-defined volume fraction, 0.646±0.001. Further small disturbances lead to the nucleation of crystallites that, if they reach a critical size of 10-15 spheres, grow rapidly, and ultimately the container is filled with crystallites. 

Inaugural Stephen H. Davis Lecture

The inagural Stephen H. Davis Symposium was held October 15, 2019, featuring lectures by John Hinch of University of Cambridge, G.M. "Bud" Homsy of University of Washington, Detlef Lohse of University of Twente, and Parviz Moin of Stanford University.

John Hinch, Bud Homsy, Stephen Davis, Julio M. Ottino, Parviz Moin, Detlef Lohse

Symposium Speakers

John HinchJohn Hinch

Professor, Fluid Dynamics, University of Cambridge

Levitation and Locomotion on an Air-table of Plates with Herringbone Grooves

Experiments in ESPCI in Paris and numerical simulations in Darmstadt have shown that plates with herringbone grooves in their base are accelerated on a smooth air-table in the direction that the chevron grooves point, while smooth plates on an air-table with herringbone grooves are accelerated in the opposite direction. Newton's third law? Not quite. Hinch will discuss a simple two-dimensional model that is constructed of the air flow down a long channel with pressure-controlled influx across the lower boundary: lubrication theory with inertia or boundary layers without an outer flow. Limiting cases are considered of low and high Reynolds numbers, and of small and large pressure drop down the channel compared with the pressure drop across the porous plate; all tested against numerical solutions. The levitation and locomotion forces are calculated, with a relatively simple prediction for the locomotive acceleration; which fits the experimental data with plausible excuses. 

Bud HomsyG.M. "Bud" Homsy

Affiliate Professor, Mechanical Engineering, University of Washington

Some Interfacial Flow Problems

Homsy will discuss his work on interfacial flows that was inspired by and influenced by Stephen H. Davis, including interfacial instabilities in the presence of chemical reactions (reactive viscous fingering); flows driven by interfacial electrical stresses (electrospraying, chaotic advection); and problems involving contact line dynamics (evaporation over rough surfaces and coating over topography). 

Detlef LohseDetlef Lohse

Professor, Physics of Fluids, University of Twente

Segregation in Multicomponent Droplet Evaporation

While the evaporation of a single component droplet is well understood, the richness of phenomena in multicomponent droplet evaporation keeps surprising. Lohse's talk will show and explain several such phenomena, namely evaporation-triggered segregation, due to either weak solutal Marangoni flow or gravitational effects, and the evaporation of ternary liquid droplet, which can lead to spontaneous nucleation of droplets consisting of a new phase. He will also show how this new phase can be utilized to self-lubricate the droplet in order to suppress the coffee stain effects. The research shown in this talk combines experiments, numerical simulations, and theory. 

Parviz MoinParviz Moin

Founding Director of the Center for Turbulence Research and the Institute for Computational and Mathematical Engineering, Stanford University

Probing Turbulence Physics Using Numerical Simulation Databases - A Case Study in Predictive Science

With the exponential growth in computer power, high fidelity numerical simulations have provided unprecedented comprehensive datasets for the study of the mechanics of turbulent flows. Moin will share a brief review of fundamental research on the structure of wall-bounded turbulent flows with particular emphasis on the role played by large scale numerical simulations in conducting controlled experiments of discovery and the insights gained as a result. On the other hand, the early promise of direct numerical simulations to provide data to improve engineering models has not been fulfilled. He will expand on this in the context of lessons learned of the limitations of data science in the development of physical models.