Applied/ACMS

Applied and Computational Mathematics Seminar

• When: Fridays at 2:25pm (except as otherwise indicated)
• Where: 901 Van Vleck Hall
• Organizers: Maurice Fabien, Chris Rycroft, and Saverio Spagnolie,
• To join the ACMS mailing list: Send mail to acms+subscribe@g-groups.wisc.edu.

Spring 2025

Date	Speaker	Title	Host(s)
Jan 31	Thomas Chandler (UW)	Fluid–structure interactions in active complex fluids	Spagnolie
Feb 7	Adrian Fraser (Colorado)	Destabilization of transverse waves by periodic shear flows	Spagnolie
Feb 14	Jim Luedtke (UW)	Using integer programming for verification of binarized neural networks	Spagnolie
Feb 21	Vladimir Zhdankin (UW)	Exploring astrophysical plasma turbulence with particle-in-cell methods	Spagnolie
Feb 28	Nick Boffi (CMU)	TBA	Li
Mar 7	Suraj Shankar (Michigan)	TBA	Spagnolie
Mar 14	Yue Lu (Harvard) [Colloquium]	TBA	Li
Mar 21	Genia Vogman (LLNL)	TBA	Li
Mar 28	Spring Break
Apr 4	TBA
Apr 11	Pierre Lermusiaux (MIT)	TBA	Chen
Apr 18	Jack Xin (UC Irvine) [Colloquium]	TBA
Apr 25	Bernardo Cockburn (Minnesota)	Transforming stabilization into spaces	Stechmann, Fabien
May 2	Sylvia Herbert (UCSD)	TBA	Chen

Abstracts

Thomas G. J. Chandler (UW)

Title: Fluid-structure interactions in active complex fluids

Fluid anisotropy is central to many biological systems, from rod-like bacteria that self-assemble into dense swarms that function as fluids, to the cell cytoskeleton where the active alignment of stiff biofilaments is crucial to cell division. Nematic liquid crystals provide a powerful model for studying these complex environments. However, large immersed bodies elastically frustrate these fluids, leading to intricate interactions. This frustration can be alleviated through body deformations, at the cost of introducing internal stresses. Additionally, active stresses, arising from particle motility or molecular activity, disrupt nematic order by driving flows. In this presentation, I will demonstrate how complex variables enable analytical solutions to a broad range of problems, offering key insights into the roles of body geometry, anchoring conditions, interaction dynamics, activity-induced flows, and body deformations in many biological settings.

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.

Jim Luedtke (UW)

Title: Using integer programming for verification of binarized neural networks

Binarized neural networks (BNNs) are neural networks in which the weights are binary and the activation functions are the sign function. Verification of BNNs against input perturbation is one way to measure robustness of BNNs. BNN verification can be formulated as an integer linear optimization problem and hence can in theory be solved by state-of-the art methods for integer programming such as the branch-and-cut algorithm implemented in solvers like Gurobi. Unfortunately, the natural formulation is often difficult to solve in practice, even by the best such solvers, due to large integrality gap induced by its so-called "big-M" constraints. We present simple but effective techniques for improving the ability of the integer programming approach to solve the verification problem for BNNs. Along the way, we hope to illustrate more generally some of the strategies integer programmers use to attack difficult problems like this. We find that our techniques enable verifying BNNs against a higher range of input perturbation than using the natural formulation directly.

This is joint work with Woojin Kim, Mathematics PhD student at UW-Madison.

Vladimir Zhdankin (UW)

Title: Exploring astrophysical plasma turbulence with particle-in-cell methods

Plasmas throughout the universe (as well as in the laboratory) tend to exist in turbulent, nonequilibrium states due to their "collisionless" nature. Described by the Vlasov-Maxwell equations in a six-dimensional phase space (of position and momentum), the basic physics of such plasmas is difficult to model from first principles. There remain open questions about entropy production, nonthermal particle acceleration, energy partition amongst different particle species, and more. Particle-in-cell simulations are a numerical tool that allow us to explore in depth the rich dynamics and statistical mechanics of collisionless plasmas, validating analytical speculation. I will describe some of the results from my group's work on this topic.

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.

Archived semesters

• Fall 2024
• Spring 2024
• Fall 2023
• Spring 2023
• Fall 2022
• Spring 2022
• Fall 2021
• Spring 2021
• Fall 2020
• Spring 2020
• Fall 2019
• Spring 2019
• Fall 2018
• Spring 2018
• Fall 2017
• Spring 2017
• Fall 2016
• Spring 2016
• Fall 2015
• Spring 2015
• Fall 2014
• Spring 2014
• Fall 2013
• Spring 2013
• Fall 2012
• Spring 2012
• Fall 2011
• Spring 2011
• Fall 2010

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