Note: Relaxation time below jamming

Harukuni Ikeda

doi:10.1063/5.0024042

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arXiv · 2007.11166

Note: Relaxation time below jamming

Harukuni Ikeda

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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 $\varphi_J$ 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.

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Harukuni Ikeda. 2020-07-22. Note: Relaxation time below jamming. https://doi.org/10.1063/5.0024042

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