# Modeling and Simulation Group Meeting

#### Extending spectral methods to Brownian inextensible filament hydrodynamics

**Speaker:**
Ondrej Maxian, partner Paul Beckman, Courant Institute, NYU

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, February 2, 2023, 12:45 p.m.

**Synopsis:**

Paul Beckman will introduce detailed balance in Markov Chains.

Main talk (slides for talk, paper)

I will present our new spectral method for the simulation of bending fluctuations in inextensible slender filaments in Stokes flow. The method is based on three major contributions: first, we discretize the filament centerline using a coarse non-uniform Chebyshev grid, on which we formulate a discrete constrained Gibbs-Boltzmann (GB) equilibrium distribution and overdamped Langevin equation for the evolution of the unit-length tangent vectors. Second, we define the hydrodynamic mobility at each point on the filament as an integral of the Rotne-Prager-Yamakawa kernel along the centerline, and apply a spectrally-accurate "slender-body'' quadrature to accurately resolve the hydrodynamics. Third, we propose a novel midpoint temporal integrator which can correctly capture the Ito drift terms that arise in the overdamped Langevin equation. After presenting the method, I will show that as few as 12 Chebyshev nodes provide a good approximation to the dynamics of fiber relaxation while allowing a time step size two orders of magnitude larger than a more resolved simulation carried out with a more traditional spatial discretization. I will conclude by applying our approach to a suspension of cross-linked semiflexible fibers, studying how semiflexible fluctuations affect bundling dynamics.