# Noise Amplification in Frictional Systems: Oscillatory Instabilities

## TL;DR

This paper investigates the oscillatory instabilities caused by complex eigenvalues in frictional granular systems, revealing how small perturbations can exponentially grow and lead to catastrophic events, with implications for earthquake physics.

## Contribution

It explores the scaling laws, development scenarios, and effects of damping on oscillatory instabilities in frictional systems, advancing understanding of their dynamics and potential real-world relevance.

## Key findings

- Giant amplification of perturbations can occur before catastrophic failure.
- Instability onset follows specific scaling laws.
- Damping influences the development and suppression of oscillatory instabilities.

## Abstract

It was discovered recently that frictional granular materials can exhibit an important mechanism for instabilities, i.e the appearance of pairs of complex eigenvalues in their stability matrix. The consequence is an oscillatory exponential growth of small perturbations which are tamed by dynamical nonlinearities. The amplification can be giant, many orders of magnitude, and it ends with a catastrophic system-spanning plastic event. Here we follow up on this discovery, explore the scaling laws characterizing the onset of the instability, the scenarios of the development of the instability with and without damping, and the nature of the eventual system spanning events. The possible relevance to earthquake physics and to the transition from static to dynamic friction is discussed.