Applied/ACMS

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Applied and Computational Mathematics Seminar


Spring 2025

Date Speaker Title Host(s)
Jan 31 https://people.math.wisc.edu/~tgchandler/ Thomas Chandler] (UW)
Feb 7 https://www.colorado.edu/aps/adrian-fraser Adrian Fraser] (Colorado) Destabilization of transverse waves by periodic shear flows Spagnolie
Feb 14 TBA
Feb 21 TBA
Feb 28 https://nmboffi.github.io/ Nick Boffi] (CMU) Li
Mar 7 TBA
Mar 14 https://lu.seas.harvard.edu/ Yue Lu] (Harvard) [Colloquium] Li
Mar 21 https://people.llnl.gov/vogman1 Genia Vogman] (LLNL) Li
Mar 28 Spring Break
Apr 4 TBA
Apr 11 https://meche.mit.edu/people/faculty/pierrel@mit.edu Pierre Lermusiaux] (MIT) Chen
Apr 18 https://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine) [Colloquium]
Apr 25 https://www-users.cse.umn.edu/~bcockbur/ Bernardo Cockburn] (Minnesota) Transforming stabilization into spaces Stechmann, Fabien
May 2 https://sylviaherbert.com/ Sylvia Herbert] (UCSD) Chen

Abstracts

Adrian Fraser (Colorado)

Title: Destabilization of transverse waves by periodic shear flows

Periodic shear flows have the peculiar property that they are unstable to large-scale, transverse perturbations, and that this instability proceeds via a negative-eddy-viscosity mechanism (Dubrulle & Frisch, 1991). In this talk, I will show an example where this property causes transverse waves to become linearly unstable: a sinusoidal shear flow in the presence of a uniform, streamwise magnetic field in the framework of incompressible MHD. This flow is unstable to a KH-like instability for sufficiently weak magnetic fields, and uniform magnetic fields permit transverse waves known as Alfvén waves. Under the right conditions, these Alfvén waves become unstable, presenting a separate branch of instability that persists for arbitrarily strong magnetic fields which otherwise suppress the KH-like instability. After characterizing these waves with the help of a simple asymptotic expansion, I will show that they drive soliton-like waves in nonlinear simulations. With time permitting, I will discuss other fluid systems where similar dynamics are or may be found, including stratified flows and plasma drift waves.

Bernardo Cockburn (Minnesota)

Title: Transforming stabilization into spaces

In the framework of finite element methods for ordinary differential equations, we consider the continuous Galerkin method (introduced in 72) and the discontinuous Galerkin method (introduced in 73/74). We uncover the fact that both methods discretize the time derivative in exactly the same form, and discuss a few of its consequences. We end by briefly describing our ongoing work on the extension of this result to some Galerkin methods for partial differential equations.

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