Measures of Chaotic Advection in Simulations of Active Nematics
Abstract
Active nematics are non-equilibrium fluids composed of rod-like self-propelled units that collectively generate large-scale coherent flows. Here, we focus on a canonical experimental system: an active nematic fluid in 2D driven by ATP, composed of densely packed, extended microtubule (MT) bundles cross-linked by kinesin motors. An intriguing feature of this system is the creation and annihilation of topological defects with topological charge ±1/2, due to the fracturing of the material. Experiments confirm that the positive (+1/2) defects serve as "virtual stirring rods" that move around each other in a complex braiding pattern. This collective braiding motion of positive defects stretches and folds the fluid itself, i.e., produces macroscale chaotic advection. The degree of self-mixing due to the chaotic advection can be measured using topological entropy and the Lyapunov exponent. Our goal is to determine whether continuum models of MT-based active nematic fluid can reproduce these measurements. To this end, we use two continuum models: the traditional Beris-Edwards (BE) model and the more recently developed Beris-Edwards model with enhanced nematic locking (BENL). The difference between the two models is the adoption of the "nematic locking principle", which states that an individual MT bundle cannot rotate independently of its neighbors due to steric interactions among elongated dense MT bundles. This principle holds in the BENL model except in small localized areas of the material domain where the material fractures, specifically near the creation and annihilation of topological defects. We employ several numerical methods to estimate measures of chaotic advection using both models. Our study shows that the BENL model more accurately reproduces experimental measures of self-mixing driven by chaotic advection in MT-based active nematic fluids.
Related
- The shifting reign of force in active nematics
- Integer defects in active nematics of ellipsoidal Quincke rollers
- Competing routes to spontaneous flow in confined active nematics
- Spontaneous Vortex Instability in Active Nematics
- Modeling density variations in two-dimensional microtubule-based active nematics
BibTeX
@misc{sabbir2026measures,
title = {{Measures of Chaotic Advection in Simulations of Active Nematics}},
author = {Md Mainul Hasan Sabbir and Brandon Klein and Daniel A. Beller and Kevin A. Mitchell},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38509},
eprint = {2609.38509},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38509},
}
RIS
TY - UNPB
TI - Measures of Chaotic Advection in Simulations of Active Nematics
AU - Md Mainul Hasan Sabbir
AU - Brandon Klein
AU - Daniel A. Beller
AU - Kevin A. Mitchell
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38509
UR - https://arxiv.org/abs/2609.38509
AB - Active nematics are non-equilibrium fluids composed of rod-like self-propelled units that collectively generate large-scale coherent flows. Here, we focus on a canonical experimental system: an active nematic fluid in 2D driven by ATP, composed of densely packed, extended microtubule (MT) bundles cross-linked by kinesin motors. An intriguing feature of this system is the creation and annihilation of topological defects with topological charge ±1/2, due to the fracturing of the material. Experiments confirm that the positive (+1/2) defects serve as "virtual stirring rods" that move around each other in a complex braiding pattern. This collective braiding motion of positive defects stretches and folds the fluid itself, i.e., produces macroscale chaotic advection. The degree of self-mixing due to the chaotic advection can be measured using topological entropy and the Lyapunov exponent. Our goal is to determine whether continuum models of MT-based active nematic fluid can reproduce these measurements. To this end, we use two continuum models: the traditional Beris-Edwards (BE) model and the more recently developed Beris-Edwards model with enhanced nematic locking (BENL). The difference between the two models is the adoption of the "nematic locking principle", which states that an individual MT bundle cannot rotate independently of its neighbors due to steric interactions among elongated dense MT bundles. This principle holds in the BENL model except in small localized areas of the material domain where the material fractures, specifically near the creation and annihilation of topological defects. We employ several numerical methods to estimate measures of chaotic advection using both models. Our study shows that the BENL model more accurately reproduces experimental measures of self-mixing driven by chaotic advection in MT-based active nematic fluids.
ER -