# Modeling and Simulation Group Meeting

#### Mini-festival of 4th years

**Speaker:**
Mariya Savinov, Olivia Pomerenk, Ryan Du, Paul Beckman, Courant Institute

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, September 28, 2023, 12:30 p.m.

**Synopsis:**

This is a minifestival of short, 10-15 minute presentations by current 4th years working in applied and computational mathematics at Courant.

Mariya will discuss their work with Prof. Alex Mogilner on the modeling and simulation of various cell skeleton structures and their dynamics. They will outline two of their published works: the first on size-dependent periodic contractile dynamics of cell extracts in water droplets, and the second on how friction can robustly control *in vitro* actomyosin contraction. Finally, Mariya will introduce ongoing research in which they utilize the immersed boundary method to investigate the dynamics of stress fibers.

Olivia will talk about her work with Leif Ristroph on the existence and stability of equilibria of free-falling thin flat plates. She will first prove the existence of a unique equilibrium gliding mode for any choice of physical properties of the plate, and then explore the stability of such equilibria using linear stability analysis. She will conclude by proposing a new flight mode in addition to those characterized in previous literature, and show some preliminary experimental demonstrations of its existence.

Ryan will show simulations of a balanced model of the ocean. At the scale of O(1-10 km), the ocean flow exhibits statistical asymmetries because of the abundance of fronts at that scale. The balanced model is a reduced-order model from the full fluids equation that can capture these statistical asymmetries and the growth of fronts.

Paul will discuss ongoing work with Mike O’Neil on numerical methods for elliptic PDEs with random boundary data. In the case where the boundary data is a Gaussian process, we will construct boundary integral equation representations of the covariance of the solution, and apply these methods to build statistical models of experimental data in acoustic and electromagnetic scattering problems.