On the dynamics of the interaction between triggered active inclusions

TL;DR

This paper investigates the time-dependent elastic forces between two active inclusions in a one-dimensional medium, revealing a transient maximum in non-linear cases that surpasses equilibrium forces and diverges at small separations.

Contribution

It provides a detailed analysis of the dynamic interaction forces, including transient behaviors and divergence phenomena, for both linear and non-linear inclusions in elastic media.

Findings

Transient maximum force significantly exceeds equilibrium force in non-linear cases

Force divergence as ~L^(-2) at small separations in non-linear inclusions

Comparison of mean-field and Casimir components of the interaction

Abstract

In a one-dimensional elastic medium with finite correlation length and purely relaxational dynamics, we calculate the time dependence of the elastic force F(t) exchanged between two active inclusions that trigger an elastic deformation at t=0. We consider (i) linear inclusions coupling to the field with a finite force, and (ii) non-linear inclusions imposing a finite deformation. In the non-linear case, the force exhibits a transient maximum much larger than the equilibrium force, diverging as ~L^(-2) at separations L shorter than the field's correlation length. Both the mean-field and the Casimir component of the interaction are calculated. We also discuss the typical appearance time and equilibration time of the force, comparing the linear and the non-linear cases. The existence of a high transient force in the non-linear case should be a generic feature of elastically-mediated interactions.