Department of Mathematical Sciences

The problem of electrohydrodynamic drop deformation is well understood in the case where the external electric field is weak. In one of his many celebrated papers (Proc. R. Soc. A, 291 1425 159-166, 1966), G. I. Taylor worked out a complete theory in this limit, including analytical expressions for the electrohydrodynamic flow engendered within and outside of the drop by the electric field acting on its own induced interfacial charge.

In this talk, Dr. Ehud Yariv will employ numerical and asymptotic tools to explore the effects of interfacial-charge convection, which were neglected by Taylor but become important in strong electric fields. In particular, he will analyze (in 2D, for simplicity) how Taylor’s fore-aft symmetric solution evolves as the electrical Reynolds number is increased from zero to arbitrarily large values. What shall be found is hinted at by the title of the talk. Connections between the results, numerical evidence in the literature for the formation of equatorial interfacial-charge “shocks” (a term which we shall challenge), and strong-field experiments exhibiting equatorial streaming, pattern formation, and transition to spontaneous drop rotation will be discussed.

Speaker: Dr. Ehud Yariv, Professor, Department of Mathematics, Technion-Israel Institute of Technology

Date/Time: December 6, 2023 at 3:30 p.m.

Location: Howe Center 104 (w/ virtual option)

For additional information, please see the Upcoming Seminars and Events below.

From June 14-16, 2023, the Department of Mathematical Sciences at Stevens will organize a conference on group theory and its applications in honor of the 80th birthday of Professor Robert Gilman.

Gilman is the director and a cofounder of the Algebra and Cryptology Center who has spent his professional career at Stevens and established himself as a leading expert in multiple subfields of algebra.

The three-day conference, titled Groups and Computation: Interactions Between Geometric Group Theory, Computability and Computer Science, will feature talks by internationally renowned experts and long-time collaborators of Gilman, including several members of the Department of Mathematical Sciences. Some talks will be on the Stevens campus; others will be held online. For more information, please visit the conference website linked below.

Kathrin Smetana, assistant professor of mathematics at Stevens Institute of Technology, was recently awarded a five-year, $461,998 grant through the National Science Foundation (NSF)’s prestigious CAREER program to develop “Randomized Multiscale Methods for Heterogeneous Nonlinear Partial Differential Equations.” In her project, Smetana and her students will focus on designing multiscale methods via randomization techniques that have originally been proposed in the context of data science. They will use these randomization techniques to detect hidden structures in the local numerical simulation data, such as the simulations of the deformation of portions of wind turbines, and, in particular, to detect the functions that are relevant for the approximation of the solution of the PDE.