@article{d3809be2b423449c8a34bb5f8e0bb4bb,
title = "A Model for Approximately Stretched-Exponential Relaxation with Continuously Varying Stretching Exponents",
abstract = "Relaxation in glasses is often approximated by a stretched-exponential form: f(t) = Aexp [ - (t/ τ) β]. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Cort{\'e} et al. (Nat Phys 4:420–424, 2008) can be well approximated by a stretched exponential with an exponent β that depends on the strain amplitude: 0.25 < β< 1. 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.",
keywords = "Glasses, Particulate media, Relaxation, Transport processes",
author = "Paulsen, {Joseph D.} and Nagel, {Sidney R.}",
note = "Funding Information: We are grateful to Leo Kadanoff, our teacher, mentor, and friend, for many years of scientific discussions. He had the ability to understand complex interacting systems by isolating the common simple ingredients. This has been an inspiration to all of us in the soft-matter physics community. We thank Thomas A. Caswell for assistance optimizing the simulations, and Karin Dahmen and Daniel Hexner for stimulating conversations. This work was supported by NSF Grant DMR-1404841 and by NSF MRSEC DMR-1420709. J.D.P. acknowledges the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. Use of computation facilities funded by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, Award No. DE-FG02-03ER46088 is gratefully acknowledged. Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",
year = "2017",
month = may,
day = "1",
doi = "10.1007/s10955-017-1723-0",
language = "English (US)",
volume = "167",
pages = "749--762",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "3-4",
}