On the Prony series representation of stretched exponential relaxation

John Mauro, Yihong Z. Mauro

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β. The fitting quality of the Prony series is analyzed as a function of the number of terms in the series. With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its “fat tail” at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.

Original languageEnglish (US)
Pages (from-to)75-87
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Volume506
DOIs
StatePublished - Sep 15 2018

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Prony series
Series Representation
exponential functions
Series
glass
frequency domain analysis
Critical value
applications of mathematics
fats
Frequency Domain Analysis
Fat Tails
divergence
Term
Exponential Decay
traps
exponents
Mathematical Analysis
Trap
Divergence
Fractional

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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On the Prony series representation of stretched exponential relaxation. / Mauro, John; Mauro, Yihong Z.

In: Physica A: Statistical Mechanics and its Applications, Vol. 506, 15.09.2018, p. 75-87.

Research output: Contribution to journalArticle

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