Critical fluctuations of elastic moduli in jammed solids

Area of Science:

• Soft Matter Physics
• Materials Science
• Statistical Mechanics

Background:

• The jamming transition describes the emergence of rigidity in disordered materials like granular packings.
• Understanding the elastic properties, specifically shear modulus, near jamming is crucial for predicting material behavior.
• Previous studies focused on average elastic properties, with less attention to sample-to-sample variations.

Purpose of the Study:

• To investigate sample-to-sample fluctuations of the shear modulus in particle packing ensembles near the jamming transition.
• To determine if these fluctuations exhibit universal scaling behavior independent of interparticle interactions.
• To explore the connection between elastic modulus fluctuations and sound wave scattering via heterogeneous-elasticity theory.

Main Methods:

• Numerical simulations of particle packings.
• Analysis of shear modulus fluctuations across different interparticle potentials.
• Examination of scaling behavior in two-dimensional systems.
• Comparison of numerical results with predictions from heterogeneous-elasticity theory.

Main Results:

• Shear modulus fluctuations exhibit a critical exponent independent of the interparticle potential, unlike the average modulus.
• This universal scaling behavior was confirmed in two-dimensional packings, suggesting dimensional independence.
• The study establishes a link between elastic modulus fluctuations and Rayleigh scattering of sound waves.

Conclusions:

• Elastic modulus fluctuations near jamming provide a universal signature, independent of microscopic details.
• The findings support the applicability of heterogeneous-elasticity theory across different pressures.
• This work lays the groundwork for a unified theoretical framework for jamming phenomena.