A Model for Approximately Stretched-Exponential Relaxation with Continuously Varying Stretching Exponents

Joseph D. Paulsen, Sidney R. Nagel

Research output: Research - peer-reviewArticle

Abstract

Relaxation in glasses is often approximated by a stretched-exponential form: (Formula presented.). Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Corté et al. (Nat Phys 4:420–424, 2008) can be well approximated by a stretched exponential with an exponent (Formula presented.) that depends on the strain amplitude: (Formula presented.). In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional form for the relaxation that is distinct from, but well approximated by, a stretched-exponential function.

LanguageEnglish (US)
Pages1-14
Number of pages14
JournalJournal of Statistical Physics
DOIs
StateAccepted/In press - Jan 31 2017

Fingerprint

Exponent
Model
exponents
Fluctuations
Distinct
Numerical Simulation
Configuration
Form
Glass
exponential functions
glass
configurations
simulation

Keywords

  • Glasses
  • Particulate media
  • Relaxation
  • Transport processes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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AB - Relaxation in glasses is often approximated by a stretched-exponential form: (Formula presented.). Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Corté et al. (Nat Phys 4:420–424, 2008) can be well approximated by a stretched exponential with an exponent (Formula presented.) that depends on the strain amplitude: (Formula presented.). In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional form for the relaxation that is distinct from, but well approximated by, a stretched-exponential function.

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