# Stress Fluctuations in Transient Active Networks

## TL;DR

This paper introduces a stochastic model of active networks inspired by biofilament experiments, capturing stress build-up and yielding behaviors, and predicts unique stress distributions and Herschel-Bulkley activity dependence.

## Contribution

It presents a novel network model incorporating growth, death, and birth processes, providing insights into stress fluctuations and non-affine effects in active solids.

## Key findings

- Stress distribution has a distinctive form.
- Stress depends on activity following Herschel-Bulkley law.
- Model reproduces features of yielded plastic solids.

## Abstract

Inspired by experiments on dynamic extensile gels of biofilaments and motors, we propose a model of a network of linear springs with a kinetics consisting of growth at a prescribed rate, death after a lifetime drawn from a distribution, and birth at a randomly chosen node. The model captures features such as the build-up of self-stress, that are not easily incorporated into hydrodynamic theories. We study the model numerically and show that our observations can largely be understood through a stochastic effective-medium model. The resulting dynamically extending force-dipole network displays many features of yielded plastic solids, and offers a way to incorporate strongly non-affine effects into theories of active solids. A rather distinctive form for the stress distribution, and a Herschel-Bulkley dependence of stress on activity, are our major predictions.