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


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-01-31

AUTHORS

Joseph D. Paulsen, Sidney R. Nagel

ABSTRACT

Relaxation in glasses is often approximated by a stretched-exponential form: f(t)=Aexp[-(t/τ)β]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(t) = A \exp [-(t/\tau )^{\beta }]$$\end{document}. 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 β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} that depends on the strain amplitude: 0.25<β<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.25< \beta < 1$$\end{document}. 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. More... »

PAGES

749-762

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10955-017-1723-0

DOI

http://dx.doi.org/10.1007/s10955-017-1723-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1083406794


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