Note: Relaxation time below jamming

Abstract

Like other critical phenomena, the jamming transition accompanies the divergence of the relaxation time $\tau$. A recent numerical study of frictionless spherical particles proves that $\tau$ is inversely proportional to the lowest non-zero eigenvalue ${\lambda }_1$ of the dynamical matrix. In this note, we derive the scaling of ${\lambda }_1$ below the jamming transition point ${\phi }_J$ by solving the linearized dynamical equation. The resultant critical exponent agrees with a previous theoretical result for sheared suspension obtained by applying the virtual work theorem to a simple shear, highlighting the universality of the relaxation dynamics below jamming.

2 pages, 1 figure

References in corpus (8)

• Fractal free energy landscapes in structural glasses
• Finite-Size Scaling at the Jamming Transition
• Jamming in finite systems: stability, anisotropy, fluctuations and scaling
• Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Toward a microscopic description of flow near the jamming threshold
• Universal relaxation dynamics of sphere packings below jamming
• Force balance controls the relaxation time of the gradient descent algorithm in the satisfiable phase

Cited by in corpus (6)

• Relaxation dynamics of non-Brownian spheres below jamming
• Strain-controlled critical slowing down in the rheology of disordered networks
• Introduction to the dynamics of disordered systems: equilibrium and gradient descent
• Critical Scaling of Compression-Driven Jamming of Athermal Frictionless Spheres in Suspension
• Universality of stress-anisotropic and stress-isotropic jamming of frictionless spheres in three dimensions: Uniaxial vs isotropic compression
• Gradient descent dynamics and the jamming transition in infinite dimensions